# Generalized vorticity in transitional quantum turbulence - Condensed Matter > Other Condensed Matter

Abstract: Transition to condensate state in the degenerate gas of bosons is studiedusing the Gross-Pitaevskii equation. It is shown that adiabatic invariance ofan enstrophy mean squared vorticity based on a generalized vorticity $curl|\psi|^2 {\bf v}-|\psi|^2$, controls dynamics of the transitional turbulencejust before formation of the condensate with its tangles of quantized vortices$|\psi|^2 {\bf v}$ is the weighted velocity field defined on the macroscopicwave function $\psi$. Scaling of the angle-averaged occupation numberspectrum, $N k \sim k^{-1}$, has been obtained for the free developingtransitional turbulence for the weak nonlinear and completely disorderedinitial conditions. Results of the three-dimensional numerical simulations havebeen used to support the theoretical consideration.