Turbulence Statistics in a Two-Dimensional Vortex Condensate

被引:36
作者
Frishman, Anna [1 ,2 ]
Herbert, Corentin [2 ,3 ]
机构
[1] Princeton Univ, Princeton Ctr Theoret Sci, Princeton, NJ 08544 USA
[2] Weizmann Inst Sci, Dept Phys Complex Syst, POB 26, IL-76100 Rehovot, Israel
[3] Univ Claude Bernard, Univ Lyon, ENS Lyon, Lab Phys,CNRS, F-69342 Lyon, France
关键词
DIRECT NUMERICAL-SIMULATION; HOMOGENEOUS TURBULENCE; CASCADE; ENERGY;
D O I
10.1103/PhysRevLett.120.204505
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Disentangling the evolution of a coherent mean-flow and turbulent fluctuations, interacting through the nonlinearity of the Navier-Stokes equations, is a central issue in fluid mechanics. It affects a wide range of flows, such as planetary atmospheres, plasmas, or wall-bounded flows, and hampers turbulence models. We consider the special case of a two-dimensional flow in a periodic box, for which the mean flow, a pair of box-size vortices called "condensate," emerges from turbulence. As was recently shown, a perturbative closure describes correctly the condensate when turbulence is excited at small scales. In this context, we obtain explicit results for the statistics of turbulence, encoded in the Reynolds stress tensor. We demonstrate that the two components of the Reynolds stress, the momentum flux and the turbulent energy, are determined by different mechanisms. It was suggested previously that the momentum flux is fixed by a balance between forcing and mean-flow advection: using unprecedently long numerical simulations, we provide the first direct evidence supporting this prediction. By contrast, combining analytical computations with numerical simulations, we show that the turbulent energy is determined only by mean-flow advection and obtain for the first time a formula describing its profile in the vortex.
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页数:6
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