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  1. 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 U c + U t sin(2 πf t t ), where U c is the mean, U t is the tidal component, and f t 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 f s , c . The relative frequency 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 ( U t = 0) case when 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 and strongly asymmetric when . The increase in form drag with increasing stems from bottom intensification of the pressure in the obstacle lee which we link to changes in flow separation and near-wake vortices.
  2. Abstract Direct numerical simulations are performed to compare the evolution of turbulent stratified shear layers with different density gradient profiles at a high Reynolds number. The density profiles include uniform stratification, two-layer hyperbolic tangent profile and a composite of these two profiles. All profiles have the same initial bulk Richardson number ( $$Ri_{b,0}$$ R i b , 0 ); however, the minimum gradient Richardson number and the distribution of density gradient across the shear layer are varied among the cases. The objective of the study is to provide a comparative analysis of the evolution of the shear layers in term of shear layer growth, turbulent kinetic energy as well as the mixing efficiency and its parameterization. The evolution of the shear layers in all cases shows the development of Kelvin–Helmholtz billows, the transition to turbulence by secondary instabilities followed by the decay of turbulence. Comparison among the cases reveals that the amount of turbulent mixing varies with the density gradient distribution inside the shear layer. The minimum gradient Richardson number and the initial bulk Richardson number do not correlate well with the integrated TKE production, dissipation and buoyancy flux. The bulk mixing efficiency for fixed $$Ri_{b,0}$$ R i b ,more »0 is found to be highest in the case with two-layer density profile and lowest in the case with uniform stratification. However, the parameterizations of the flux coefficient based on buoyancy Reynolds number and the ratio of Ozmidov and Ellison scales show similar scaling in all cases.« less
  3. Direct numerical simulations are performed to investigate a stratified shear layer at high Reynolds number ( $Re$ ) in a study where the Richardson number ( $Ri$ ) is varied among cases. Unlike previous work on a two-layer configuration in which the shear layer resides between two layers with constant density, an unbounded fluid with uniform stratification is considered here. The evolution of the shear layer includes a primary Kelvin–Helmholtz shear instability followed by a wide range of secondary shear and convective instabilities, similar to the two-layer configuration. During transition to turbulence, the shear layers at low $Ri$ exhibit a period of thickness contraction (not observed at lower $Re$ ) when the momentum and buoyancy fluxes are counter-gradient. The behaviour in the turbulent regime is significantly different from the case with a two-layer density profile. The transition layers, which are zones with elevated shear and stratification that form at the shear-layer edges, are stronger and also able to support a significant internal wave flux. After the shear layer becomes turbulent, mixing in the transition layers is shown to be more efficient than that which develops in the centre of the shear layer. Overall, the cumulative mixing efficiency ( $E^C$ )more »is larger than the often assumed value of 1/6. Also, $E^C$ is found to be smaller than that in the two-layer configuration at moderate Ri . It is relatively less sensitive to background stratification, exhibiting little variation for $0.08 \leqslant Ri \leqslant 0.2$ . The dependence of mixing efficiency on buoyancy Reynolds number during the turbulence phase is qualitatively similar to homogeneous sheared turbulence.« less
  4. Abstract

    Large eddy simulations are employed to investigate the role of tidal modulation strength on wake vortices and dissipation in flow past three‐dimensional topography, specifically a conical abyssal hill. The barotropic current is of the formUc + Ut sin(Ωtt), whereUcandUtare the mean and oscillatory components, respectively, and Ωtis the tidal frequency. A regime with strong stratification and weak rotation is considered. The velocity ratioR = Ut/Ucis varied from 0 to 1. Simulation results show that the frequency of wake vortices reduces gradually with increasingRfrom its natural shedding frequency atR = 0 to Ωt/2 whenR ≥ 0.2. The ratio ofRand the excursion number, denoted as, controls the shift in the vortex frequency. When, vortices are trapped in the wake during tidal deceleration, extending the vortex shedding cycle to two tidal cycles. Elevated dissipation rates in the obstacle lee are observed in the lateral shear layer, hydraulic jet, and the near wake. The regions of strong dissipation are spatially intermittent, with values exceedingduring the maximum‐velocity phase, whereDis the base diameter of the hill. The maximum dissipation rate during the tidal cycle increases monotonically withRin the downstream wake. Additionally, the normalized area‐integrated dissipation rate in the hydraulic response region scales withRas (1 + R)4. Results show that themore »wake dissipation energetically dominates the internal wave flux in this class of low‐Froude number geophysical flows.

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  5. Turbulence and mixing in a near-bottom convectively driven flow are examined by numerical simulations of a model problem: a statically unstable disturbance at a slope with inclination $\unicode[STIX]{x1D6FD}$ in a stable background with buoyancy frequency $N$ . The influence of slope angle and initial disturbance amplitude are quantified in a parametric study. The flow evolution involves energy exchange between four energy reservoirs, namely the mean and turbulent components of kinetic energy (KE) and available potential energy (APE). In contrast to the zero-slope case where the mean flow is negligible, the presence of a slope leads to a current that oscillates with $\unicode[STIX]{x1D714}=N\sin \unicode[STIX]{x1D6FD}$ and qualitatively changes the subsequent evolution of the initial density disturbance. The frequency, $N\sin \unicode[STIX]{x1D6FD}$ , and the initial speed of the current are predicted using linear theory. The energy transfer in the sloping cases is dominated by an oscillatory exchange between mean APE and mean KE with a transfer to turbulence at specific phases. In all simulated cases, the positive buoyancy flux during episodes of convective instability at the zero-velocity phase is the dominant contributor to turbulent kinetic energy (TKE) although the shear production becomes increasingly important with increasing  $\unicode[STIX]{x1D6FD}$ . Energy that initially resides whollymore »in mean available potential energy is lost through conversion to turbulence and the subsequent dissipation of TKE and turbulent available potential energy. A key result is that, in contrast to the explosive loss of energy during the initial convective instability in the non-sloping case, the sloping cases exhibit a more gradual energy loss that is sustained over a long time interval. The slope-parallel oscillation introduces a new flow time scale $T=2\unicode[STIX]{x03C0}/(N\sin \unicode[STIX]{x1D6FD})$ and, consequently, the fraction of initial APE that is converted to turbulence during convective instability progressively decreases with increasing $\unicode[STIX]{x1D6FD}$ . For moderate slopes with $\unicode[STIX]{x1D6FD}<10^{\circ }$ , most of the net energy loss takes place during an initial, short ( $Nt\approx 20$ ) interval with periodic convective overturns. For steeper slopes, most of the energy loss takes place during a later, long ( $Nt>100$ ) interval when both shear and convective instability occur, and the energy loss rate is approximately constant. The mixing efficiency during the initial period dominated by convectively driven turbulence is found to be substantially higher (exceeds 0.5) than the widely used value of 0.2. The mixing efficiency at long time in the present problem of a convective overturn at a boundary varies between 0.24 and 0.3.« less
  6. Abstract

    Wake vortices in tidally modulated currents past a conical hill in a stratified fluid are investigated using large‐eddy‐simulation. The vortex shedding frequency is altered from its natural steady‐current value leading to synchronization of wake vortices with the tide. The relative frequency (f*), defined as the ratio of natural shedding frequency (fs,c) in a current without tides to the tidal frequency (ft), is varied to expose different regimes of tidal synchronization. Whenf*increases and approaches 0.25, vortex shedding at the body changes from a classical asymmetric Kármán vortex street. The wake evolves downstream to restore the Kármán vortex‐street asymmetry but the discrete spectral peak, associated with wake vortices, is found to differ from bothftandfs,c, a novel result. The spectral peak occurs at the first subharmonic of the tidal frequency when 0.5 ≤ f*< 1 and at the second subharmonic when 0.25 ≤ f*< 0.5.