RELAXATION OF EULER EQUATIONS AND HYDRODYNAMIC INSTABILITIES

RELAXATION OF EULER EQUATIONS AND HYDRODYNAMIC INSTABILITIES

We present a relaxed version of incompressible Euler equations that permits foliated flows involving two velocities. These relaxed equations allow a two-phase evolution of some vortex sheets as an alternative to discontinuous solutions of Euler equations. In the case of two perfect fluids of differe...

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Veröffentlicht in:Quarterly of applied mathematics 1992-06, Vol.50 (2), p.235-255
Hauptverfasser: DUCHON, JEAN, ROBERT, RAOUL
Format: Artikel
Sprache:eng
Schlagworte:
Analytics
Cauchy problem
Conservation equations
Curl
Euler equations
Exact sciences and technology
Flow velocity
Fluid dynamics
Fundamental areas of phenomenology (including applications)
General theory
Kinetic energy
Mathematics
Physics
Velocity distribution
Vortex sheets
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Beschreibung
Zusammenfassung:We present a relaxed version of incompressible Euler equations that permits foliated flows involving two velocities. These relaxed equations allow a two-phase evolution of some vortex sheets as an alternative to discontinuous solutions of Euler equations. In the case of two perfect fluids of different densities superposed one over the other, we show that this relaxation process yields a linearly well-posed two-phase solution.
ISSN:0033-569X
1552-4485
DOI:10.1090/qam/1162274