Bose condensation and small-scale structure generation in a random force driven 2D turbulence

Abstract

We consider two-dimensional flow stirred by a small-scale, white-in-time random noise in the zero viscosity limit. Numerical simulations show that, after a transient state, an inertial-range energy spectrum E(k)∝${\mathit{k}}^{\mathrm{-}\mathit{x}}$ with x=5/3±0.05 is established by the inverse cascade process. This range grows in time until a Bose condensate is formed at the largest scales in the system (k≊1). Prior to condensate formation the statistics of velocity differences are extremely close to Gaussian, and only after Bose condensation strong deviations from Gaussian statistics are detected at small scales. The structures responsible for this effect are identified.