Two-dimensional supersonic nonlinear Schrödinger flow past an extended obstacle

El, Gennady, Kamchatnov, A. M., Khodorovskii, V. V., Annibale, E. S. and Gammal, A. (2009) Two-dimensional supersonic nonlinear Schrödinger flow past an extended obstacle. Physical Review E, 80 (4). 046317. ISSN 1539-3755

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Official URL: https://doi.org/10.1103/PhysRevE.80.046317

Abstract

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schrödinger (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.

Item Type: Article
Subjects: F100 Chemistry
F300 Physics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: John Coen
Date Deposited: 15 Apr 2020 11:03
Last Modified: 15 Apr 2020 11:15
URI: http://nrl.northumbria.ac.uk/id/eprint/42777

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