Exact time-dependent flows for non-shallow water equations
type: Item
instance of: scholarly article
title: Exact time-dependent flows for non-shallow water equations
zbMATH Open document ID: 0563.76021
DOI: 10.1007/BF00945076
author: J. Blot
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1984-01-01T00:00:00Z
review text: The authors discuss two classes of exact solutions of nonlinear, non- shallow water equations. Invoking several transformation of variables of the original systems, the first class is shown to be governed by a third order nonlinear ordinary differential equation which is found to be singular at both ends of the interval of interest. This equation is solved by a numerical technique and found to describe flows between two intersecting planes. The second class of solution is expressed in terms of incomplete beta functions and delineates flows under a free surface which is a function of time only. The solutions are then compared with those obtained earlier by \textit{N. C. Freeman} [J. Fluid Mech., 56, 257- 263 (1972; Zbl 0256.76009)], \textit{P. L. Sachdev} [J. Fluid Mech., 96, 797-802 (1980; Zbl 0418.76013)] and \textit{M. S. Longuet-Higgins} [J. Fluid Mech., 55, 529-543 (1972; Zbl 0257.76013)]. Several special solutions are examined. Numerical results are also presented.
reviewed by: Lokenath Debnath
Mathematics Subject Classification ID: 76B15
zbMATH DE Number: 3898429
zbMATH Keywords: two classes of exact solutions
zbMATH Keywords: nonlinear, non-shallow water equations
zbMATH Keywords: Numerical results
MaRDI profile type: Publication
cites work: Simple waves on shear flows: similarity solutions
cites work: Exact, self-similar, time-dependent free surface flows under gravity
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cites work: Similarity transformations for the two-dimensional, unsteady, stream-function equation
description: scientific article; zbMATH DE number 3898429