{"title":"Jump Conditions for Boussinesq Equations Due to an Abrupt Depth Transition","authors":"Eduardo Monsalve, Kim Pham, Agnès Maurel","doi":"10.1137/23m1602437","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1792-1817, August 2024. <br/> Abstract. We revisit the problem of nonlinear water wave propagation in the presence of an abrupt depth transition. To this end, we use an asymptotic approach conducted to order 3 with respect to the shallowness parameter, in order to capture the first nonlinear and dispersive contributions. However, the discontinuity of bathymetry, as opposed to slowly varying bathymetry, requires the use of a consistent three-scale analysis framework and the consideration of different regions, far from the step and free surface, near the free surface, and near the step. This framework enables consistent navigation, ultimately providing Boussinesq equations supplemented by jump conditions at the depth discontinuity that encompass the effect of step on wave propagation.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"4 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1602437","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1792-1817, August 2024. Abstract. We revisit the problem of nonlinear water wave propagation in the presence of an abrupt depth transition. To this end, we use an asymptotic approach conducted to order 3 with respect to the shallowness parameter, in order to capture the first nonlinear and dispersive contributions. However, the discontinuity of bathymetry, as opposed to slowly varying bathymetry, requires the use of a consistent three-scale analysis framework and the consideration of different regions, far from the step and free surface, near the free surface, and near the step. This framework enables consistent navigation, ultimately providing Boussinesq equations supplemented by jump conditions at the depth discontinuity that encompass the effect of step on wave propagation.
期刊介绍：
SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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