Nonlinear theory of magnetohydrodynamic flows of a compressible fluid in the shallow water approximation

2016 ◽  
Vol 123 (3) ◽  
pp. 520-539 ◽  
Author(s):  
D. A. Klimachkov ◽  
A. S. Petrosyan
Keyword(s):  
Shallow Water ◽  
Nonlinear Theory ◽  
Compressible Fluid ◽  
Magnetohydrodynamic Flows ◽  
Shallow Water Approximation

scholarly journals Shallow water waves in a rotating rectangular basin

2000 ◽  
Vol 24 (10) ◽  
pp. 649-661 ◽  
Author(s):  
Mohamed Atef Helal
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Equations Of Motion ◽  
System Of Nonlinear Equations ◽  
System Of Equations ◽  
Order Of Approximation ◽  
Shallow Water Waves ◽  
Nonlinear System Of Equations ◽  
Rectangular Basin ◽  
Shallow Water Approximation

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.

Cuspon-type Waves and Their Properties

2021 ◽  
Vol 24 (2) ◽  
pp. 145-155
Author(s):  
G. Omel’yanov
Keyword(s):  
Shallow Water ◽  
Traveling Waves ◽  
Water Surface ◽  
First Derivative ◽  
Shallow Water Approximation

The general Degasperis-Prosesi equation (gDP) describes the evolution of the water surface in a unidirectional shallow water approximation. We consider essentially non-integrable versions of this model and analyze their cuspon-type solutions, that is continuous traveling waves with the unbounded first derivative.

Bathymetry reconstruction based on the zero-inertia shallow water approximation

2012 ◽  
Vol 27 (5) ◽  
pp. 721-732 ◽  
Author(s):  
Alelign Gessese ◽  
Kabila Mawanzi Wa ◽  
Mathieu Sellier
Keyword(s):  
Shallow Water ◽  
Shallow Water Approximation

Tsunami Excitation by Submarine Slides in Shallow-water Approximation

2001 ◽  
Vol 158 (4) ◽  
pp. 759-797 ◽  
Author(s):  
S. Tinti ◽  
E. Bortolucci ◽  
C. Chiavettieri
Keyword(s):  
Shallow Water ◽  
Shallow Water Approximation ◽  
Submarine Slides
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