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With the aim of assessing internal wave-driven mixing in the ocean, we develop a new technique for numerical simulations of stratified turbulence. Since the spatial scales of energetic ocean currents and internal gravity waves are typically much larger than that of turbulence, fully incorporating both in a model would require a high computational cost and is therefore out of our scope. Alternatively, we cut out a small domain periodically distorted by an unresolved large-scale flow field and locally simulate the energy cascade to the smallest scales. This technique enables us to concentrate the computational resources on resolving the breaking process of small-scale waves and the resulting turbulence while properly incorporating energy supply from large-scale flow components. This time, we demonstrate the results of two typical problems: the parametric subharmonic instability (PSI) of a plane internal gravity wave and the ageostrophic anticyclonic instability (AAI) of an elliptic vorte...

In turbulent convection, a complex nonlinear problem, quantification of heat transport remains a challenge. Two competing theories for extreme turbulence or large Raleigh number (Ra) are (a) classical 1/3 scaling where the heat transport is proportional to Ra^{1/3}, and (b) ultimate ½ scaling where heat transport is proportional to Ra^{1/2}. We simulate compressible turbulent convection up to Ra = 10^{18}, which is the highest Ra achieved so far, and show agreement with the classical 1/3 scaling. We also show that the Reynolds number scales as Ra^{1/2}. Our work is a major step towards the resolution of heat transport in turbulent convection.