Wave-vortex interactions in fluids and superfluids

Research output: Contribution to journalReview article

Abstract

This article reviews the methods of wave-mean interaction theory for classical fluid dynamics, and for geophysical fluid dynamics in particular, providing a few examples for illustration. It attempts to bring the relevant equations into their simplest possible form, which highlights the organizing role of the circulation theorem in the theory. This is juxtaposed with a simple account of superfluid dynamics and the attendant wave-vortex interactions as they arise in the nonlinear Schrödinger equation. Here the fundamental physical situation is more complex than in the geophysical case, and the current mathematical understanding is more tentative. Classical interaction theory might be put to good use in the theoretical and numerical study of quantum fluid dynamics.

Original languageEnglish (US)
Pages (from-to)205-228
Number of pages24
JournalAnnual Review of Fluid Mechanics
Volume42
DOIs
StatePublished - Jan 1 2010

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Keywords

  • Circulation theorem
  • Lagrangian-mean theory
  • Nonlinear Schrödinger equation
  • Pseudomomentum
  • Wave-driven circulation

ASJC Scopus subject areas

  • Condensed Matter Physics

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