Results 221 to 230 of about 13,716 (261)

On ?The shallow water equations? By M. Shinbrot

Journal of Engineering Mathematics, 1972
The paper [1] above describes two steady shallow water flows which differ from the known flows of this type. It is suggested that the conditions imposed in obtaining these solutions are not consistent.
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Normalized shallow water equations

Moscow University Physics Bulletin, 2010
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Elizarova, T. G., Afanasieva, M. V.
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A shallow water equation on the circle

Communications on Pure and Applied Mathematics, 1999
The purpose of this paper is to study the spatially periodic case of the shallow water equation \[ \partial v/\partial t+ v\partial t/\partial x+\partial p/\partial x= 0\tag{1} \] in which the ``pressure'' \(p\) is \((1- d^2/dx^2)^{-1}(v^2+{1\over 2} v^{\prime 2})\). The equation has been much studied in recent years, starting with \textit{R.
Constantin, A., McKean, H. P.
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Analytic solutions to the shallow water equations

Physical Review E, 2005
Analytic, two-dimensional steady-state solutions to the rotating shallow water equations over variable topography are derived, by exploiting a drastic simplification of the equilibrium problem that occurs for nondivergent flows. For such flows, the equilibrium system decouples, and the cross-stream component of the momentum equation formally reduces to
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The shallow-water equations

2009
We now enter the realm of hyperbolic equations. Instead of starting with an introduction to numerical methods for hyperbolic equations in general, we prefer to begin by plunging into the particular case of the shallow-water equations. Other hyperbolic equations will be considered in Chapters 9 and 10.
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SLOW EIGENMODES OF THE SHALLOW-WATER EQUATIONS

Waves and Stability in Continuous Media, 2002
We present a survey of recent work on the lowest end of the eigenmode spectrum of the shallow water equations in a rotating reference frame. The results are complemented with numerical simulations of the fully nonlinear equations. Having care of using physically correct, mass-conserving boundary conditions, a description in terms of slow eigenmodes ...
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Global Weak Solutions for a Shallow Water Equation

Communications in Mathematical Physics, 2000
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Constantin, Adrian, Molinet, Luc
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A shock solution for the nonlinear shallow water equations

Journal of Fluid Mechanics, 2010
A global shock solution for the nonlinear shallow water equations (NSWEs) is found by assigning proper seaward boundary data that preserve a constant incoming Riemann invariant during the shock wave evolution. The correct shock relations, entropy conditions and asymptotic behaviour near the shoreline are provided along with an in-depth analysis of the ...
Antuono, Matteo
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Derivation of the Shallow Water Equations

2020
This chapter presents a derivation of the shallow water equations, which describe flows where horizontal length-scales are much larger than the vertical. This occurs when hydrodynamic processes are small in comparison to gravity effects, and is therefore appropriate for tidal flows in channels where the tidal wavelength \(\lambda _w\) is greater than ...
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The shallow water equation

Abstract This chapter first presents a simple derivation of the shallow water equation. It then proposes an implicit (time) and centered (space) discretization and tests it in one dimension. The chapter then examines solutions to look at front steepening and testing the dependence of the wave velocity on the water column depth expected ...
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