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Vamsi K. Chalamalla and Sutanu Sarkar

Abstract

Direct numerical simulation (DNS) and large-eddy simulation (LES) are employed to study the mixing brought about by convective overturns in a stratified, oscillatory bottom layer underneath internal tides. The phasing of turbulence, the onset and breakdown of convective overturns, and the pathway to irreversible mixing are quantified. Mixing efficiency shows a systematic dependence on tidal phase, and during the breakdown of large convective overturns it is approximately 0.6, a value that is substantially larger than the commonly assumed value of 0.2 used for calculating scalar mixing from the turbulent dissipation rate. Diapycnal diffusivity is calculated using the irreversible diapycnal flux and, for tall overturns of O(50) m, the diffusivity is found to be almost 1000 times higher than the molecular diffusivity. The Thorpe (overturn) length scale is often used as a proxy for the Ozmidov length scale and thus infers the turbulent dissipation rate from overturns. The accuracy of overturn-based estimates of the dissipation rate is assessed for this flow. The Ozmidov length scale L O and Thorpe length scale L T are found to behave differently during a tidal cycle: L T decreases during the convective instability, while L O increases; there is a significant phase lag between the maxima of L T and L O; and finally L T is not linearly related to L O. Thus, the Thorpe-inferred dissipation rates are quite different from the actual values. Interestingly, the ratio of their cycle-averaged values is found to be O(1), a result explained on the basis of available potential energy.

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Masoud Jalali, Vamsi K. Chalamalla, and Sutanu Sarkar

Abstract

Evidence in support of overturn-based methods, often used to infer turbulent dissipation rate from density profiles, is typically from regions with weaker turbulence than that at rough-topography hotspots. The present work uses direct numerical simulations (DNS) of an idealized problem of sloping topography as well as high-resolution large-eddy simulation (LES) of turbulent flow at more realistic topography in order to investigate the accuracy of overturn-based methods in sites with internal wave breaking. Two methods are assessed: Thorpe sorting, where the overturn length L T is based on local distortion of measured density from the background, and inversion sorting, where the inversion length scale L I measures the statically unstable local region. The overturn boundaries are different between the two methods. Thorpe sorting leads to an order of magnitude overestimate of the turbulent dissipation in the DNS during large convective overturn events when inversion sorting is more accurate. The LES of steep, realistic topography leads to a similar conclusion of a substantial overestimate of dissipation by Thorpe sorting. Energy arguments explain the better performance of inversion sorting in convectively driven turbulence and the better performance of Thorpe sorting in shear-driven turbulence.

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