深度突变导致的布森斯方程跃迁条件

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-08-13 DOI:10.1137/23m1602437

Eduardo Monsalve, Kim Pham, Agnès Maurel

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引用次数: 0

摘要

SIAM 应用数学杂志》，第 84 卷第 4 期，第 1792-1817 页，2024 年 8 月。摘要我们重新探讨了存在突然深度转换时的非线性水波传播问题。为此，我们采用了关于浅度参数的 3 阶渐近方法，以捕捉第一非线性和分散贡献。然而，相对于缓慢变化的水深而言，水深的不连续性要求使用一致的三尺度分析框架，并考虑远离台阶和自由表面、自由表面附近和台阶附近的不同区域。这种框架可以实现一致的导航，最终提供布森斯克方程，并在深度不连续处辅以跃迁条件，以涵盖台阶对波传播的影响。

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Jump Conditions for Boussinesq Equations Due to an Abrupt Depth Transition

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.

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

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.