Mixing, Dissipation Rate, and Their Overturn-Based Estimates in a Near-Bottom Turbulent Flow Driven by Internal Tides

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 LO and Thorpe length scale LT are found to behave differently during a tidal cycle: LT decreases during the convective instability, while LO increases; there is a significant phase lag between the maxima of LT and LO; and finally LT is not linearly related to LO. 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.

Observations of Small-Scale Secondary Instabilities during the Shoaling of Internal Bores on a Deep-Ocean Slope

“…This is because convection is known for being a much more efficient mixing mechanism than shear-driven turbulence: for pure RayleighTaylor convection G ' 1 (Dalziel et al 2008;Gayen et al 2013). In other recent numerical work on large convective overturning events, that is, cases that have some resemblance to that presented here, Chalamalla and Sarkar (2015) found G 2 [0.67, 1], which is also close to the mixing efficiency of pure convection. For breaking waves such as those observed here, small-scale convectivelike structures occur because of potential energy anomalies (density inversions) created during the overturning motions.…”

“…Very recently, the link between R OT and the evolution of turbulence was also explored for convective instabilities (Chalamalla and Sarkar 2015;Mater et al 2015). Again, the authors found larger R OT for younger turbulence (more potential energy) but also concluded that on average hR OT i ; O(1), where hi represent some carefully chosen ensemble average.…”

Biases in Thorpe-Scale Estimates of Turbulence Dissipation. Part I: Assessments from Large-Scale Overturns in Oceanographic Data

“…Additional campaigns tracking billows like those generated at IWISE L are needed to separate sampling biases from physically based biases that may exist. Such campaigns should also consider the influence that boundary length scales have on the scaling-an important physical bias in topographically influenced overturning not explicitly investigated here (see, e.g., Chalamalla and Sarkar 2015). Interestingly, and despite fewer profiles, the bias is not as apparent at the IWISE N2 site that shows excellent agreement in the lower 500 m-a finding we suggest may be related to strong bottom shear and local dissipation.…”

Convection Enhances Mixing in the Southern Ocean

“…Higher mixing efficiencies occur in stratified flows with the presence of turbulent convection. Mixing efficiencies of 0.75 in the case of Rayleigh‐Taylor instability (Davies Wykes & Dalziel, ), 0.5 in the case of Rayleigh‐Bénard convection (Gayen, Hughes, & Griffiths, ; Hughes et al, ), 0.6 in the case of convectively driven instability due to internal waves (Chalamalla & Sarkar, ), and approaching 1 in the case of horizontal convection (Gayen, Griffiths, et al, ; Gayen et al, ; Vreugdenhil et al, ) have been found. In addition, the presence of rough topography could enhance mixing efficiency in the abyssal ocean (Mashayek et al, ).…”