TY - JOUR

T1 - The effect of small-scale forcing on large-scale structures in two-dimensional flows

AU - Chekhlov, Alexei

AU - Orszag, Steven A.

AU - Sukoriansky, Semion

AU - Galperin, Boris

AU - Staroselsky, Ilya

N1 - Funding Information:
The authors acknowledge fruitful discussions with Victor Yakhot. One of us (AC) was supported by the AFOSR under Grant number F49620-93-1-0296. We would also like to acknowledge support by ONR under Contracts N00014-92-J-1363, N00014-92-C-0089 and N00014-90-C-0039, NASA under Contract NAS5-32804, and the Perlstone Center for Aeronautical Engineering Studies. Some of the computations were performed on Cray Y-MP of NAVOCEANO Supercomputer Center, Stennis Space Center, Mississippi.

PY - 1996/1/1

Y1 - 1996/1/1

N2 - 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.

AB - 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.

KW - Eddy viscosity

KW - Geophysics

KW - Stabilized negative viscosity

KW - Zonal jets

KW - β-plane turbulence

UR - http://www.scopus.com/inward/record.url?scp=0000595980&partnerID=8YFLogxK

U2 - 10.1016/0167-2789(96)00102-9

DO - 10.1016/0167-2789(96)00102-9

M3 - Article

AN - SCOPUS:0000595980

VL - 98

SP - 321

EP - 334

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 2-4

ER -