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class="js-work-strip profile--work_container" data-work-id="34430484"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/34430484/River_Meandering_as_a_Self_Organization_Process"><img alt="Research paper thumbnail of River Meandering as a Self-Organization Process" class="work-thumbnail" src="https://attachments.academia-assets.com/54306737/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/34430484/River_Meandering_as_a_Self_Organization_Process">River Meandering as a Self-Organization Process</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Simulations of freely meandering rivers and empirical data show that the meandering process self-...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Simulations of freely meandering rivers and empirical data show that the meandering process self-organizes the river morphology, or planform, into a critical state characterized by fractal geometry.The meandering process oscillates in space and time between a state in which the river planform is ordered and one in which it is chaotic. Clusters of river cutoffs tend to cause a transition between these two states and to force the system into stationary fluctuations around the critical state.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="41651daddbd128bbb96502471ab85824" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":54306737,"asset_id":34430484,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/54306737/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="34430484"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="34430484"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 34430484; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=34430484]").text(description); $(".js-view-count[data-work-id=34430484]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 34430484; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='34430484']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 34430484, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "41651daddbd128bbb96502471ab85824" } } $('.js-work-strip[data-work-id=34430484]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":34430484,"title":"River Meandering as a Self-Organization Process","translated_title":"","metadata":{"abstract":"Simulations of freely meandering rivers and empirical data show that the meandering process self-organizes the river morphology, or planform, into a critical state characterized by fractal geometry.The meandering process oscillates in space and time between a state in which the river planform is ordered and one in which it is chaotic. Clusters of river cutoffs tend to cause a transition between these two states and to force the system into stationary fluctuations around the critical state."},"translated_abstract":"Simulations of freely meandering rivers and empirical data show that the meandering process self-organizes the river morphology, or planform, into a critical state characterized by fractal geometry.The meandering process oscillates in space and time between a state in which the river planform is ordered and one in which it is chaotic. 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The rivers are the Purus (central Amazon, planform data), Jurua虂 (central Amazon, planform and oxbow lake data), and Madre de Dios (Peruvian Amazon, oxbow lake data). Long reaches were found to be power- law scaling over more than two orders of mag- nitude. These river planforms are self-affine fractals. Oxbow lake data suggest that the lakes are sampled from a skewed hyperbolic (Pareto) size-frequency distribution. <br />To examine the long-term behavior of freely meandering rivers, a deterministic continuum model of meandering rivers has been used for extensive simulations of free meandering mo- tion. The simulation outcomes are consistent with a dynamical state of self-organized criticality, which has the following characteristic behavior: (1) stationary mean sinuosity of the final state; (2) robustness, in the sense that the same final state is reached from any initial conditions; and (3) formation of a spatiotemporal fractal structure. <br />Sensitivity tests showed that this behavior is not affected by valley confinement down to a valley width of 50 w (river width), and by chute cutoffs of mature meanders up to 3 w long, but the average sinuosity value reached in the final state is sensitive to valley width less than 100 w, and chutes longer than 1.5 w. <br />Comparison with empirical data confirmed the validity of the simulations as models of river meandering. All tests found data and simulation results to be in close agreement.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="f68ccbb65a79db9cd0082bf3f161fa61" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":37462278,"asset_id":12158661,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/37462278/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="12158661"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="12158661"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 12158661; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=12158661]").text(description); $(".js-view-count[data-work-id=12158661]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 12158661; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='12158661']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 12158661, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "f68ccbb65a79db9cd0082bf3f161fa61" } } $('.js-work-strip[data-work-id=12158661]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":12158661,"title":"Planform Geometry and Dynamics of Meandering Rivers","translated_title":"","metadata":{"abstract":"Three freely meandering rivers in the Amazon basin were analyzed for statistical scaling properties and oxbow lake size-frequency distributions. The rivers are the Purus (central Amazon, planform data), Jurua虂 (central Amazon, planform and oxbow lake data), and Madre de Dios (Peruvian Amazon, oxbow lake data). Long reaches were found to be power- law scaling over more than two orders of mag- nitude. These river planforms are self-affine fractals. Oxbow lake data suggest that the lakes are sampled from a skewed hyperbolic (Pareto) size-frequency distribution.\r\nTo examine the long-term behavior of freely meandering rivers, a deterministic continuum model of meandering rivers has been used for extensive simulations of free meandering mo- tion. The simulation outcomes are consistent with a dynamical state of self-organized criticality, which has the following characteristic behavior: (1) stationary mean sinuosity of the final state; (2) robustness, in the sense that the same final state is reached from any initial conditions; and (3) formation of a spatiotemporal fractal structure.\r\nSensitivity tests showed that this behavior is not affected by valley confinement down to a valley width of 50 w (river width), and by chute cutoffs of mature meanders up to 3 w long, but the average sinuosity value reached in the final state is sensitive to valley width less than 100 w, and chutes longer than 1.5 w.\r\nComparison with empirical data confirmed the validity of the simulations as models of river meandering. All tests found data and simulation results to be in close agreement."},"translated_abstract":"Three freely meandering rivers in the Amazon basin were analyzed for statistical scaling properties and oxbow lake size-frequency distributions. The rivers are the Purus (central Amazon, planform data), Jurua虂 (central Amazon, planform and oxbow lake data), and Madre de Dios (Peruvian Amazon, oxbow lake data). Long reaches were found to be power- law scaling over more than two orders of mag- nitude. These river planforms are self-affine fractals. Oxbow lake data suggest that the lakes are sampled from a skewed hyperbolic (Pareto) size-frequency distribution.\r\nTo examine the long-term behavior of freely meandering rivers, a deterministic continuum model of meandering rivers has been used for extensive simulations of free meandering mo- tion. The simulation outcomes are consistent with a dynamical state of self-organized criticality, which has the following characteristic behavior: (1) stationary mean sinuosity of the final state; (2) robustness, in the sense that the same final state is reached from any initial conditions; and (3) formation of a spatiotemporal fractal structure.\r\nSensitivity tests showed that this behavior is not affected by valley confinement down to a valley width of 50 w (river width), and by chute cutoffs of mature meanders up to 3 w long, but the average sinuosity value reached in the final state is sensitive to valley width less than 100 w, and chutes longer than 1.5 w.\r\nComparison with empirical data confirmed the validity of the simulations as models of river meandering. All tests found data and simulation results to be in close agreement.","internal_url":"https://www.academia.edu/12158661/Planform_Geometry_and_Dynamics_of_Meandering_Rivers","translated_internal_url":"","created_at":"2015-04-29T17:14:29.497-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":30515984,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":37462278,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/37462278/thumbnails/1.jpg","file_name":"Stolum_Planform_geometry_GSABulletin_1998.pdf","download_url":"https://www.academia.edu/attachments/37462278/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Planform_Geometry_and_Dynamics_of_Meande.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/37462278/Stolum_Planform_geometry_GSABulletin_1998-libre.pdf?1430353130=\u0026response-content-disposition=attachment%3B+filename%3DPlanform_Geometry_and_Dynamics_of_Meande.pdf\u0026Expires=1733030436\u0026Signature=LsVbLYfsAW0USEdfZhbnddl0uVmkaoG3RmUfzjwc1jCIHyLVn9be3cfe7987oBLYBCqlx7oQMbX~zcOXa5LbuP6a42bFjVEty87izaRs5AxgRYET2iYymRbhtQHDiT5x~O62AANtSpYx4dcD50PI9IDKv2KDPAP5PrIGtV2TFoexc7aZsjzBUnsEGxKUX8xPhrwfKTCvFcnVTuMdt-rb3UP-GyoTflvG6XJJH9ufGJcE-UTtpjAF-oWzjsrJ~S-Z6lfDIRblOFGMlbSu1031pzRy3351y~FPqDI9-nXnTc6N2~WtMTSLukDyPdUPnb3DxLdOjqJXjgXKKFojUDvhSw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Planform_Geometry_and_Dynamics_of_Meandering_Rivers","translated_slug":"","page_count":14,"language":"en","content_type":"Work","owner":{"id":30515984,"first_name":"Hans Henrik","middle_initials":"","last_name":"Stolum","page_name":"HansHenrikStolum","domain_name":"independent","created_at":"2015-04-29T11:30:34.767-07:00","display_name":"Hans Henrik Stolum","url":"https://independent.academia.edu/HansHenrikStolum"},"attachments":[{"id":37462278,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/37462278/thumbnails/1.jpg","file_name":"Stolum_Planform_geometry_GSABulletin_1998.pdf","download_url":"https://www.academia.edu/attachments/37462278/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Planform_Geometry_and_Dynamics_of_Meande.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/37462278/Stolum_Planform_geometry_GSABulletin_1998-libre.pdf?1430353130=\u0026response-content-disposition=attachment%3B+filename%3DPlanform_Geometry_and_Dynamics_of_Meande.pdf\u0026Expires=1733030436\u0026Signature=LsVbLYfsAW0USEdfZhbnddl0uVmkaoG3RmUfzjwc1jCIHyLVn9be3cfe7987oBLYBCqlx7oQMbX~zcOXa5LbuP6a42bFjVEty87izaRs5AxgRYET2iYymRbhtQHDiT5x~O62AANtSpYx4dcD50PI9IDKv2KDPAP5PrIGtV2TFoexc7aZsjzBUnsEGxKUX8xPhrwfKTCvFcnVTuMdt-rb3UP-GyoTflvG6XJJH9ufGJcE-UTtpjAF-oWzjsrJ~S-Z6lfDIRblOFGMlbSu1031pzRy3351y~FPqDI9-nXnTc6N2~WtMTSLukDyPdUPnb3DxLdOjqJXjgXKKFojUDvhSw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics"},{"id":2455,"name":"Fluvial Processes","url":"https://www.academia.edu/Documents/in/Fluvial_Processes"},{"id":19520,"name":"Fluvial Geomorphology","url":"https://www.academia.edu/Documents/in/Fluvial_Geomorphology"},{"id":149878,"name":"Fluvial Sedimentology","url":"https://www.academia.edu/Documents/in/Fluvial_Sedimentology"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="12242131"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/12242131/Percolation_theory_applied_to_simulated_meander_belt_sandbodies"><img alt="Research paper thumbnail of Percolation theory applied to simulated meander belt sandbodies" class="work-thumbnail" src="https://attachments.academia-assets.com/37536990/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/12242131/Percolation_theory_applied_to_simulated_meander_belt_sandbodies">Percolation theory applied to simulated meander belt sandbodies</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The evolution of meander belts is simulated using a single-channel model of freely meandering dyn...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The evolution of meander belts is simulated using a single-channel model of freely meandering dynamics with constant discharge and no avulsion. This means that lateral migration of the river is not confined by a valley (i.e., it takes place on a sloping plain), and that chute cutoffs and avulsions do not occur. The meander belt undulates within a relatively narrow tract roughly 50 channel width units wide. This limited width is caused by a river planform fractal geometry in the form of self-affine scale covariance of meanders. The simulated meander belt pattern compares well with actual meander belts of free meandering rivers, suggesting that the assumptions of the model are reasonably realistic for freely meandering rivers in nature. The spatial sandbody distribution in deposits from this system is an outcome of the processes of isolation of point-bars from the active river by neck cutoffs, and vertical attenuation by subsidence and/or deposition. For a constant total subsidence and deposition (tsd) rate, the vertical spatial distribution is well described by percolation theory. This was demonstrated by analysis of a simulated spatial distribution of point-bar sandbodies. The tsd rate controls the density of single sandbodies and amalgamated sandbody clusters within the formation, and is therefore equivalent to the inverse of the probability of site occupation in site percolation models. Percolation theory predicts the existence of a critical tsd rate in the vertical direction, and that sandbody clusters follow a power-law size distribution over a large scale range at the critical value. These predictions were confirmed. The analysis indicates that a scaling law of composite and single sandbodies exists at the percolation threshold (the threshold of sandbody connectivity at a given scale): <br />N(M>m) = am^-1 <br />where N(M > m) is the number of single or amalgamated sandbodies larger than size m (area of point-bar enclosed by an oxbow lake, or area of amalgamated cluster of point-bars). The exponent is the scaling exponent D, and a is a constant of proportionality. Both parameters go to a minimum value at the critical threshold.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b150e722238a5bd445f7ed6964373a31" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":37536990,"asset_id":12242131,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/37536990/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="12242131"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="12242131"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 12242131; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=12242131]").text(description); $(".js-view-count[data-work-id=12242131]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 12242131; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='12242131']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 12242131, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "b150e722238a5bd445f7ed6964373a31" } } $('.js-work-strip[data-work-id=12242131]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":12242131,"title":"Percolation theory applied to simulated meander belt sandbodies","translated_title":"","metadata":{"abstract":"The evolution of meander belts is simulated using a single-channel model of freely meandering dynamics with constant discharge and no avulsion. This means that lateral migration of the river is not confined by a valley (i.e., it takes place on a sloping plain), and that chute cutoffs and avulsions do not occur. The meander belt undulates within a relatively narrow tract roughly 50 channel width units wide. This limited width is caused by a river planform fractal geometry in the form of self-affine scale covariance of meanders. The simulated meander belt pattern compares well with actual meander belts of free meandering rivers, suggesting that the assumptions of the model are reasonably realistic for freely meandering rivers in nature. The spatial sandbody distribution in deposits from this system is an outcome of the processes of isolation of point-bars from the active river by neck cutoffs, and vertical attenuation by subsidence and/or deposition. For a constant total subsidence and deposition (tsd) rate, the vertical spatial distribution is well described by percolation theory. This was demonstrated by analysis of a simulated spatial distribution of point-bar sandbodies. The tsd rate controls the density of single sandbodies and amalgamated sandbody clusters within the formation, and is therefore equivalent to the inverse of the probability of site occupation in site percolation models. Percolation theory predicts the existence of a critical tsd rate in the vertical direction, and that sandbody clusters follow a power-law size distribution over a large scale range at the critical value. These predictions were confirmed. The analysis indicates that a scaling law of composite and single sandbodies exists at the percolation threshold (the threshold of sandbody connectivity at a given scale):\r\nN(M\u003em)\t= am^-1\r\nwhere N(M \u003e m) is the number of single or amalgamated sandbodies larger than size m (area of point-bar enclosed by an oxbow lake, or area of amalgamated cluster of point-bars). The exponent is the scaling exponent D, and a is a constant of proportionality. Both parameters go to a minimum value at the critical threshold."},"translated_abstract":"The evolution of meander belts is simulated using a single-channel model of freely meandering dynamics with constant discharge and no avulsion. This means that lateral migration of the river is not confined by a valley (i.e., it takes place on a sloping plain), and that chute cutoffs and avulsions do not occur. The meander belt undulates within a relatively narrow tract roughly 50 channel width units wide. This limited width is caused by a river planform fractal geometry in the form of self-affine scale covariance of meanders. The simulated meander belt pattern compares well with actual meander belts of free meandering rivers, suggesting that the assumptions of the model are reasonably realistic for freely meandering rivers in nature. The spatial sandbody distribution in deposits from this system is an outcome of the processes of isolation of point-bars from the active river by neck cutoffs, and vertical attenuation by subsidence and/or deposition. For a constant total subsidence and deposition (tsd) rate, the vertical spatial distribution is well described by percolation theory. This was demonstrated by analysis of a simulated spatial distribution of point-bar sandbodies. The tsd rate controls the density of single sandbodies and amalgamated sandbody clusters within the formation, and is therefore equivalent to the inverse of the probability of site occupation in site percolation models. Percolation theory predicts the existence of a critical tsd rate in the vertical direction, and that sandbody clusters follow a power-law size distribution over a large scale range at the critical value. These predictions were confirmed. The analysis indicates that a scaling law of composite and single sandbodies exists at the percolation threshold (the threshold of sandbody connectivity at a given scale):\r\nN(M\u003em)\t= am^-1\r\nwhere N(M \u003e m) is the number of single or amalgamated sandbodies larger than size m (area of point-bar enclosed by an oxbow lake, or area of amalgamated cluster of point-bars). The exponent is the scaling exponent D, and a is a constant of proportionality. Both parameters go to a minimum value at the critical threshold.","internal_url":"https://www.academia.edu/12242131/Percolation_theory_applied_to_simulated_meander_belt_sandbodies","translated_internal_url":"","created_at":"2015-05-05T05:12:14.269-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":30515984,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":37536990,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/37536990/thumbnails/1.jpg","file_name":"Stolum_and_Friend_Point_bars_percolation_analysis_EPSL_1997.pdf","download_url":"https://www.academia.edu/attachments/37536990/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Percolation_theory_applied_to_simulated.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/37536990/Stolum_and_Friend_Point_bars_percolation_analysis_EPSL_1997-libre.pdf?1430851723=\u0026response-content-disposition=attachment%3B+filename%3DPercolation_theory_applied_to_simulated.pdf\u0026Expires=1733030436\u0026Signature=RzmfSWEVgsVvmbHrOV2UjyCfg6dYpGRPIecIgBq4mqcMZzp~AiL10YT0mI3lLs4aSCo14KfRSJal~Pf7llvQuAOZ~GLC0uxuWz8xy~Xv5BX0C1oGBiwEGjCF9e5e-UB5~eZj6NM13CYv6SWU-AkrsJF8wFMyk5P8GLn1meuiNe~pkxY-uSXc9Qr88sdBtoJyiwuQAeCWf1N1JzlBPxng1fMqZrNnufuA80~PCkla2CLGfvpfaLamwbCy~TppRhFf0p1r1hi76QTBko8bcXzqXc5SAY~rE~FLsmoHjTp7nbAAiLUKgic3yPRrqmA255HKG7vBlr6eWINR~CLZeVtYdg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Percolation_theory_applied_to_simulated_meander_belt_sandbodies","translated_slug":"","page_count":13,"language":"en","content_type":"Work","owner":{"id":30515984,"first_name":"Hans Henrik","middle_initials":"","last_name":"Stolum","page_name":"HansHenrikStolum","domain_name":"independent","created_at":"2015-04-29T11:30:34.767-07:00","display_name":"Hans Henrik Stolum","url":"https://independent.academia.edu/HansHenrikStolum"},"attachments":[{"id":37536990,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/37536990/thumbnails/1.jpg","file_name":"Stolum_and_Friend_Point_bars_percolation_analysis_EPSL_1997.pdf","download_url":"https://www.academia.edu/attachments/37536990/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Percolation_theory_applied_to_simulated.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/37536990/Stolum_and_Friend_Point_bars_percolation_analysis_EPSL_1997-libre.pdf?1430851723=\u0026response-content-disposition=attachment%3B+filename%3DPercolation_theory_applied_to_simulated.pdf\u0026Expires=1733030436\u0026Signature=RzmfSWEVgsVvmbHrOV2UjyCfg6dYpGRPIecIgBq4mqcMZzp~AiL10YT0mI3lLs4aSCo14KfRSJal~Pf7llvQuAOZ~GLC0uxuWz8xy~Xv5BX0C1oGBiwEGjCF9e5e-UB5~eZj6NM13CYv6SWU-AkrsJF8wFMyk5P8GLn1meuiNe~pkxY-uSXc9Qr88sdBtoJyiwuQAeCWf1N1JzlBPxng1fMqZrNnufuA80~PCkla2CLGfvpfaLamwbCy~TppRhFf0p1r1hi76QTBko8bcXzqXc5SAY~rE~FLsmoHjTp7nbAAiLUKgic3yPRrqmA255HKG7vBlr6eWINR~CLZeVtYdg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics"},{"id":4060,"name":"Applied Statistics","url":"https://www.academia.edu/Documents/in/Applied_Statistics"},{"id":19520,"name":"Fluvial Geomorphology","url":"https://www.academia.edu/Documents/in/Fluvial_Geomorphology"},{"id":149878,"name":"Fluvial Sedimentology","url":"https://www.academia.edu/Documents/in/Fluvial_Sedimentology"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="2895179" id="papers"><div class="js-work-strip profile--work_container" data-work-id="34430484"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/34430484/River_Meandering_as_a_Self_Organization_Process"><img alt="Research paper thumbnail of River Meandering as a Self-Organization Process" class="work-thumbnail" src="https://attachments.academia-assets.com/54306737/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/34430484/River_Meandering_as_a_Self_Organization_Process">River Meandering as a Self-Organization Process</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Simulations of freely meandering rivers and empirical data show that the meandering process self-...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Simulations of freely meandering rivers and empirical data show that the meandering process self-organizes the river morphology, or planform, into a critical state characterized by fractal geometry.The meandering process oscillates in space and time between a state in which the river planform is ordered and one in which it is chaotic. Clusters of river cutoffs tend to cause a transition between these two states and to force the system into stationary fluctuations around the critical state.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="41651daddbd128bbb96502471ab85824" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":54306737,"asset_id":34430484,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/54306737/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="34430484"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="34430484"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 34430484; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=34430484]").text(description); $(".js-view-count[data-work-id=34430484]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 34430484; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='34430484']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 34430484, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "41651daddbd128bbb96502471ab85824" } } $('.js-work-strip[data-work-id=34430484]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":34430484,"title":"River Meandering as a Self-Organization Process","translated_title":"","metadata":{"abstract":"Simulations of freely meandering rivers and empirical data show that the meandering process self-organizes the river morphology, or planform, into a critical state characterized by fractal geometry.The meandering process oscillates in space and time between a state in which the river planform is ordered and one in which it is chaotic. Clusters of river cutoffs tend to cause a transition between these two states and to force the system into stationary fluctuations around the critical state."},"translated_abstract":"Simulations of freely meandering rivers and empirical data show that the meandering process self-organizes the river morphology, or planform, into a critical state characterized by fractal geometry.The meandering process oscillates in space and time between a state in which the river planform is ordered and one in which it is chaotic. Clusters of river cutoffs tend to cause a transition between these two states and to force the system into stationary fluctuations around the critical state.","internal_url":"https://www.academia.edu/34430484/River_Meandering_as_a_Self_Organization_Process","translated_internal_url":"","created_at":"2017-08-31T17:20:16.656-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":30515984,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":54306737,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/54306737/thumbnails/1.jpg","file_name":"Stolum_River_meandeirng_Science_1996.pdf","download_url":"https://www.academia.edu/attachments/54306737/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"River_Meandering_as_a_Self_Organization.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/54306737/Stolum_River_meandeirng_Science_1996-libre.pdf?1504228259=\u0026response-content-disposition=attachment%3B+filename%3DRiver_Meandering_as_a_Self_Organization.pdf\u0026Expires=1733030436\u0026Signature=EB0pe-heAQf~6U0w0uroYhRJ8363L8iNRONlPmLyMZ~5eYd4xRXs3vMX5rT8Wqx6U8A4S0mfYbMIue2Wx5jqD6zLJlggyOrs~1-0W2tnTSaey~LcR1RokjvIWhPPK5QTGO3x8lRN4L7C9t6zCBImuQUR2tGTdfY0MPR5Jxod50qlcl6-kXHioiVNQSVMuxwMAb7F16YPpNdhJWcsV3zR~85oJUX5jjn5fvQt005hPvekBeSL-9XZNXkHS~p8R9UiilDCNdlFVQi1vRlRrxqSzVQHO6MtuwhGvfyG94vJjfHWnm5Gw6AMloDxCn~hyr8qqBqlAhjP4H0z6hROIU4DJg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"River_Meandering_as_a_Self_Organization_Process","translated_slug":"","page_count":4,"language":"en","content_type":"Work","owner":{"id":30515984,"first_name":"Hans Henrik","middle_initials":"","last_name":"Stolum","page_name":"HansHenrikStolum","domain_name":"independent","created_at":"2015-04-29T11:30:34.767-07:00","display_name":"Hans Henrik Stolum","url":"https://independent.academia.edu/HansHenrikStolum"},"attachments":[{"id":54306737,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/54306737/thumbnails/1.jpg","file_name":"Stolum_River_meandeirng_Science_1996.pdf","download_url":"https://www.academia.edu/attachments/54306737/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"River_Meandering_as_a_Self_Organization.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/54306737/Stolum_River_meandeirng_Science_1996-libre.pdf?1504228259=\u0026response-content-disposition=attachment%3B+filename%3DRiver_Meandering_as_a_Self_Organization.pdf\u0026Expires=1733030436\u0026Signature=EB0pe-heAQf~6U0w0uroYhRJ8363L8iNRONlPmLyMZ~5eYd4xRXs3vMX5rT8Wqx6U8A4S0mfYbMIue2Wx5jqD6zLJlggyOrs~1-0W2tnTSaey~LcR1RokjvIWhPPK5QTGO3x8lRN4L7C9t6zCBImuQUR2tGTdfY0MPR5Jxod50qlcl6-kXHioiVNQSVMuxwMAb7F16YPpNdhJWcsV3zR~85oJUX5jjn5fvQt005hPvekBeSL-9XZNXkHS~p8R9UiilDCNdlFVQi1vRlRrxqSzVQHO6MtuwhGvfyG94vJjfHWnm5Gw6AMloDxCn~hyr8qqBqlAhjP4H0z6hROIU4DJg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="12158661"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/12158661/Planform_Geometry_and_Dynamics_of_Meandering_Rivers"><img alt="Research paper thumbnail of Planform Geometry and Dynamics of Meandering Rivers" class="work-thumbnail" src="https://attachments.academia-assets.com/37462278/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/12158661/Planform_Geometry_and_Dynamics_of_Meandering_Rivers">Planform Geometry and Dynamics of Meandering Rivers</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Three freely meandering rivers in the Amazon basin were analyzed for statistical scaling properti...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Three freely meandering rivers in the Amazon basin were analyzed for statistical scaling properties and oxbow lake size-frequency distributions. The rivers are the Purus (central Amazon, planform data), Jurua虂 (central Amazon, planform and oxbow lake data), and Madre de Dios (Peruvian Amazon, oxbow lake data). Long reaches were found to be power- law scaling over more than two orders of mag- nitude. These river planforms are self-affine fractals. Oxbow lake data suggest that the lakes are sampled from a skewed hyperbolic (Pareto) size-frequency distribution. <br />To examine the long-term behavior of freely meandering rivers, a deterministic continuum model of meandering rivers has been used for extensive simulations of free meandering mo- tion. The simulation outcomes are consistent with a dynamical state of self-organized criticality, which has the following characteristic behavior: (1) stationary mean sinuosity of the final state; (2) robustness, in the sense that the same final state is reached from any initial conditions; and (3) formation of a spatiotemporal fractal structure. <br />Sensitivity tests showed that this behavior is not affected by valley confinement down to a valley width of 50 w (river width), and by chute cutoffs of mature meanders up to 3 w long, but the average sinuosity value reached in the final state is sensitive to valley width less than 100 w, and chutes longer than 1.5 w. <br />Comparison with empirical data confirmed the validity of the simulations as models of river meandering. All tests found data and simulation results to be in close agreement.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="f68ccbb65a79db9cd0082bf3f161fa61" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":37462278,"asset_id":12158661,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/37462278/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="12158661"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="12158661"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 12158661; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=12158661]").text(description); $(".js-view-count[data-work-id=12158661]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 12158661; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='12158661']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 12158661, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "f68ccbb65a79db9cd0082bf3f161fa61" } } $('.js-work-strip[data-work-id=12158661]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":12158661,"title":"Planform Geometry and Dynamics of Meandering Rivers","translated_title":"","metadata":{"abstract":"Three freely meandering rivers in the Amazon basin were analyzed for statistical scaling properties and oxbow lake size-frequency distributions. The rivers are the Purus (central Amazon, planform data), Jurua虂 (central Amazon, planform and oxbow lake data), and Madre de Dios (Peruvian Amazon, oxbow lake data). Long reaches were found to be power- law scaling over more than two orders of mag- nitude. These river planforms are self-affine fractals. Oxbow lake data suggest that the lakes are sampled from a skewed hyperbolic (Pareto) size-frequency distribution.\r\nTo examine the long-term behavior of freely meandering rivers, a deterministic continuum model of meandering rivers has been used for extensive simulations of free meandering mo- tion. The simulation outcomes are consistent with a dynamical state of self-organized criticality, which has the following characteristic behavior: (1) stationary mean sinuosity of the final state; (2) robustness, in the sense that the same final state is reached from any initial conditions; and (3) formation of a spatiotemporal fractal structure.\r\nSensitivity tests showed that this behavior is not affected by valley confinement down to a valley width of 50 w (river width), and by chute cutoffs of mature meanders up to 3 w long, but the average sinuosity value reached in the final state is sensitive to valley width less than 100 w, and chutes longer than 1.5 w.\r\nComparison with empirical data confirmed the validity of the simulations as models of river meandering. All tests found data and simulation results to be in close agreement."},"translated_abstract":"Three freely meandering rivers in the Amazon basin were analyzed for statistical scaling properties and oxbow lake size-frequency distributions. The rivers are the Purus (central Amazon, planform data), Jurua虂 (central Amazon, planform and oxbow lake data), and Madre de Dios (Peruvian Amazon, oxbow lake data). Long reaches were found to be power- law scaling over more than two orders of mag- nitude. These river planforms are self-affine fractals. Oxbow lake data suggest that the lakes are sampled from a skewed hyperbolic (Pareto) size-frequency distribution.\r\nTo examine the long-term behavior of freely meandering rivers, a deterministic continuum model of meandering rivers has been used for extensive simulations of free meandering mo- tion. The simulation outcomes are consistent with a dynamical state of self-organized criticality, which has the following characteristic behavior: (1) stationary mean sinuosity of the final state; (2) robustness, in the sense that the same final state is reached from any initial conditions; and (3) formation of a spatiotemporal fractal structure.\r\nSensitivity tests showed that this behavior is not affected by valley confinement down to a valley width of 50 w (river width), and by chute cutoffs of mature meanders up to 3 w long, but the average sinuosity value reached in the final state is sensitive to valley width less than 100 w, and chutes longer than 1.5 w.\r\nComparison with empirical data confirmed the validity of the simulations as models of river meandering. All tests found data and simulation results to be in close agreement.","internal_url":"https://www.academia.edu/12158661/Planform_Geometry_and_Dynamics_of_Meandering_Rivers","translated_internal_url":"","created_at":"2015-04-29T17:14:29.497-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":30515984,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":37462278,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/37462278/thumbnails/1.jpg","file_name":"Stolum_Planform_geometry_GSABulletin_1998.pdf","download_url":"https://www.academia.edu/attachments/37462278/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Planform_Geometry_and_Dynamics_of_Meande.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/37462278/Stolum_Planform_geometry_GSABulletin_1998-libre.pdf?1430353130=\u0026response-content-disposition=attachment%3B+filename%3DPlanform_Geometry_and_Dynamics_of_Meande.pdf\u0026Expires=1733030436\u0026Signature=LsVbLYfsAW0USEdfZhbnddl0uVmkaoG3RmUfzjwc1jCIHyLVn9be3cfe7987oBLYBCqlx7oQMbX~zcOXa5LbuP6a42bFjVEty87izaRs5AxgRYET2iYymRbhtQHDiT5x~O62AANtSpYx4dcD50PI9IDKv2KDPAP5PrIGtV2TFoexc7aZsjzBUnsEGxKUX8xPhrwfKTCvFcnVTuMdt-rb3UP-GyoTflvG6XJJH9ufGJcE-UTtpjAF-oWzjsrJ~S-Z6lfDIRblOFGMlbSu1031pzRy3351y~FPqDI9-nXnTc6N2~WtMTSLukDyPdUPnb3DxLdOjqJXjgXKKFojUDvhSw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Planform_Geometry_and_Dynamics_of_Meandering_Rivers","translated_slug":"","page_count":14,"language":"en","content_type":"Work","owner":{"id":30515984,"first_name":"Hans Henrik","middle_initials":"","last_name":"Stolum","page_name":"HansHenrikStolum","domain_name":"independent","created_at":"2015-04-29T11:30:34.767-07:00","display_name":"Hans Henrik Stolum","url":"https://independent.academia.edu/HansHenrikStolum"},"attachments":[{"id":37462278,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/37462278/thumbnails/1.jpg","file_name":"Stolum_Planform_geometry_GSABulletin_1998.pdf","download_url":"https://www.academia.edu/attachments/37462278/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Planform_Geometry_and_Dynamics_of_Meande.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/37462278/Stolum_Planform_geometry_GSABulletin_1998-libre.pdf?1430353130=\u0026response-content-disposition=attachment%3B+filename%3DPlanform_Geometry_and_Dynamics_of_Meande.pdf\u0026Expires=1733030436\u0026Signature=LsVbLYfsAW0USEdfZhbnddl0uVmkaoG3RmUfzjwc1jCIHyLVn9be3cfe7987oBLYBCqlx7oQMbX~zcOXa5LbuP6a42bFjVEty87izaRs5AxgRYET2iYymRbhtQHDiT5x~O62AANtSpYx4dcD50PI9IDKv2KDPAP5PrIGtV2TFoexc7aZsjzBUnsEGxKUX8xPhrwfKTCvFcnVTuMdt-rb3UP-GyoTflvG6XJJH9ufGJcE-UTtpjAF-oWzjsrJ~S-Z6lfDIRblOFGMlbSu1031pzRy3351y~FPqDI9-nXnTc6N2~WtMTSLukDyPdUPnb3DxLdOjqJXjgXKKFojUDvhSw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics"},{"id":2455,"name":"Fluvial Processes","url":"https://www.academia.edu/Documents/in/Fluvial_Processes"},{"id":19520,"name":"Fluvial Geomorphology","url":"https://www.academia.edu/Documents/in/Fluvial_Geomorphology"},{"id":149878,"name":"Fluvial Sedimentology","url":"https://www.academia.edu/Documents/in/Fluvial_Sedimentology"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="12242131"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/12242131/Percolation_theory_applied_to_simulated_meander_belt_sandbodies"><img alt="Research paper thumbnail of Percolation theory applied to simulated meander belt sandbodies" class="work-thumbnail" src="https://attachments.academia-assets.com/37536990/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/12242131/Percolation_theory_applied_to_simulated_meander_belt_sandbodies">Percolation theory applied to simulated meander belt sandbodies</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The evolution of meander belts is simulated using a single-channel model of freely meandering dyn...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The evolution of meander belts is simulated using a single-channel model of freely meandering dynamics with constant discharge and no avulsion. This means that lateral migration of the river is not confined by a valley (i.e., it takes place on a sloping plain), and that chute cutoffs and avulsions do not occur. The meander belt undulates within a relatively narrow tract roughly 50 channel width units wide. This limited width is caused by a river planform fractal geometry in the form of self-affine scale covariance of meanders. The simulated meander belt pattern compares well with actual meander belts of free meandering rivers, suggesting that the assumptions of the model are reasonably realistic for freely meandering rivers in nature. The spatial sandbody distribution in deposits from this system is an outcome of the processes of isolation of point-bars from the active river by neck cutoffs, and vertical attenuation by subsidence and/or deposition. For a constant total subsidence and deposition (tsd) rate, the vertical spatial distribution is well described by percolation theory. This was demonstrated by analysis of a simulated spatial distribution of point-bar sandbodies. The tsd rate controls the density of single sandbodies and amalgamated sandbody clusters within the formation, and is therefore equivalent to the inverse of the probability of site occupation in site percolation models. Percolation theory predicts the existence of a critical tsd rate in the vertical direction, and that sandbody clusters follow a power-law size distribution over a large scale range at the critical value. These predictions were confirmed. The analysis indicates that a scaling law of composite and single sandbodies exists at the percolation threshold (the threshold of sandbody connectivity at a given scale): <br />N(M>m) = am^-1 <br />where N(M > m) is the number of single or amalgamated sandbodies larger than size m (area of point-bar enclosed by an oxbow lake, or area of amalgamated cluster of point-bars). The exponent is the scaling exponent D, and a is a constant of proportionality. Both parameters go to a minimum value at the critical threshold.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b150e722238a5bd445f7ed6964373a31" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":37536990,"asset_id":12242131,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/37536990/download_file?st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&st=MTczMzAyNjgzNiw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="12242131"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="12242131"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 12242131; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=12242131]").text(description); $(".js-view-count[data-work-id=12242131]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 12242131; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='12242131']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 12242131, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "b150e722238a5bd445f7ed6964373a31" } } $('.js-work-strip[data-work-id=12242131]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":12242131,"title":"Percolation theory applied to simulated meander belt sandbodies","translated_title":"","metadata":{"abstract":"The evolution of meander belts is simulated using a single-channel model of freely meandering dynamics with constant discharge and no avulsion. This means that lateral migration of the river is not confined by a valley (i.e., it takes place on a sloping plain), and that chute cutoffs and avulsions do not occur. The meander belt undulates within a relatively narrow tract roughly 50 channel width units wide. This limited width is caused by a river planform fractal geometry in the form of self-affine scale covariance of meanders. The simulated meander belt pattern compares well with actual meander belts of free meandering rivers, suggesting that the assumptions of the model are reasonably realistic for freely meandering rivers in nature. The spatial sandbody distribution in deposits from this system is an outcome of the processes of isolation of point-bars from the active river by neck cutoffs, and vertical attenuation by subsidence and/or deposition. For a constant total subsidence and deposition (tsd) rate, the vertical spatial distribution is well described by percolation theory. This was demonstrated by analysis of a simulated spatial distribution of point-bar sandbodies. The tsd rate controls the density of single sandbodies and amalgamated sandbody clusters within the formation, and is therefore equivalent to the inverse of the probability of site occupation in site percolation models. Percolation theory predicts the existence of a critical tsd rate in the vertical direction, and that sandbody clusters follow a power-law size distribution over a large scale range at the critical value. These predictions were confirmed. The analysis indicates that a scaling law of composite and single sandbodies exists at the percolation threshold (the threshold of sandbody connectivity at a given scale):\r\nN(M\u003em)\t= am^-1\r\nwhere N(M \u003e m) is the number of single or amalgamated sandbodies larger than size m (area of point-bar enclosed by an oxbow lake, or area of amalgamated cluster of point-bars). The exponent is the scaling exponent D, and a is a constant of proportionality. Both parameters go to a minimum value at the critical threshold."},"translated_abstract":"The evolution of meander belts is simulated using a single-channel model of freely meandering dynamics with constant discharge and no avulsion. This means that lateral migration of the river is not confined by a valley (i.e., it takes place on a sloping plain), and that chute cutoffs and avulsions do not occur. The meander belt undulates within a relatively narrow tract roughly 50 channel width units wide. This limited width is caused by a river planform fractal geometry in the form of self-affine scale covariance of meanders. The simulated meander belt pattern compares well with actual meander belts of free meandering rivers, suggesting that the assumptions of the model are reasonably realistic for freely meandering rivers in nature. The spatial sandbody distribution in deposits from this system is an outcome of the processes of isolation of point-bars from the active river by neck cutoffs, and vertical attenuation by subsidence and/or deposition. For a constant total subsidence and deposition (tsd) rate, the vertical spatial distribution is well described by percolation theory. This was demonstrated by analysis of a simulated spatial distribution of point-bar sandbodies. The tsd rate controls the density of single sandbodies and amalgamated sandbody clusters within the formation, and is therefore equivalent to the inverse of the probability of site occupation in site percolation models. Percolation theory predicts the existence of a critical tsd rate in the vertical direction, and that sandbody clusters follow a power-law size distribution over a large scale range at the critical value. These predictions were confirmed. The analysis indicates that a scaling law of composite and single sandbodies exists at the percolation threshold (the threshold of sandbody connectivity at a given scale):\r\nN(M\u003em)\t= am^-1\r\nwhere N(M \u003e m) is the number of single or amalgamated sandbodies larger than size m (area of point-bar enclosed by an oxbow lake, or area of amalgamated cluster of point-bars). The exponent is the scaling exponent D, and a is a constant of proportionality. 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