**Author**: William R. Young, Scripps Institution of Oceanography .

**Names and affiliation of other authors**:

**Oral or poster**: Oral presentation

**Abstract**:

I'll review theoretical and numerical work in support of the Kraichnan scenario of statistically steady

forced-dissipative two-dimensional turbulence. According to Kraichnan's hypothesis, a direct cascade of enstrophy

and an inverse cascade of energy coexist provided that dissipative drag (due, for example, to an Ekman layer) is

strong enough to halt the inverse cascade before significant energy accumulates at the domain scale. This drag

does steepen the slope of the enstrophy cascading spectrum below minus three. But the steeper slope at high

wavenumbers might be regarded as only a small modification of Kraichnan's vision. A more significant issue is

that if the turbulence is maintained by an applied body force (the most common experimental protocol) then the

cascade rate (watts per kilogram injected by the body force) is unknown a priori. So a main open problem is to

understand the dependence of the time-mean energy injection, and the strength of its unsteady fluctuations, on the

control parameters. This is important because the mean-injection rate determines the overall energy level and thus

large-scale flow properties such as eddy diffusivities. Direct numerical simulation indicates that the strength

of the drag is the most decisive parameter controlling mean injection. I'll show that variational method provide

generously small lower bound on the mean injection and discuss various "phenomenological" models of the energy

injection.

Nonlinear Processes in Oceanic and Atmospheric Flows. July 2-4, 2008. Castro Urdiales, Cantabria, Spain.