scholarly journals A GRID MODEL FOR SHALLOW WATER WAVES

1986 ◽  
Vol 1 (20) ◽  
pp. 20 ◽  
Author(s):  
Leo H. Holthuijsen ◽  
Nico Booij
Keyword(s):  
Wave Propagation ◽  
Water Waves ◽  
Wave Breaking ◽  
Traditional Approach ◽  
High Wind ◽  
Local Wind ◽  
Shallow Water Waves ◽  
Spectral Action ◽  
Mean Wave Period ◽  
Constant Period

Waves in coastal regions can be affected by the bottom, by currents and by the local wind. The traditional approach in numerical modelling of these waves is to compute the wave propagation with so-called wave rays for mono-chromatic waves (one constant period and one deep water direction) and to supplement this with computations of bottom dissipation. This approach has two important disadvantages. Firstly, spectral computations, e.g. to determine a varying mean wave period or varying shortcrestedness, would be rather inefficient in this approach. Secondly, interpretation of the results of the refraction computations is usually cumbersome because of crossing wave rays. The model presented here has been designed to correct these shortcomings: the computations are carried out efficiently for a large number of wave components and the effects of currents, bottom friction, local wind and wave breaking are added. This requires the exploitation of the concept of the spectral action balance equation and numerical wave propagation on a grid rather than along wave rays. The model has been in operation for problems varying from locally generated waves over tidal flats to swell penetration into Norwegian fjords. A comparison with extensive measurements is described for young swell under high wind penetrating the Rhine estuary.

scholarly journals Mass Transport Velocity in Shallow-Water Waves Reflected in a Rotating Ocean with a Coastal Boundary

2007 ◽  
Vol 37 (10) ◽  
pp. 2429-2445 ◽  
Author(s):  
Frode Hoydalsvik
Keyword(s):  
Mass Transport ◽  
Shallow Water ◽  
Water Waves ◽  
Traditional Approach ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Transport Velocity ◽  
Uniform Solution ◽  
Mass Transport Velocity ◽  
Sloping Bottom

Abstract The mass transport velocity in shallow-water waves reflected at right angles from an infinite and straight coast is studied theoretically in a Lagrangian reference frame. The waves are weakly nonlinear and monochromatic, and propagate in a homogenous, viscous, and rotating ocean. Unlike the traditional approach where the domain is divided into thin boundary layers and a core region, the uniform solution is obtained here without constraints on the thickness of the bottom wave boundary layer. It is shown that the mass transport velocity is not only sensitive to topography, but depends heavily on the interplay between the vertical length scales. Similarities and differences between the cases of a constant depth, a linearly sloping bottom, and a wavy and linearly sloping bottom are discussed. The mass transport velocity can be divided into two main categories—that induced by waves with a frequency close to the inertial frequency, and that induced by waves with a much larger frequency. For waves significantly affected by rotation to first order, the cross-shore mass transport velocity is very small relative to the alongshore mass transport velocity, and the direction of the mass transport velocity is reversed relative to that in waves of much higher frequencies.

scholarly journals POST-BOUSSINESQ MODEL FOR NONLINEAR IRREGULAR WAVE PROPAGATION IN PORTS AND WAVE-STRUCTURE INTERACTION

2020 ◽  
pp. 27
Author(s):  
Theofanis Karambas ◽  
Christos Makris ◽  
Vasilis Baltikas
Keyword(s):  
Wave Propagation ◽  
Water Waves ◽  
Wave Breaking ◽  
Wave Structure ◽  
Wave Transformation ◽  
Boussinesq Model ◽  
Weakly Nonlinear ◽  
Structure Interaction ◽  
Irregular Wave ◽  
Wave Structure Interaction

In this work, an updated version of the Karambas and Memos (2009) Boussinesq model for weakly nonlinear fully dispersive water waves, is introduced. It is implemented for wave propagation and transformation (due to shoaling, refraction, diffraction, bottom friction, wave breaking, runup, wave-structure interaction etc.) in nearshore zones and inside ports. One of the main goals is the model's thorough validation, thus it is tested against experimental data of wave transmission over and through breakwaters, uni- and multi-directional spectral wave transformation over complex bathymetries and diffraction through a breakwater gap. Case studies of model application over realistic variable bathymetries at characteristic Greek ports are also presented. Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/w8-AfAW6EYM

scholarly journals On the Multipeakon Dissipative Behavior of the Modified Coupled Camassa-Holm Model for Shallow Water System

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zhixi Shen ◽  
Yujuan Wang ◽  
Hamid Reza Karimi ◽  
Yongduan Song
Keyword(s):  
Differential Equations ◽  
Energy Loss ◽  
Shallow Water ◽  
Water Waves ◽  
Wave Breaking ◽  
Water Wave ◽  
Water System ◽  
Shallow Water Waves ◽  
Two Component ◽  
Shallow Water System

This paper investigates the multipeakon dissipative behavior of the modified coupled two-component Camassa-Holm system arisen from shallow water waves moving. To tackle this problem, we convert the original partial differential equations into a set of new differential equations by using skillfully defined characteristic and variables. Such treatment allows for the construction of the multipeakon solutions for the system. The peakon-antipeakon collisions as well as the dissipative behavior (energy loss) after wave breaking are closely examined. The results obtained herein are deemed valuable for understanding the inherent dynamic behavior of shallow water wave breaking.

RESPONSE CHARACTERISTICS OF GRAVEL BEACH FROM THE VIEWPOINT OF SHALLOW WATER WAVES AND MOVEMENT OF GRAVELS

2020 ◽  
Vol 76 (2) ◽  
pp. I_565-I_570
Author(s):  
Shin-ichi AOKI ◽  
Tomoki HAMANO ◽  
Taishi NAKAYAMA ◽  
Eiichi OKETANI ◽  
Takahiro HIRAMATSU ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Response Characteristics ◽  
Gravel Beach

Integrable Models

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Fluid Mechanics ◽  
Soliton Solution ◽  
Water Waves ◽  
Heisenberg Model ◽  
Kdv Equation ◽  
Short Review ◽  
Lax Pair ◽  
Shallow Water Waves ◽  
Initial Value ◽  
The Kdv Equation

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.

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