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  • Author or Editor: Sutanu Sarkar x
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Hieu T. Pham and Sutanu Sarkar

Abstract

Large-eddy simulations are performed to investigate the development of the ageostrophic secondary circulation (ASC) and associated transport in a submesoscale front. Based on the observations in the northern Bay of Bengal and in the Pacific cold tongue, the model front has a large cross-front density difference that is partially compensated with lateral temperature and salinity gradients. Vertical stratification is varied in different cases to explore its effect on the ASC. The evolution of the ASC differs with stratification. When the front is unstratified, shear instabilities, which develop from the geostrophic shear, cause the front to slump. Cold water from the light side propagates across the front on the surface, while warm water from the dense side spreads in the opposite direction at depth. In cases with stratifications, a shear layer driven by the cross-front pressure gradient forms at the surface to initiate the ASC. Shear-driven turbulence associated with the enhanced shear in the layer causes the front to slump, and the development of the ASC onward is similar to the unstratified case. Irrespective of the initial stratification of the strong fronts simulated here, the surface layer evolves into a gravity current. The ASC is composed of the surface gravity current and a countercurrent that are separated by a middle layer with enhanced stratification and a thermal inversion. Turbulent dissipation is enhanced at the nose of the gravity current and in a sheared region somewhat behind the leading edge of the countercurrent. The gravity current propagates at a speed proportional to the buoyancy difference across the front in the case with no stratification.

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John R. Taylor and Sutanu Sarkar

Abstract

A stratified bottom Ekman layer over a nonsloping, rough surface is studied using a three-dimensional unsteady large eddy simulation to examine the effects of an outer layer stratification on the boundary layer structure. When the flow field is initialized with a linear temperature profile, a three-layer structure develops with a mixed layer near the wall separated from a uniformly stratified outer layer by a pycnocline. With the free-stream velocity fixed, the wall stress increases slightly with the imposed stratification, but the primary role of stratification is to limit the boundary layer height. Ekman transport is generally confined to the mixed layer, which leads to larger cross-stream velocities and a larger surface veering angle when the flow is stratified. The rate of turning in the mixed layer is nearly independent of stratification, so that when stratification is large and the boundary layer thickness is reduced, the rate of veering in the pycnocline becomes very large. In the pycnocline, the mean shear is larger than observed in an unstratified boundary layer, which is explained using a buoyancy length scale, u */N(z). This length scale leads to an explicit buoyancy-related modification to the log law for the mean velocity profile. A new method for deducing the wall stress based on observed mean velocity and density profiles is proposed and shows significant improvement compared to the standard profile method. A streamwise jet is observed near the center of the pycnocline, and the shear at the top of the jet leads to local shear instabilities and enhanced mixing in that region, despite the fact that the Richardson number formed using the mean density and shear profiles is larger than unity.

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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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Vicky Verma, Hieu T. Pham, and Sutanu Sarkar

Abstract

The interaction between upper-ocean submesoscale fronts evolving with coherent features, such as vortex filaments and eddies, and convective turbulence generated by surface cooling of varying magnitude is investigated. Here, we decompose the flow into finescale (FS) and submesoscale (SMS) fields explicitly to investigate the energy pathways and the strong interaction between them. Most of the surface cooling flux is transferred to the FS kinetic energy through the FS buoyancy flux carried by the convective plumes. Overall, the SMS strengthens due to surface cooling. The frontogenetic tendency at the submesoscale increases, which counters the enhanced horizontal diffusion by convection-induced turbulence. Downwelling/upwelling strengthens, and the peak SMS vertical buoyancy flux increases as surface cooling is increased. Furthermore, the production of FS energy by SMS velocity gradients (the interscale transfer term, which mediates forward energy cascade) is significant, up to half of the production by convection. Examination of potential vorticity reveals that surface cooling promotes higher levels of secondary symmetric instability (SI), which coexists with the persistent baroclinic instability. The forward interscale transfer is found to increase in the regions with SI.

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Pranav Puthan, Geno Pawlak, and Sutanu Sarkar

Abstract

Large-eddy simulations (LES) are employed to investigate the role of time-varying currents on the form drag and vortex dynamics of submerged 3D topography in a stratified rotating environment. The current is of the form Uc + Utsin(2πftt), where Uc is the mean, Ut is the tidal component, and ft is its frequency. A conical obstacle is considered in the regime of low Froude number. When tides are absent, eddies are shed at the natural shedding frequency fs , c. The relative frequency f*=fs,c/ft is varied in a parametric study, which reveals states of high time-averaged form drag coefficient. There is a twofold amplification of the form drag coefficient relative to the no-tide (Ut = 0) case when f* lies between 0.5 and 1. The spatial organization of the near-wake vortices in the high drag states is different from a Kármán vortex street. For instance, the vortex shedding from the obstacle is symmetric when f*=5/12 and strongly asymmetric when f*=5/6. The increase in form drag with increasing f* stems from bottom intensification of the pressure in the obstacle lee which we link to changes in flow separation and near-wake vortices.

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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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Hieu T. Pham, Sutanu Sarkar, and Kraig B. Winters

Abstract

Direct numerical simulation (DNS) is used to investigate the role of shear instabilities in turbulent mixing in a model of the upper Equatorial Undercurrent (EUC). The background flow consists of a westward-moving surface mixed layer above a stably stratified EUC flowing to the east. An important characteristic of the eastward current is that the gradient Richardson number Rig is larger than ¼. Nevertheless, the overall flow is unstable and DNS is used to investigate the generation of intermittent bursts of turbulent motions within the EUC region where Rig > ¼. In this model, an asymmetric Holmboe instability emerges at the base of the mixed layer, moves at the speed of the local velocity, and ejects wisps of fluid from the EUC upward. At the crests of the Holmboe waves, secondary Kelvin–Helmholtz instabilities develop, leading to three-dimensional turbulent motions. Vortices formed by the Kelvin–Helmholtz instability are occasionally ejected downward and stretched by the EUC into a horseshoe configuration creating intermittent bursts of turbulence at depth. Vertically coherent oscillations, with wavelength and frequency matching those of the Holmboe waves, propagate horizontally in the EUC where the turbulent mixing by the horseshoe vortices occurs. The oscillations are able to transport momentum and energy from the mixed layer downward into the EUC. They do not overturn the isopycnals, however, and, though correlated in space and time with the turbulent bursts, are not directly responsible for their generation. These wavelike features and intermittent turbulent bursts are qualitatively similar to the near-N oscillations and the deep-cycle turbulence observed at the upper flank of the Pacific Equatorial Undercurrent.

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Hieu T. Pham, Sutanu Sarkar, and Kraig B. Winters

Abstract

Dynamical processes leading to deep-cycle turbulence in the Equatorial Undercurrent (EUC) are investigated using a high-resolution large-eddy simulation (LES) model. Components of the model include a background flow similar to the observed EUC, a steady westward wind stress, and a diurnal surface buoyancy flux. An LES of a 3-night period shows the presence of narrowband isopycnal oscillations near the local buoyancy frequency N as well as nightly bursts of deep-cycle turbulence at depths well below the surface mixed layer, the two phenomena that have been widely noted in observations. The deep cycle of turbulence is initiated when the surface heating in the evening relaxes, allowing a region with enhanced shear and a gradient Richardson number Rig less than 0.2 to form below the surface mixed layer. The region with enhanced shear moves downward into the EUC and is accompanied by shear instabilities and bursts of turbulence. The dissipation rate during the turbulence bursts is elevated by up to three orders of magnitude. Each burst is preceded by westward-propagating oscillations having a frequency of 0.004–0.005 Hz and a wavelength of 314–960 m. The Rig that was marginally stable in this region decreases to less than 0.2 prior to the bursts. A downward turbulent flux of momentum increases the shear at depth and reduces Rig. Evolution of the deep-cycle turbulence includes Kelvin–Helmholtz-like billows as well as vortices that penetrate downward and are stretched by the EUC shear.

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Hieu T. Pham, William D. Smyth, Sutanu Sarkar, and James N. Moum

Abstract

The seasonal cycles of the various oceanic and atmospheric factors influencing the deep cycle of turbulence in the eastern Pacific cold tongue are explored. Moored observations at 140°W have shown seasonal variability in the stratification, velocity shear, and turbulence above the Pacific Equatorial Undercurrent (EUC). In boreal spring, the thermocline and EUC shoal and turbulence decreases. Marginal instability (clustering of the local gradient Richardson number around the critical value of 1/4), evident throughout the rest of the year, has not been detected during spring. While the daily averaged turbulent energy dissipation in the EUC is weakest during the spring, it is not clear whether the diurnal fluctuations that define the deep cycle cease. Large-eddy simulations are performed using climatological initial and boundary conditions representative of January, April, July, and October. Deep cycle turbulence is evident in all cases; the mechanism remains the same, and the maximum turbulence levels are similar. In the April simulation, however, the deep cycle is confined to the uppermost ~30 m, explaining why it has not been detected in moored microstructure observations.

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