Turbulence of Capillary Waves on Shallow Water

We consider the developed turbulence of capillary waves on shallow water. Analytic theory shows that an isotropic cascade spectrum is unstable with respect to small angular perturbations, in particular, spontaneous breakdown reflection symmetry and generation nonzero momentum. By computer modeling we show indeed a random pumping, generating average zero momentum, produces total A strongly anisotropic large-scale pumping whose degree anisotropy decreases along cascade. It tends saturation inertial interval then further dissipation interval. Surprisingly, neither direction momentum nor compensated locked by our square box preferred directions (side or diagonal) but fluctuate.