Accuracy of Thorpe scale dissipation estimates during mixing driven by internal tide breaking

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 Thorpe (overturn) length scale is often used as a proxy for the Ozmidov length scale and thus infer turbulent dissipation rate from overturns. The accuracy of overturn-based estimates of the dissipation rate is assessed for this flow using two different methods (modified and conventional) of detecting an overturn. The modified method is based on detecting inversions through statical instability.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 phase lag ($\approx 1/N$) between the maxima of Thorpe inferred dissipation and the model dissipation. Thus, the instantaneous values of overturn-inferred dissipation rates from both Thorpe and modified overturn methods are quite different from the actual values. Interestingly, the ratio of their cycle-averaged values is found to be O(1) in the case of the modified overturn scale method, a result explained on the basis of available potential energy. On the other hand, conventional Thorpe scale method is found to overestimate the cycle averaged dissipation by one to two orders magnitude. Comparison of time series of dissipation rates show that conventional Thorpe scale method highly overestimate the dissipation during the breaking of large density overturns, however it compares well with the model dissipation during shear driven turbulence.