The effects of quadratic drag on the inverse cascade of two-dimensional turbulence

N. Grianik, I. M. Held, K. S. Smith, G. K. Vallis

Research output: Contribution to journalArticle

Abstract

We explore the effects of a quadratic drag, similar to that used in bulk aerodynamic formulas, on the inverse cascade of homogeneous two-dimensional turbulence. If a two-dimensional fluid is forced at a relatively small scale, then an inverse cascade of energy will be generated that may then be arrested by such a drag at large scales. Both scaling arguments and numerical experiments support the idea that in a statistically steady state the length scale of energy-containing eddies will not then depend on the energy input to the system; rather, the only external parameter that defines this scale is the quadratic drag coefficient itself. A universal form of the spectrum is suggested, and numerical experiments are in good agreement. Further, the turbulent transfer of a passive tracer in the presence of a uniform gradient is well predicted by scaling arguments based solely on the energy cascade rate and the nonlinear drag coefficient.

Original languageEnglish (US)
Pages (from-to)73-78
Number of pages6
JournalPhysics of Fluids
Volume16
Issue number1
DOIs
StatePublished - Jan 2004

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Cascades (fluid mechanics)
Drag coefficient
drag
Drag
cascades
Turbulence
turbulence
drag coefficients
Aerodynamics
Experiments
scaling
Fluids
energy
aerodynamics
tracers
vortices
gradients
fluids

ASJC Scopus subject areas

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

Cite this

The effects of quadratic drag on the inverse cascade of two-dimensional turbulence. / Grianik, N.; Held, I. M.; Smith, K. S.; Vallis, G. K.

In: Physics of Fluids, Vol. 16, No. 1, 01.2004, p. 73-78.

Research output: Contribution to journalArticle

Grianik, N. ; Held, I. M. ; Smith, K. S. ; Vallis, G. K. / The effects of quadratic drag on the inverse cascade of two-dimensional turbulence. In: Physics of Fluids. 2004 ; Vol. 16, No. 1. pp. 73-78.
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