Near-bottom instabilities under fully nonlinear waves of depression

2010 ◽  
pp. 459-464
Keyword(s):  
Nonlinear Waves ◽  
Fully Nonlinear

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>

Propagation of Fully Nonlinear Waves in Deepwater, Transition Zone and Shallow-Water

2007 ◽  
Author(s):  
Hoda M. El Safty ◽  
Alaa M. Mansour ◽  
A. G. Abul-Azm
Keyword(s):  
Shallow Water ◽  
Transition Zone ◽  
Nonlinear Waves ◽  
Wave Number ◽  
Numerical Wave Tank ◽  
Tank Model ◽  
Wave Tank ◽  
Fully Nonlinear ◽  
Nonlinear Solution ◽  
Numerical Wave

In this paper, a fully nonlinear numerical wave tank model has been used to simulate the propagation of fully nonlinear waves in different water depths. In the numerical wave tank model, the fully nonlinear dynamic and kinematic free-surface boundary conditions have been applied and the boundary integral equation (BIE) solution to the Laplacian problem has been obtained using the Mixed Eulerian-Lagrangian (MEL) approach. The model solution has been verified through the comparison with the available experimental data. A convergence and accuracy study has been carried out to examine the time stepping scheme and the required mesh density. The nonlinearity effects were evident in the solution by the asymmetrical wave profile around both vertical and horizontal axis along with sharp high crests and broad flat troughs. Fully nonlinear wave propagation in deepwater, in transition zone and in shallow water has been simulated. The nonlinear solution has been compared to the linear solution for various waves. Shoaling coefficient and wave-number have been derived based on the nonlinear solution and compared to the linear theory solution for various wave characteristics.

scholarly journals A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry

2006 ◽  
Vol 53 (5-6) ◽  
pp. 487-504 ◽  
Author(s):  
Per A. Madsen ◽  
David R. Fuhrman ◽  
Benlong Wang
Keyword(s):  
Nonlinear Waves ◽  
Type Method ◽  
Fully Nonlinear

Nonlinear Waves, Solitons and Chaos

2000 ◽  
Author(s):  
Eryk Infeld ◽  
George Rowlands
Keyword(s):  
Nonlinear Waves
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