Simulations of Dissipative, Shore-Oblique Infragravity Waves

2003 ◽  
Vol 33 (8) ◽  
pp. 1722-1732 ◽  
Author(s):  
Stephen M. Henderson ◽  
A. J. Bowen

Abstract A model of forced, dissipative shore-oblique shallow water waves predicts net cross-shore infragravity wave propagation, in qualitative agreement with field observations. Forcing applied near the shore generates edge waves, whose energy is mostly trapped shoreward of the edge wave turning point. Forcing applied sufficiently far seaward of the turning point generates only evanescent waves, whose energy decays almost exponentially with distance from regions of forcing. Weakly dissipative edge waves are nearly cross-shore standing, whereas strongly dissipative edge waves propagate obliquely across-shore. Groups of directionally spread incident waves can nonlinearly force evanescent bound waves, which propagate shoreward, lowering the sea level under large incident waves. Unlike the bound waves described by previous researchers, evanescent bound waves are not released when incident waves break and do not radiate far from the breakpoint. Regions of evanescent waves between the shoreface and shore-parallel sandbars are barriers to energy transport, which can decouple bar- and shore-trapped waves even when dissipation is weak.

1975 ◽  
Vol 70 (1) ◽  
pp. 113-126 ◽  
Author(s):  
Jürgen Willebrand

Certain tertiary resonant interactions of gravity waves which have been found previously can be obtained more easily by using a simple extension of Whitham's formalism. The contribution of these interactions to the total energy transfer in an inhomogeneous random field of gravity waves is calculated. It is found to be small for open-ocean waves, but to be of some importance for shallow-water waves, where topography or mean shear currents may produce strong inhomogeneities. The nonlinear splitting of the group velocity is found to be unimportant in wave fields with sufficiently smooth spectra.


Author(s):  
Shin-ichi AOKI ◽  
Tomoki HAMANO ◽  
Taishi NAKAYAMA ◽  
Eiichi OKETANI ◽  
Takahiro HIRAMATSU ◽  
...  

Author(s):  
S. G. Rajeev

Some exceptional situations in fluid mechanics can be modeled by equations that are analytically solvable. The most famous example is the Korteweg–de Vries (KdV) equation for shallow water waves in a channel. The exact soliton solution of this equation is derived. The Lax pair formalism for solving the general initial value problem is outlined. Two hamiltonian formalisms for the KdV equation (Fadeev–Zakharov and Magri) are explained. Then a short review of the geometry of curves (Frenet–Serret equations) is given. They are used to derive a remarkably simple equation for the propagation of a kink along a vortex filament. This equation of Hasimoto has surprising connections to the nonlinear Schrödinger equation and to the Heisenberg model of ferromagnetism. An exact soliton solution is found.


2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Kenan Šehić ◽  
Henrik Bredmose ◽  
John D. Sørensen ◽  
Mirza Karamehmedović

2000 ◽  
Vol 24 (10) ◽  
pp. 649-661 ◽  
Author(s):  
Mohamed Atef Helal

This paper is mainly concerned with the motion of an incompressible fluid in a slowly rotating rectangular basin. The equations of motion of such a problem with its boundary conditions are reduced to a system of nonlinear equations, which is to be solved by applying the shallow water approximation theory. Each unknown of the problem is expanded asymptotically in terms of the small parameterϵwhich generally depends on some intrinsic quantities of the problem of study. For each order of approximation, the nonlinear system of equations is presented successively. It is worthy to note that such a study has useful applications in the oceanography.


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