The dynamical role of vortices in the two-dimensional inverse cascade of turbulence

Abstract

We study the inverse energy cascade of two-dimensional turbulence by means of high-resolution numerical simulations forced at intermediate wavenumbers. To clarify the role of vortices generated near the forcing scale, we decompose the vorticity and velocity fields into vortex and background components. Although the vortex component carries only a small fraction of the total energy, it has a clear effect on the energy spectrum and produces deviations from dimensional Kolmogorov scaling, which is realized by the background flow. We derive a generalized von Karman--Howarth balance for the decomposed fields and obtain a relation involving the third-order correlation between vortex and background velocity increments. The simulations support this prediction, which we interpret as a constant inertial-range flux associated with vortex-background correlations.