July 2, 2018

Atmosphere and ocean flows present us with a complicated jigsaw puzzle of energetic motions on many scales, ranging from slow planetary waves on scales of 10,000 kilometers or so all the way down to small-scale three-dimensional turbulence, where dissipation of kinetic energy might take place on a scale of just a few millimeters.  All of these motions are nonlinearly coupled to each other, and understanding the smallest scales is crucial for predicting the largest scales.    In this connection recent progress has been made at CAOS by Jin-Han Xie and Oliver Bühler, who extended some of the classical turbulence theory of Kolmogorov, which was developed in the 1940s.  A first result of this extension is described in this paper, which is currently in press with the Journal of Fluid Mechanics.   Work is currently underway to extend these results to the rotating and stratified flows that are typical of atmosphere and ocean fluid dynamics.