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We demonstrate via direct numerical simulations that a periodic, oscillatingmean flow spontaneously develops from turbulently generated internal waves. Weconsider a minimal physical model where the fluid self-organizes in aconvective layer adjacent to a stably stratified one. Internal waves areexcited by turbulent convective motions, then nonlinearly interact to produce amean flow reversing on timescales much longer than the waves' period. Ourresults demonstrate for the first time that the three-scale dynamics due toconvection, waves, and mean flow is generic and hence can occur in manyastrophysical and geophysical fluids. We discuss efforts to reproduce the meanflow in reduced models, where the turbulence is bypassed. We demonstrate thatwave intermittency, resulting from the chaotic nature of convection, plays akey role in the mean-flow dynamics, which thus cannot be captured using onlysecond-order statistics of the turbulent motions.

Order Out of Chaos: Slowly Reversing Mean Flows Emerge from Turbulently Generated Internal Waves