Kernel representation of long-wave dynamics on a uniform slope
Kernel representation of long-wave dynamics on a uniform slope
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均匀斜率上长波动力学的核表示
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
T. Shimozono
中科院分区：
文献类型：
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作者：
T. Shimozono
长波在均匀倾斜海滩上的传播被表述为一个瞬态响应问题，初始静止的水受到入射波的影响。坡面上的水面高程和水平流速都可以表示为坡脚处水面位移率的卷积，具有时间和空间的奇异核函数。该核通常以无穷级数的形式表示，可容纳长波的动态过程，如浅滩，反射和斜坡上的多次反射，并对任何光滑入射波产生线性浅水方程的精确解。为了避免核奇异性，可以采用双指数公式对核卷积进行数值实现。核公式可以很容易地扩展到非线性动力学通过hodograph变换，这反过来又使非线性波的性质和发生在近岸地区的破波的瞬时预测。这种长波动力学的一般描述为长期研究的问题提供了新的见解。
Long-wave propagation on a uniformly sloping beach is formulated as a transient-response problem, with initially stationary water subjected to an incident wave. Both the water surface elevation and the horizontal flow velocity on the slope can be represented as convolutions of the rate of displacement of the water surface at the toe of the slope with a singular kernel function of time and space. The kernel, which is typically expressed in the form of an infinite series, accommodates the dynamic processes of long waves, such as shoaling, reflection, and multiple reflections over the slope and yields exact solutions of the linear shallow water equations for any smooth incident wave. The kernel convolution can be implemented numerically by using double exponential formulas to avoid the kernel singularity. The kernel formulation can be extended readily to nonlinear dynamics via the hodograph transform, which in turn enables the instantaneous prediction of nonlinear wave properties and of the occurrence of wave breaking in the near-shore area. This general description of long-wave dynamics provides new insights into the long-studied problem.