scholarly journals Shallow water dynamics on linear shear flows and plane beaches

2017 ◽  
Vol 29 (7) ◽  
pp. 073602 ◽  
Author(s):  
Maria Bjørnestad ◽  
Henrik Kalisch
Keyword(s):  
Shallow Water ◽  
Shear Flows ◽  
Water Dynamics ◽  
Linear Shear ◽  
Shallow Water Dynamics

Stability of blow-up solution for the two component Camassa–Holm equations

2020 ◽  
Vol 120 (3-4) ◽  
pp. 319-336
Author(s):  
Xintao Li ◽  
Shoujun Huang ◽  
Weiping Yan
Keyword(s):  
Shallow Water ◽  
Wave Breaking ◽  
Water Regime ◽  
Blow Up ◽  
Dynamical Behavior ◽  
Water Dynamics ◽  
Two Component ◽  
Breaking Mechanism ◽  
Self Similar ◽  
Shallow Water Dynamics

This paper studies the wave-breaking mechanism and dynamical behavior of solutions near the explicit self-similar singularity for the two component Camassa–Holm equations, which can be regarded as a model for shallow water dynamics and arising from the approximation of the Hamiltonian for Euler’s equation in the shallow water regime.

Stability of linear shear flows in shallow water

1995 ◽  
Vol 303 ◽  
pp. 203-214 ◽  
Author(s):  
Charles Knessl ◽  
Joseph B. Keller
Keyword(s):  
Shallow Water ◽  
Shear Flows ◽  
Special Functions ◽  
Rigid Wall ◽  
Eigenvalue Equation ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Linear Shear ◽  
The Stability ◽  
Rigid Walls

The stability or instability of various linear shear flows in shallow water is considered. The linearized equations for waves on the surface of each flow are solved exactly in terms of known special functions. For unbounded shear flows, the exact reflection and transmission coefficients R and T for waves incident on the flow, are found. They are shown to satisfy the relation |R|2= 1+ |T|2, which proves that over reflection occurs at all wavenumbers. For flow bounded by a rigid wall, R is found. The poles of R yield the eigenvalue equation from which the unstable mides can be found. For flow in a channel, with two rigid walls, the eigenvalue equation for the modes is obtained. The results are compared with previous numerical results.

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