Asymptotic Behavior of a Shallow-Water Soliton Reflected at a Sloping Beach

1988 ◽  
pp. 77-84
Author(s):  
N. Sugimoto ◽  
T. Kakutani
Keyword(s):  
Asymptotic Behavior ◽  
Shallow Water ◽  
Sloping Beach

Robustness of nearshore vortices

2018 ◽  
Vol 850 ◽  
Author(s):  
James C. McWilliams ◽  
Cigdem Akan ◽  
Yusuke Uchiyama
Keyword(s):  
Shallow Water ◽  
Surf Zone ◽  
3D Models ◽  
Density Stratification ◽  
Water Model ◽  
Shallow Water Model ◽  
Dynamical Models ◽  
Coherent Vortices ◽  
Dipole Vortex ◽  
Sloping Beach

Coherent vortices with horizontal swirl arise spontaneously in the wave-driven nearshore surf zone. Here, a demonstration is made of the much greater robustness of coherent barotropic dipole vortices on a sloping beach in a 2D shallow-water model compared with fully 3D models either without or with stable density stratification. The explanation is that active vortex tilting and stretching or instability in 3D disrupt an initially barotropic dipole vortex. Without stratification in 3D, the vorticity retains a dipole envelope structure but is internally fragmented. With stratification in 3D, the disrupted vortex reforms as a coherent but weaker surface-intensified baroclinic dipole vortex. An implication is that barotropic or depth-integrated dynamical models of the wave-driven surf zone misrepresent an important aspect of surf-eddy behaviour.

Water waves of finite amplitude on a sloping beach

1958 ◽  
Vol 4 (1) ◽  
pp. 97-109 ◽  
Author(s):  
G. F. Carrier ◽  
H. P. Greenspan
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Finite Amplitude ◽  
Explicit Solutions ◽  
Shallow Water Theory ◽  
Non Linear ◽  
Wave Forms ◽  
Time Histories ◽  
Sloping Beach

In this paper, we investigate the behaviour of a wave as it climbs a sloping beach. Explicit solutions of the equations of the non-linear inviscid shallow-water theory are obtained for several physically interesting wave-forms. In particular it is shown that waves can climb a sloping beach without breaking. Formulae for the motions of the instantaneous shoreline as well as the time histories of specific wave-forms are presented.

Bragg Reflection of Shallow-Water Waves on a Sloping Beach

1997 ◽  
Author(s):  
Yong-Sik Cho ◽  
Jong-In Lee ◽  
Jong-Kyu Lee
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Bragg Reflection ◽  
Shallow Water Waves ◽  
Sloping Beach

scholarly journals Conservation laws for shallow water waves on a sloping beach

1986 ◽  
Vol 9 (2) ◽  
pp. 387-396
Author(s):  
Yilmaz Akyildiz
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Water Waves ◽  
Simple Wave ◽  
Shallow Water Waves ◽  
Linear Partial Differential Equations ◽  
Wave Solutions ◽  
Hodograph Plane ◽  
Sloping Beach ◽  
Linear Nature

Shallow water waves are governed by a pair of non-linear partial differential equations. We transfer the associated homogeneous and non-homogeneous systems, (corresponding to constant and sloping depth, respectively), to the hodograph plane where we find all the non-simple wave solutions and construct infinitely many polynomial conservation laws. We also establish correspondence between conservation laws and hodograph solutions as well as Bäcklund transformations by using the linear nature of the problems on the hodogrpah plane.

Edge waves over a shelf: full linear theory

1984 ◽  
Vol 142 ◽  
pp. 79-95 ◽  
Author(s):  
D. V. Evans ◽  
P. Mciver
Keyword(s):  
Shallow Water ◽  
Wide Class ◽  
Shallow Water Equations ◽  
Water Waves ◽  
Explicit Solution ◽  
Mode Shapes ◽  
Edge Waves ◽  
Wave Solutions ◽  
Linearized Theory ◽  
Sloping Beach

Edge-wave solutions to the linearized shallow-water equations for water waves are well known for a variety of bottom topographies. The only explicit solution using the full linearized theory describes edge waves over a uniformly sloping beach, although the existence of such waves has been established for a wide class of bottom geometries. In this paper the full linearized theory is used to derive the properties of edge waves over a shelf. In particular, curves are presented showing the variation of frequency with wavenumber along the shelf, together with some mode shapes for a particular shelf geometry.

Motion of a bore over a sloping beach

1960 ◽  
Vol 7 (2) ◽  
pp. 302-316 ◽  
Author(s):  
H. B. Keller ◽  
D. A. Levine ◽  
G. B. Whitham
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Approximate Formula ◽  
Close Agreement ◽  
Approximate Theory ◽  
Rigorous Proof ◽  
Shallow Water Theory ◽  
Difference Form ◽  
Fitting In ◽  
Sloping Beach

The results of numerical calculations are presented for the motion of a bore over a uniformly sloping beach. The shallow water equations are solved in finite difference form, and a technique is developed for fitting in the bore at each step. The results are compared with the approximate formula given by Whitham (1958) and close agreement is found. The approximate theory is considered further here; the main addition is a rigorous proof that, within the shallow water theory, the height of the bore always tends to zero at the shoreline.

scholarly journals Conservation laws for shallow water waves on a sloping beach

1982 ◽  
Vol 23 (9) ◽  
pp. 1723-1727 ◽  
Author(s):  
Yilmaz Akyildiz
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Sloping Beach

scholarly journals Long Wave Run-Up Resonance in a Multi-Reflection System

2020 ◽  
Vol 10 (18) ◽  
pp. 6172
Author(s):  
Shanshan Xu ◽  
Frédéric Dias
Keyword(s):  
Boundary Condition ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Incoming Wave ◽  
Wave Trapping ◽  
Relaxation Zone ◽  
Long Wave ◽  
Nonlinear Shallow Water Equations ◽  
Run Up ◽  
Sloping Beach

Wave reflection and wave trapping can lead to long wave run-up resonance. After reviewing the theory of run-up resonance in the framework of the linear shallow water equations, we perform numerical simulations of periodic waves incident on a linearly sloping beach in the framework of the nonlinear shallow water equations. Three different types of boundary conditions are tested: fully reflective boundary, relaxation zone, and influx transparent boundary. The effect of the boundary condition on wave run-up is investigated. For the fully reflective boundary condition, it is found that resonant regimes do exist for certain values of the frequency of the incoming wave, which is consistent with theoretical results. The influx transparent boundary condition does not lead to run-up resonance. Finally, by decomposing the left- and right-going waves into a multi-reflection system, we find that the relaxation zone can lead to run-up resonance depending on the length of the relaxation zone.

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