Dynamics of Saturated Energy Condensation in Two-Dimensional Turbulence

TL;DR

This paper investigates the saturation dynamics of energy condensation in two-dimensional turbulence, revealing how the system reaches a stationary state influenced by viscosity and forcing, with implications for numerical simulations and vortex structure.

Contribution

It provides analytical and numerical insights into the saturation process, vortex movement, and structure in 2D turbulence, highlighting resolution issues in simulations.

Findings

Saturation time inversely proportional to viscosity

Saturation energy depends on viscosity and forcing

Vortex profile has Gaussian core with exponential wings

Abstract

In two-dimensional forced Navier-Stokes turbulence, energy cascades to the largest scales in the system to form a pair of coherent vortices known as the Bose condensate. We show, both numerically and analytically, that the energy condensation saturates and the system reaches a statistically stationary state. The time scale of saturation is inversely proportional to the viscosity and the saturation energy level is determined by both the viscosity and the force. We further show that, without sufficient resolution to resolve the small-scale enstrophy spectrum, numerical simulations can give a spurious result for the saturation energy level. We also find that the movement of the condensate is similar to the motion of an inertial particle with an effective drag force. Furthermore, we show that the profile of the saturated coherent vortices can be described by a Gaussian core with exponential wings.