Crude closure dynamics through large scale statistical theories

Marcus J. Grote, Andrew J. Majda

Research output: Contribution to journalArticle

Abstract

Crude closure algorithms based on equilibrium large scale statistical theories involving only a few constraints are developed here. These algorithms involve the nonlinear evolution of either a single parameter, the energy, for dynamic closore based on equilibrium energy-enstrophy statistical theory, or two parameters, the energy and circulation, for crude dynamic closure based on the equilibrium point vortex statistical theory. The crude closure algorithms are tested systematically through numerical experiments with the Navier-Stokes equations in two dimensions on a rectangular domain with stress-free boundary conditions and strong small scale forcing at moderately large Reynolds numbers. A series of successively more stringent tests is devised with conditions ranging from freely decaying flows to spin-up from rest by random forcing with like signed vortices, and finally to random forcing by vortices with alternating or opposite signs. Comparison of standard spectral simulations with crude dynamic closure based on the two-parameter theory yields at most 5% velocity errors for all of these examples. The velocity errors can be as large as 10% for the one-parameter closure theory but are often comparable to those obtained with the two-parameter closure. The results of numerical experiments with Ekman drag are also discussed here.

Original languageEnglish (US)
Pages (from-to)3431-3442
Number of pages12
JournalPhysics of Fluids
Volume9
Issue number11
StatePublished - Nov 1997

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closures
Vortex flow
velocity errors
vortices
Navier Stokes equations
Drag
Reynolds number
Experiments
Boundary conditions
free boundaries
Navier-Stokes equation
vorticity
drag
energy
boundary conditions
simulation

ASJC Scopus subject areas

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

Cite this

Crude closure dynamics through large scale statistical theories. / Grote, Marcus J.; Majda, Andrew J.

In: Physics of Fluids, Vol. 9, No. 11, 11.1997, p. 3431-3442.

Research output: Contribution to journalArticle

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