The wave-turbulence jigsaw puzzle in atmosphere and ocean fluid dynamics Oliver Bühler New York University Courant Institute of Mathematical Science Despite enormous Reynolds numbers, three-dimensional turbulence and small-scale viscous dissipation are rare and highly intermittent in the atmosphere and oceans, and usually take place only in compact isolated pockets of vigorous turbulence that are embedded in laminar flows dominated by waves and nearly two-dimensional vortices. This makes the interpretation and prediction of observed power spectra and of the net dissipation in such systems a very challenging topic both from a theoretical and numerical perspective. It also has implications for the predictability of such flows. This talk will describe the basic issues and report on recent progress on diagnostic techniques that can disentangle part of this wave-turbulence jigsaw puzzle.