Divorticity and Dihelicity in Two-dimensional Hydrodynamics

The theory of two-dimensional (2D) fully developed turbulence (FDT) (Kraichnan [1], Batchelor [2]), until recently, remained almost an academic exercise, not withstanding its possible connections with large-scale flows in thin fluid shells such as atmospheres and oceans. 2D FDT has now been produced to a close approximation in a variety of laboratory experiments (Couder [3], Kellay et al. [4], Martin et al. [5], Rutgers [6], Rivera et al. [7], Vorobieff et al. [8], Rivera et al. [9], [10]) (see Clercx and van Heijst [11] for a recent review as well as references). Vorticity at very small length scales behaves like a passive scalar (Weiss [12], Falkovich and Lebedev [13], and Nam et al. [14]) and is advected by the large-scale flow structures (Legras te al. [15], Chen et al. [16]). This leads to thin sheets with large vorticity gradients (Saffman [17]). Kuznetsov et al. [18] gave qualitative arguments to support the formation