Theory of two-dimensional oblique dispersive shock waves in supersonic flow of a superfluid

Journal Article · Tue Dec 15 04:00:00 EST 2009 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.80.061601· OSTI ID:21352283

Hoefer, M A ^[1]; Ilan, B ^[2]

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1. Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027 (United States)
2. School of Natural Sciences, University of California, Merced, California 95343 (United States)

Dispersive shock waves (DSWs) are studied theoretically in the context of two-dimensional (2D) supersonic flow of a superfluid. Employing Whitham averaging theory for the repulsive Gross-Pitaevskii (GP) equation, suitable jump and entropy conditions are obtained for an oblique DSW, a fundamental building block for 2D flows with boundaries. In analogy to oblique viscous shock waves (VSWs), these conditions yield analytic relations between Mach number (M), velocity deflection angle (theta), and wave angle (beta). Unlike VSWs, the M-theta-beta phase diagram for DSWs displays four distinct regions associated with phase transitions in supersonic flow over a corner which are predicted and verified by numerical computations of the GP equation. Quasistationary DSWs, shock detachment due to transonic flow, spontaneous excitation of vortices, and the onset of turbulent dynamics associated with cavitation of the superfluid are observed.

• OSTI ID: 21352283
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 80; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CALCULATION METHODS
DIAGRAMS
DIMENSIONLESS NUMBERS
ENTROPY
FLUID FLOW
INFORMATION
MACH NUMBER
MATHEMATICS
NUMERICAL ANALYSIS
PHASE DIAGRAMS
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
SHOCK WAVES
SUPERFLUIDITY
SUPERSONIC FLOW
THERMODYNAMIC PROPERTIES
TRANSONIC FLOW
TURBULENCE
TWO-DIMENSIONAL CALCULATIONS
VELOCITY
VORTICES