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The Evolution of Large‐Horizontal‐Scale Disturbances in Marginally Stable, Inviscid, Shear Flows. II. Solutions of the Boussinesq Equation
Author(s) -
Hickernell Fred J.
Publication year - 1983
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198369123
Subject(s) - inviscid flow , scale (ratio) , bounded function , mathematics , mathematical analysis , shear (geology) , boussinesq approximation (buoyancy) , mechanics , geology , physics , heat transfer , natural convection , quantum mechanics , rayleigh number , petrology
In part I the Boussinesq equation was found to describe large‐horizontal‐scale disturbances in certain marginally stable flows. In this paper the properties of the solutions of this equation are explored. Solutions that are bounded for all time and those that blow up in finite time are observed analytically and numerically. Sufficient conditions for both boundedness and blowup are given.