Nonlinear Processes in Oceanic and Atmospheric Flows

Presentation

Energy injection and the inverse cascade of body-forced, two-dimensional turbulence

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

Names and affiliation of other authors:

Oral or poster: Oral presentation

Downloadable talk file:

Energy injection and the inverse cascade of body-forced, two-dimensional turbulence

(WRY_2DTurb.pdf, 4479496 bytes)

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.

*Satellite images from NASA and ESA

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