Structure of coherent vortices generated by the inverse cascade of two-dimensional turbulence in a finite box

Abstract

We discuss the structure and geometrical characteristics of coherent vortices appearing as a result of the inverse cascade in two-dimensional turbulence in a finite box. We demonstrate that the universal velocity profile, established by J. Laurie et al. [Phys. Rev. Lett. 113, 254503 (2014)], corresponds to the passive regime of flow fluctuations. We find the vortex core radius and the vortex size, and we argue that the amount of vortices generated in the box depends on the system parameters.

Turbulence Statistics in a Two-Dimensional Vortex Condensate

“…As shown previously [10,11,14], within the quasilinear approximation -justified for δ 1 -and once (2) is observed to hold.…”

“…In this Letter, we present new results on the statistics of the Reynolds stress. First, using long time integration, we provide the first numerical evidence supporting the explicit formula for the momentum flux [10,11]. Second, we show that the turbulent energy is determined by a different mechanism; we explain its structure by combining a first-principles theoretical framework and numerical results, hence describing the full Reynolds tensor.…”

“…The average turbulent energy profile.-Symmetry considerations imply that the magnitude of the diagonal terms of the Reynolds tensor, u 2 and v 2 , as well as the mechanism that dictates them, are different than those for the momentum flux [10,11]. We therefore take a different approach than [17], where the turbulent energy is computed within the same framework used for the momentum flux.…”

How vortices and shocks provide for a flux loop in two-dimensional compressible turbulence

“…On the contrary, large-scale motions are usually less dissipative, so that an inverse cascade can proceed unimpeded, either producing larger and larger scales or reaching the box size and creating a coherent mode of growing amplitude. That process is now actively studied in 2D incompressible turbulence [3,4,[9][10][11][12][13], including in a curved space, where vortex rings rather than vortices are created [14]. The energy of an incompressible flow in an unbounded domain grows unlimited when the friction factors go to zero at a finite energy input rate.…”

Rare Event Algorithm Links Transitions in Turbulent Flows with Activated Nucleations

“…The noise η forces the flow dynamics and is precisely defined in the Supplemental Material file. When β = 0, those equations are the twodimensional stochastic Navier-Stokes equations for which a few rare transitions have been observed in the past between dipole and jet states [19], and for which impressive explicit relation between the energy injection rate and the Reynolds stresses have been recently derived [20][21][22]. Such relations have been further justified and extended to the case β = 0 [23], see also [18].…”