The effect of small-scale forcing on large-scale structures in two-dimensional flows

Alexei Chekhlov, Steven A. Orszag, Semion Sukoriansky, Boris Galperin, Ilya Staroselsky

Research output: Contribution to journalArticlepeer-review

83 Scopus citations


The effect of small-scale forcing on large-scale structures in β-plane two-dimensional (2D) turbulence is studied using long-term direct numerical simulations (DNS). We find that nonlinear effects remain strong at all times and for all scales and establish an inverse energy cascade that extends to the largest scales available in the system. The large-scale flow develops strong spectral anisotropy: k-5/3 Kolmogorov scaling holds for almost all φ, φ = arctan(ky/kx), except in the small vicinity of kx = 0, where Rhines's k-5 scaling prevails. Due to the k-5 scaling, the spectral evolution of β-plane turbulence becomes extremely slow which, perhaps, explains why this scaling law has never before been observed in DNS. Simulations with different values of β indicate that the β-effect diminishes at small scales where the flow is nearly isotropic. Thus, for simulations of β-plane turbulence forced at small scales sufficiently removed from the scales where β-effect is strong, large eddy simulation (LES) can be used. A subgrid scale (SGS) parameterization for such LES must account for the small-scale forcing that is not explicitly resolved and correctly accommodate two inviscid conservation laws, viz. energy and enstrophy. This requirement gives rise to a new anisotropic stabilized negative viscosity (SNV) SGS representation which is discussed in the context of LES of isotropic 2D turbulence.

Original languageEnglish
Pages (from-to)321-334
Number of pages14
JournalPhysica D: Nonlinear Phenomena
Issue number2-4
StatePublished - 1 Jan 1996


  • Eddy viscosity
  • Geophysics
  • Stabilized negative viscosity
  • Zonal jets
  • β-plane turbulence

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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