Coherent vortex versus chaotic state in two-dimensional turbulence

We examine analytically and numerically the state of a two-dimensional fluid in a finite box appearing as a result of the inverse cascade supported by a permanent pumping. We ar-gue that there are two different states. One of the states is dominated by big coherent vortices with a well-defined mean profile. The other state is dominated by strong chaotic large-scale fluctuations. The character of the realized state depends on the ratio vk2f /alpha where v is the kinematic viscosity coefficient, kf is the characteristic wave vector of the pumping force and alpha the bottom friction coefficient. If the ratio vk2f /alpha is large then one expects to observe the first state, whereas in the opposite state the second (chaotic) state is expected. To check the prediction we performed the direct numerical simulations of hydrodynamics of a weakly compressible two-dimensional fluid with no-slip boundary conditions. The pumping force is static and contains some spacial harmonics. The simulations are performed for different values of pumping and of the ratio vk2f /alpha. We introduce the criterion based on presence/absence of long time correlations to distinguish two above states. The numerical results confirm the analytical predictions.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This study examines the state of a two-dimensional fluid in a finite box resulting from an inverse cascade supported by a permanent pumping through analytical and numerical approaches. Two different states are identified: one dominated by coherent vortices with a well-defined profile, and the other dominated by chaotic large-scale fluctuations. The realized state depends on the ratio vk2f/alpha, where v is the viscosity coefficient, kf is the wave vector of the pumping force, and alpha is the bottom friction coefficient.