CONDENSATE TURBULENCE IN 2 DIMENSIONS

The nonlinear Schrodinger equation with repulsion (also called the Gro ss-Pitaevsky equation) is solved numerically with damping at small sca les and pumping at intermediate scales and without any large-scale dam ping. Inverse cascade creating a wave condensate is studied. At modera te pumping, it is shown that the evolution comprises three stages: (i) short period (few nonlinear times) of setting the distribution of flu ctuations with the flux of waves towards large scales, (ii) long inter mediate period of self-saturated condensation with the rate of condens ate growth being inversely proportional to the condensate amplitude, t he number of waves growing as root t, the total energy linearly increa sing with time and the level of over-condensate fluctuations going dow n as 1/root t, and (iii) final stage with a constant level of over-con densate fluctuations and with the condensate linearly growing with tim e. Most of the waves are in the condensate. The flatness initially inc reases and then goes down as the over-condensate fluctuations are supp ressed. At the final stage, the second structure function [\psi(1)-psi (2)\(2)]proportional to lnr(12) while the fourth and sixth functions a re close to their Gaussian values. Spontaneous symmetry breaking is ob served: turbulence is much more anisotropic at large scales than at pu mping scales. Another scenario may take place for a very strong pumpin g: the condensate contains 25-30 % of the total number of waves, the h armonics with small wave numbers grow as well.