Forced-dissipative two-dimensional turbulence: A scaling regime controlled by drag

We consider two-dimensional turbulence driven by a steady prescribed sinusoidal body force working at an average rate epsilon. Energy dissipation is due mainly to drag, which damps all wave number at a rate mu. Simulations at statistical equilibrium reveal a scaling regime in which epsilon proportional to mu(1/3), with no significant dependence of epsilon on hyperviscosity, domain size, or numerical resolution. This power-law scaling is explained by a crude closure argument that identifies advection by the energetic large-scale eddies as the crucial process that limits epsilon by disrupting the phase relation between the body force and fluid velocity. The average input epsilon is due mainly to spatial regions in which the large-scale velocity is much less than the root-mean-square velocity. We argue that epsilon proportional to mu(1/3) characterizes energy injection by a steady or slowly changing spectrally confined body force.