Standing shocks in a rotating channel

Tivon E. Jacobson, Esteban Tabak

Research output: Contribution to journalArticle

Abstract

This paper discusses the stationary shallow water shocks occurring in a reentrant rotating channel with wind stress and topography. Asymptotic predictions for the shock location, strength, and associated energy dissipation are developed by taking the topographic perturbation to be small. It is shown that under appropriate conditions, a mean flow develops under the action of the wind stress, with a transverse profile determined by the need to support stationary shocks. The scaling arguments for the asymptotics are developed by demanding integrated energy and momentum balance, with the result that the free surface perturbation is of the order of the square root of the topographic perturbation. Shock formation requires that linear waves be nondispersive, which sets a solvability condition on the mean flow and which leads to a class of generalized Kelvin waves. Two-dimensional shock-resolving numerical simulations validate the asymptotic expressions and demonstrate the presence of stationary separated flow shocks in some cases.

Original languageEnglish (US)
Pages (from-to)3765-3778
Number of pages14
JournalPhysics of Fluids
Volume16
Issue number10
DOIs
StatePublished - Oct 2004

Fingerprint

Wind stress
shock
Topography
Energy dissipation
Momentum
perturbation
Water
Computer simulation
Kelvin waves
separated flow
shallow water
topography
energy dissipation
momentum
scaling
profiles
predictions

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Standing shocks in a rotating channel. / Jacobson, Tivon E.; Tabak, Esteban.

In: Physics of Fluids, Vol. 16, No. 10, 10.2004, p. 3765-3778.

Research output: Contribution to journalArticle

Jacobson, Tivon E. ; Tabak, Esteban. / Standing shocks in a rotating channel. In: Physics of Fluids. 2004 ; Vol. 16, No. 10. pp. 3765-3778.
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