Kraichnan-Leith-Batchelor similarity theory and two-dimensional inverse cascades

We study the scaling properties and Kraichnan Leith Batchelor (KLB) theory of forced inverse cascades in generalized two-dimensional (21)) fluids (a-turbulence models) simulated at resolution 8192(2). We consider alpha = 1 (surface quasigeostrophic flow), alpha = 2 (2D Euler flow) and alpha = 3. The forcing scale is well resolved, alpha direct cascade is present and there is no large-scale dissipation. Coherent vortices spanning a range of sizes, most larger than the forcing scale, are present for both alpha= 1 and ce =2. The active scalar field for alpha=3 contains comparatively few and small vortices. The energy spectral slopes in the inverse cascade are steeper than the KLB prediction (7 a)/3 in all three systems. Since we stop the simulations well before the cascades have reached the domain scale, vortex formation and spectral steepening are not due to condensation effects; nor are they caused by large-scale dissipation, which is absent. One- and two-point p.d.f.s, hyperflatness factors and structure functions indicate that the inverse cascades are intermittent and non-Gaussian over much of the inertial range for alpha= 1 and alpha= 2, while the alpha= 3 inverse cascade is much closer to Gaussian and non -intermittent. For alpha= 3 the steep spectrum is close to that associated with enstrophy equipartition. Continuous analysis shows approximate KLB scaling cc,' (k) k Ia =) and (k) k '13 (a = 2) in the interstitial regions between the coherent vortices. Our results demonstrate that coherent vortex formation (a = 1 and alpha= 2) and non-realizability (a = 3) cause 21) inverse cascades to deviate from the KI.B predictions, but that the flow between the vortices exhibits KLB scaling and non-intermittent statistics for alpha= 1 and alpha= 2.