From weak discontinuities to nondissipative shock waves

Journal Article · Fri Jan 15 00:00:00 EST 2010 · Journal of Experimental and Theoretical Physics

DOI:https://doi.org/10.1134/S1063776110010164· OSTI ID:21455272

Garifullin, R. N., E-mail: [e-mail]; Suleimanov, B. I., E-mail: bisul@mail.r ^[1]

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1. Ufa Scientific Center, Russian Academy of Sciences, Institute of Mathematics with Computing Center (Russian Federation)

An analysis is presented of the effect of weak dispersion on transitions from weak to strong discontinuities in inviscid fluid dynamics. In the neighborhoods of transition points, this effect is described by simultaneous solutions to the Korteweg-de Vries equation u{sub t}'+ uu{sub x}' + u{sub xxx}' = 0 and fifth-order nonautonomous ordinary differential equations. As x{sup 2} + t{sup 2} {yields}{infinity}, the asymptotic behavior of these simultaneous solutions in the zone of undamped oscillations is given by quasi-simple wave solutions to Whitham equations of the form r{sub i}(t, x) = tl{sub i} x/t{sup 2}.

• OSTI ID: 21455272
• Journal Information: Journal of Experimental and Theoretical Physics, Vol. 110, Issue 1; Other Information: DOI: 10.1134/S1063776110010164; Copyright (c) 2010 Pleiades Publishing, Ltd.; ISSN 1063-7761
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
42 ENGINEERING
ASYMPTOTIC SOLUTIONS
FLUID MECHANICS
KORTEWEG-DE VRIES EQUATION
OSCILLATIONS
SHOCK WAVES
VISCOSITY
ZONES
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL SOLUTIONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS