Eddy stress and shear in 2-D flow

Abstract

Upscale transfers of energy and momentum in quasi-2-D flows are seen in atmosphere, oceans and numerical experiments. Mechanisms that drive upscale transfer have been described in terms of sheared vortices becoming tilted and thinned, losing energy and developing eddy stresses which force, rather than resist, mean flow. Some of these concepts are mistaken. If initially isotropic eddy vorticity is passively advected in uniform shear, no eddy stress develops and there is no loss of eddy energy. When active vorticity self-advection is included, stresses arise yielding downgradient momentum transfer – just the opposite of what was hitherto expected.

Keywords:

• eddy
• stress
• shear

Acknowledgements

I am grateful to George Carnevale, Patrick Cummins, Greg Eyink, Jackson Herring, Rick Salmon, Ted Shepherd, Sadayoshi Toh and Bill Young for discussions. Dimitris Menemenlis and his family kindly suggested ‘platymorph’.