Energy stability of the Ekman boundary layer

Joseph J. Dudis, Stephen H. Davis

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

The critical value RE of the Reynolds number R is predicted by the application of the energy theory. When R ≪ RE, the Ekman layer is the unique steady solution of the Navier-Stokes equations and the same boundary conditions, and is, further, stable in a slightly weaker sense than asymptotically stable in the mean. The critical value RE is determined by numerically integrating the relevant Euler-Lagrange equations. An analytic lower bound to RE is obtained. Comparisons are made between RE and RL, the critical value of R according to linear theory, in order to demark the region of parameter space, RE ≪ R ≪ RL, in which subcritical instabilities are allowable.

Original languageEnglish (US)
Pages (from-to)405-413
Number of pages9
JournalJournal of fluid Mechanics
Volume47
Issue number2
DOIs
StatePublished - May 31 1971

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

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