Two-dimensional supersonic nonlinear Schroedinger flow past an extended obstacle

Journal Article · Thu Oct 15 04:00:00 EDT 2009 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.80.046317· OSTI ID:21294424

El, G A; Khodorovskii, V V ^[1]; Kamchatnov, A M ^[2]; Annibale, E S; Gammal, A ^[3]

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1. Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU (United Kingdom)
2. Institute of Spectroscopy, Russian Academy of Sciences, 142190 Troitsk, Moscow Region (Russian Federation)
3. Instituto de Fisica, Universidade de Sao Paulo, CP 66318, 05315-970 Sao Paulo, SP (Brazil)

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schroedinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear ''ship-wave'' pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.

• OSTI ID: 21294424
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print) Journal Issue: 4 Vol. 80; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOSE-EINSTEIN CONDENSATION
BOUNDARY-VALUE PROBLEMS
COMPRESSIBLE FLOW
COMPUTERIZED SIMULATION
EXACT SOLUTIONS
MODULATION
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PISTONS
QUANTIZATION
SCHROEDINGER EQUATION
SHOCK WAVES
SOLITONS
STEADY FLOW
SUPERFLUIDITY
SUPERSONIC FLOW
TWO-DIMENSIONAL CALCULATIONS