Fig. 1.

Snapshot of the 2D vorticity field $\zeta ={\partial }_x{v}_y-{\partial }_y{v}_x$ right after the onset of the turbulent regime as obtained from a numerical solution of Eq. 1, using a pseudospectral code. The computation has been performed with 1,024 (effective) points in each direction under the constraint of periodic boundary conditions. The Ekman parameter equals $\alpha \tau =-1$, implying that there are two energy sources acting at large scales—the two positive terms in the expression for $\gamma \left(k\right)$. The strength of the cubic nonlinearity is set to $\beta \tau v_0=0.5$ and for the advective term we have used ${\lambda }_0=3.5$. One can clearly see the highly disordered distribution of vortices justifying the classification of the regime as turbulent.