Two-dimensional supersonic nonlinear Schrödinger flow past an extended obstacle

Abstract

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional defocusing nonlinear Schrödinger (NLS) equation. This problem is of fundamental importance as a dispersive analogue of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed 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.

arXiv comment34 pages, 23 figures

References in corpus (20)

• Watching dark solitons decay into vortex rings in a Bose-Einstein condensate
• On Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics
• Motion of a heavy impurity through a Bose-Einstein condensate
• Stationary and non-stationary fluid flow of a Bose-Einstein condensate through a penetrable barrier
• Pressure drag in linear and nonlinear quantum fluids
• Resolution of a shock in hyperbolic systems modified by weak dispersion
• Bogoliubov-Cerenkov radiation in a Bose-Einstein condensate flowing against an obstacle
• Oblique dark solitons in supersonic flow of a Bose-Einstein condensate
• Stabilization of Solitons Generated by a Supersonic Flow of Bose-Einstein Condensate Past an Obstacle
• Dissipationless shock waves in repulsive Bose-Einstein condensates
• On the Whitham equations for the defocusing nonlinear Schrodinger equation with step initial data
• Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction
• The piston dispersive shock wave problem
• Wave patterns generated by a supersonic moving body in a binary Bose-Einstein condensate
• Linear "ship waves" generated in stationary flow of a Bose-Einstein condensate past an obstacle
• Transcritical flow of a Bose-Einstein condensate through a penetrable barrier
• Spatial dispersive shock waves generated in supersonic flow of Bose-Einstein condensate past slender body
• Stationary wave patterns generated by an impurity moving with supersonic velocity through a Bose-Einstein condensate
• Two-dimensional periodic waves in a supersonic flow of a Bose-Einstein condensate
• Incoherence of Bose-Einstein condensates at supersonic speeds due to quantum noise

Cited by in corpus (23)

• Dispersive shock waves and modulation theory
• Dispersive shock waves theory for non-integrable equations
• Generation of dispersive shock waves by the flow of a Bose-Einstein condensate past a narrow obstacle
• Dispersive shock waves in the Kadomtsev-Petviashvili and Two Dimensional Benjamin-Ono equations
• Many-Body Dissipative Flow of a Confined Scalar Bose-Einstein Condensate Driven by a Gaussian Impurity
• Wave breaking and formation of dispersive shock waves in a defocusing nonlinear optical material
• Numerical study of the Kadomtsev--Petviashvili equation and dispersive shock waves
• Condition for convective instability of dark solitons
• Flying in a superfluid: starting flow past an airfoil
• Modulation theory and resonant regimes for dispersive shock waves in nematic liquid crystals
• Dark solitons, dispersive shock waves, and transverse instabilities
• Nonlocality and fluctuations near the optical analog of a sonic horizon
• Oblique spatial dispersive shock waves in nonlinear Schrödinger flows
• On critical behaviour in generalized Kadomtsev--Petviashvili equations
• Whitham Shocks and Resonant Dispersive Shock Waves Governed by the Higher Order Korteweg-de Vries Equation
• Response of a dusty plasma system to external charge perturbations
• Jet-like tunneling from a trapped vortex
• Refraction of dispersive shock waves
• Hirota method for oblique solitons in two-dimensional supersonic nonlinear Schroedinger flow
• Interaction of oblique dark solitons in two-dimensional supersonic nonlinear Schrödinger flow
• Stationary one-dimensional dispersive shock waves
• Fate of the "vacuum point'' and of grey solitons in dispersive quantum shock waves in a one-dimensional Bose gas
• Phase transitions of photon fluid flows driven by a virtual all-optical piston