Nonlinear dynamics of flows of a heavy compressible gas in the shallow water approximation

The system of the equations of motion for a compressible gas in the gravitational field over a smooth underlying surface has been analyzed in the shallow water approximation. All continuous centered self-similar solutions and all discontinuous self-similar solutions have been obtained. The problem o...

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Bibliographic Details
Published in:Journal of experimental and theoretical physics 2012-06, Vol.114 (6), p.1058-1071
Main Authors: Karelsky, K. V., Petrosyan, A. S., Chernyak, A. V.
Format: Article
Language:English
Subjects:
APPROXIMATIONS
Classical and Quantum Gravitation
COMPRESSED GASES
COMPRESSION
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Elementary Particles
EQUATIONS OF MOTION
GAS FLOW
GRAVITATIONAL FIELDS
MATHEMATICAL SOLUTIONS
Nonlinear
NONLINEAR PROBLEMS
Particle and Nuclear Physics
Physics
Physics and Astronomy
Quantum Field Theory
Relativity Theory
Soft Matter Physics
Solid State Physics
Statistical
SURFACES
WATER
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Summary:The system of the equations of motion for a compressible gas in the gravitational field over a smooth underlying surface has been analyzed in the shallow water approximation. All continuous centered self-similar solutions and all discontinuous self-similar solutions have been obtained. The problem of the decay of an arbitrary discontinuity for the equations of motion of the compressible gas has been solved in the explicit form in the shallow water approximation. The existence of four different configurations implementing the solution of the problem of the decay of an arbitrary discontinuity has been demonstrated. The conditions necessary and sufficient for the implementation of each configuration have been determined.
ISSN:1063-7761
1090-6509
DOI:10.1134/S1063776112050032