A Highly Accurate Boussinesq Method for Fully Nonlinear Waves from Shallow to Deep Water

2002 ◽  
Author(s):  
Per A. Madsen ◽  
Harry Bingham ◽  
Hua Liu
Keyword(s):  
Deep Water ◽  
Nonlinear Waves ◽  
Fully Nonlinear

Fully nonlinear solution of bi-chromatic deep-water waves

2014 ◽  
Vol 91 ◽  
pp. 290-299 ◽  
Author(s):  
Zhiliang Lin ◽  
Longbin Tao ◽  
Yongchang Pu ◽  
Alan J. Murphy
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Fully Nonlinear ◽  
Nonlinear Solution ◽  
Deep Water Waves

Fully nonlinear internal waves in a two-fluid system

1999 ◽  
Vol 396 ◽  
pp. 1-36 ◽  
Author(s):  
WOOYOUNG CHOI ◽  
ROBERTO CAMASSA
Keyword(s):  
Solitary Wave ◽  
Euler Equations ◽  
Deep Water ◽  
Large Amplitude ◽  
Nonlinear Models ◽  
Weak Nonlinearity ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
The Waves ◽  
Two Fluid

Model equations that govern the evolution of internal gravity waves at the interface of two immiscible inviscid fluids are derived. These models follow from the original Euler equations under the sole assumption that the waves are long compared to the undisturbed thickness of one of the fluid layers. No smallness assumption on the wave amplitude is made. Both shallow and deep water configurations are considered, depending on whether the waves are assumed to be long with respect to the total undisturbed thickness of the fluids or long with respect to just one of the two layers, respectively. The removal of the traditional weak nonlinearity assumption is aimed at improving the agreement with the dynamics of Euler equations for large-amplitude waves. This is obtained without compromising much of the simplicity of the previously known weakly nonlinear models. Compared to these, the fully nonlinear models' most prominent feature is the presence of additional nonlinear dispersive terms, which coexist with the typical linear dispersive terms of the weakly nonlinear models. The fully nonlinear models contain the Korteweg–de Vries (KdV) equation and the Intermediate Long Wave (ILW) equation, for shallow and deep water configurations respectively, as special cases in the limit of weak nonlinearity and unidirectional wave propagation. In particular, for a solitary wave of given amplitude, the new models show that the characteristic wavelength is larger and the wave speed is smaller than their counterparts for solitary wave solutions of the weakly nonlinear equations. These features are compared and found in overall good agreement with available experimental data for solitary waves of large amplitude in two-fluid systems.

Numerical Simulations of Large Deep Water Waves: The Application of a Boundary Element Method

2006 ◽  
Author(s):  
Caroline H. Hague ◽  
Chris Swan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Deep Water ◽  
Water Waves ◽  
Physical Space ◽  
Wave Model ◽  
Three Dimensions ◽  
Fully Nonlinear ◽  
Highly Nonlinear ◽  
Element Method

This paper concerns the description of extreme surface water waves in deep water. A fully nonlinear numerical wave model in three dimensions is presented, based on the Boundary Element Method (BEM), and is applied to nonlinear focusing of wave components with varying frequency and direction of propagation to form highly nonlinear groups. By using multiple fluxes at corners and edges of the numerical domain the “corner problem” associated with BEM-based models in physical space is overcome. A two-dimensional version of the method is also employed to model unidirectional cases, and examples presented include the focusing of Top Hat spectra in deep water to form highly nonlinear wave groups at or close to their breaking limit. The ability of the model to accurately simulate these sea states is highlighted by comparison to the fully nonlinear model of Bateman, Swan and Taylor (2001, 2003).

scholarly journals Linear superposition of nonlinear waves

2009 ◽  
Vol 75 (2) ◽  
pp. 145-152 ◽  
Author(s):  
SWADESH MAHAJAN ◽  
HIDEAKI MIURA
Keyword(s):  
Nonlinear Waves ◽  
Linear Superposition ◽  
Fluid System ◽  
Amplitude Wave ◽  
Fully Nonlinear ◽  
Arbitrary Amplitude ◽  
Nonlinear Solutions ◽  
Two Fluid

AbstractExact nonlinear (arbitrary amplitude) wave-like solutions of an incompressible, magnetized, non-dissipative two-fluid system are found. It is shown that, in 1-D propagation, these fully nonlinear solutions display a rare property; they can be linearly superposed.

Explicit nonlinear waves of fluid models on extended domains and unbounded growth with backscatter

2020 ◽  
Author(s):  
Artur Prugger ◽  
Jens Rademacher
Keyword(s):  
Nonlinear Waves ◽  
Large Scale ◽  
Water Model ◽  
Explicit Solutions ◽  
Stationary Waves ◽  
Fluid Models ◽  
Fully Nonlinear ◽  
Geostrophic Balance ◽  
Linear Waves ◽  
Rotating Shallow Water

<p>Large scale motions in geophysical fluid models are often characterised by linear waves, which are obtained by linearising the equations. But there are also many explicit solutions of the fully nonlinear equations when posed the full space. The exact solutions we are investigating often characterise Rossby waves, since they are in geostrophic balance. They also can be compositions of waves, some are interacting with each other and some do not, showing wave interactions as explicit solutions in the fully nonlinear problem.</p><p>In this talk I will briefly introduce the idea behind these explicit nonlinear waves and show some of their properties, and their occurrence in different fluid models in extended domains.</p><p>As an application, we especially focus on a rotating shallow water model with simplified backscatter. In this case one finds not only geostrophic explicit solutions, but also ageostrophic ones. Moreover, here energy accumulates in selected scales due to the backscatter terms and causes exponentially and unboundedly growing ageostrophic nonlinear waves. This also relates to instability of coexisting stationary waves and is an instance of the role of nonlinear waves in energy transfer, and illustrates their role in preventing energy equidistribution for general data.</p>

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