Accession Number:

ADA247841

Title:

Effective Equations and the Inverse Cascade Theory for Kolmogorov Flows

Descriptive Note:

Final rept.

Corporate Author:

INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s):

• E, Weinan
• Shu, Chi-Wang

Report Date:

1992-01-01

Pagination or Media Count:

23.0

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.

Descriptors:

• *MATHEMATICAL MODELS
• QUANTITY
• THEORY
• NUMERICAL ANALYSIS
• TIME
• SPECTRA
• LOW ENERGY
• INVERSION
• FLOW
• EQUATIONS
• LOW FREQUENCY

Subject Categories:

• Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE