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Piston dispersive shock wave problem.

M A Hoefer1, M J Ablowitz, P Engels

  • 1National Institute of Standards and Technology, Boulder, Colorado 80305, USA. hoefer@boulder.nist.gov

Physical Review Letters
|March 21, 2008
PubMed
Summary
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Dispersive shock waves (DSWs) in nonlinear Schrödinger fluids exhibit unique behavior. For sufficient piston speeds, a periodic wave train forms, unlike classical shock waves.

Area of Science:

  • Fluid dynamics
  • Nonlinear physics
  • Wave phenomena

Background:

  • The classical piston shock problem is a foundational concept in shock wave theory.
  • Dispersive shock waves (DSWs) are analogous phenomena in fluids governed by nonlinear equations.

Purpose of the Study:

  • To analyze the analogous dispersive shock wave (DSW) problem for a fluid described by the nonlinear Schrödinger equation.
  • To investigate the behavior of DSWs generated by a moving piston (step potential).

Main Methods:

  • Asymptotic solutions were calculated for a piston moving at uniform speed into a quiescent dispersive fluid.
  • The study focused on the nonlinear Schrödinger equation to model fluid behavior.

Main Results:

Related Experiment Videos

  • A bifurcation in shock behavior was observed for increasing piston velocities.
  • Above a critical velocity, DSWs develop a periodic wave train in their wake.
  • These wave trains feature vacuum points and a fixed maximum density, irrespective of further velocity increases.

    • Conclusions:

    • The study reveals novel dynamics for DSWs, diverging from classical shock wave behavior.
    • The findings have potential applications in Bose-Einstein condensates and nonlinear optics.
    • The observed bifurcation and wave train formation offer new insights into nonlinear wave propagation.