Effective Equations and the Inverse Cascade Theory for Kolmogorov Flows

Abstract

We study the two dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that in this limit the low frequency energy spectrum evolves to a universal k to the -4th power decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that will smooth initial data, the solution to the effective equation develops a k to the -4th power type singularity at a finite time. This gives a convenient explanation for the k to the -4th power decay law exhibited by the original Kolmogorov flows.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1992
Accession Number
ADA247841

Entities

People

  • Chi-Wang Shu
  • Weinan E

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