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Note on the propagation of a shallow water wave in water of variable depth

机译:关于浅水波在可变深度的水中的传播的注意

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摘要

In this technical note, the phenomena of non-linear water-wave propagation above a seabed with variable depth is re-examined. The conventional Korteweg-de Vries (KdV) equation is re-derived for the general case of variable water depth. In the new form of KdV equation, the seabed bottom function is included. Two different bottom profiles are considered in this study; case 1: b'(x') = cε sin λx' and case 2: b'(x') = cεe~(-λ(x'-x'_0)~2). The effects of three bottom profile parameters, c, λ and ε on the wave profile are examined. Numerical results indicate that both ε and λ affect the wave profile significantly in case 1, while ε significantly affects the wave profile in case 2.
机译:在本技术说明中,将重新检查非线性水波在深度可变的海床上空传播的现象。对于水深可变的一般情况,重新推导了传统的Korteweg-de Vries(KdV)方程。在新形式的KdV方程中,包含了海床底部函数。在这项研究中考虑了两个不同的底部轮廓。情况1:b'(x')=cεsinλx'和情况2:b'(x')=cεe〜(-λ(x'-x'_0)〜2)。研究了三个底部剖面参数c,λ和ε对波浪剖面的影响。数值结果表明,在情况1中ε和λ均显着影响波形,而在情况2中ε显着影响波形。

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