Hieu Pham

Dynamics of a stratified shear layer above a region of uniform stratification

Direct numerical simulations (DNS) are performed to investigate the behaviour of a weakly stratified shear layer in the presence of a strongly stratified region beneath it. Both, coherent Kelvin―Helmholtz (KH) rollers and small-scale turbulence, are observed during the evolution of the shear layer. The deep stratification measured by the Richardson number J d is varied to study its effect on the dynamics. In all cases, a pycnocline is found to develop at the edges of the shear layer. The region of maximum shear shifts downward with increasing time. Internal waves are excited, initially by KH rollers, and later by small-scale turbulence. The wave field generated by the KH rollers is narrowband and of stronger amplitude than the broadband wave field generated by turbulence. Linear theory based on Doppler-shifted frequency of the KH mode is able to predict the angle of the internal wave phase lines during the direct generation of internal waves by KH rollers. Waves generated by turbulence are relatively weaker with a broader range of excitation angles which, in the deep region, tend towards a narrower band. The linear theory that works for the internal waves excited by KH rollers does not work for the turbulence generated waves. The momentum transported by the internal waves into the interior can be large, about 10 % of the initial momentum in the shear layer, when J d ≃ 0.25. Integration of the turbulent kinetic energy budget in time and over the shear layer thickness shows that the energy flux can be up to 17 % of the turbulent production, 33 % of the turbulent dissipation rate and 75 % of the buoyancy flux. These numbers quantify the dynamical importance of internal waves. In contrast to linear theory where the effect of deep stratification on the shear layer instabilities has been found to be weak, the present nonlinear simulations show that the evolution of the shear layer is significantly altered because of the significant momentum and energy carried away by the internal waves.

Internal waves and turbulence in a stable stratified jet

Direct numerical simulations are performed to investigate the interaction between a stably stratified jet and internal gravity waves from an adjacent shear layer with mild stratification. Results from two simulations are presented: one with the jet located far from the shear layer (far jet) and the other with the shear layer right on top of the jet (near jet). The near jet problem is motivated by velocity and stratification profiles observed in equatorial undercurrents. In the far case, internal waves excited by the Kelvin–Helmholtz (K-H) rollers do not penetrate the jet. They are reflected and trapped in the region between the shear layer and the jet and lead to little dissipation. In the near case, internal waves with wavelength larger than that of the K-H rollers are found in and below the jet. Pockets of hot fluid, associated with horseshoe vortices that originate from the shear layer, penetrate into the jet region, initiate turbulence and disrupt the internal wave field. Coherent patches of enhanced dissipation moving with the mean velocity are observed. The dissipation in the stably stratified near jet is large, up to three orders of magnitude stronger than that in the propagating wave field or the jet of the far case.

Large-Eddy Simulation of Deep-Cycle Turbulence in an Equatorial Undercurrent Model

AbstractDynamical 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 thr...

Large Eddy Simulations of a Stratified Shear Layer

The performance of the large eddy simulation (LES) approach in predicting the evolution of a shear layer in the presence of stratification is evaluated. The LES uses a dynamic procedure to compute subgrid model coefficients based on filtered velocity and density fields. Two simulations at different Reynolds numbers are simulated on the same computational grid. The fine LES simulated at a low Reynolds number produces excellent agreement with direct numerical simulations (DNS): the linear evolution of momentum thickness and bulk Richardson number followed by an asymptotic approach to constant values is correctly represented and the evolution of the integrated turbulent kinetic energy budget is well captured. The model coefficients computed from the velocity and the density fields are similar and have a value in range of 0:01 0:02. The coarse LES simulated at a higher Reynolds number Re1⁄4 50,000 shows acceptable results in terms of the bulk characteristics of the shear layer, such as momentum thickness and bulk Richardson number. Analysis of the turbulent budgets shows that, while the subgrid stress is able to remove sufficient energy from the resolved velocity fields, the subgrid scalar flux and thereby the subgrid scalar dissipation are underestimated by the model. [DOI: 10.1115/1.4026416]

Transport and mixing of density in a continuously stratified shear layer

Scalar transport and mixing by active turbulence in a high Reynolds number inhomogeneous stratified shear layer are investigated using three-dimensional Direct Numerical Simulation. Two density profiles are considered: (i) two layers of homogenous fluid with different density, namely the two-layer case, and (ii) a continuously stratified background ambient, namely the Jd case. The evolution of the mixing layer includes shear instability, formation of Kelvin–Helmholtz rollers, transition to turbulence, fully developed active turbulence, and, finally, decay toward a laminar state. In the Jd case, internal gravity waves carrying momentum and energy are observed to propagate away from the shear layer. Although different during the initial evolution, the eddy diffusivity and mixing efficiency when plotted as a function of buoyancy, Reynolds number takes similar values between the two cases later in time during the stage when turbulence decays. During this stage, the mixing efficiency computed based on the buoy...

ASIRI : an ocean–atmosphere initiative for Bay of Bengal

AbstractAir–Sea Interactions in the Northern Indian Ocean (ASIRI) is an international research effort (2013–17) aimed at understanding and quantifying coupled atmosphere–ocean dynamics of the Bay of Bengal (BoB) with relevance to Indian Ocean monsoons. Working collaboratively, more than 20 research institutions are acquiring field observations coupled with operational and high-resolution models to address scientific issues that have stymied the monsoon predictability. ASIRI combines new and mature observational technologies to resolve submesoscale to regional-scale currents and hydrophysical fields. These data reveal BoB’s sharp frontal features, submesoscale variability, low-salinity lenses and filaments, and shallow mixed layers, with relatively weak turbulent mixing. Observed physical features include energetic high-frequency internal waves in the southern BoB, energetic mesoscale and submesoscale features including an intrathermocline eddy in the central BoB, and a high-resolution view of the exchange...

Near-N Oscillations and Deep-Cycle Turbulence in an Upper-Equatorial Undercurrent Model

AbstractDirect 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 conf...

Evolution of an asymmetric turbulent shear layer in a thermocline

Large eddy simulations are used to examine the evolution of a shear layer in a thermocline with non-uniform density stratification. Unlike previous studies, the density in the present study is continuously stratified and has stratification in the upper half different from the lower half of the shear layer. The stratification in the upper half is fixed at Ju = 0.05, while the stratification in the lower half is increased to Jd = 0.05, 0.15, 0.25 and 0.35, leading to a progressively stronger asymmetry of the Rig profile in the four cases. Here, J is the bulk Richardson number and Rig is the gradient Richardson number. The type of shear instability and the properties of the ensuing turbulence are found to depend strongly on the degree of asymmetry in stratification. The shear instability changes from a Kelvin–Helmholtz (KH) mode at Jd = 0.05 to a Holmboe (H) mode at Jd = 0.35 and exhibits characteristics of both KH and H modes at intermediate values of Jd. Differences in the evolution among the cases are quantified using density visualisations and statistics such as mean shear, mean stratification and turbulent kinetic energy.

Ageostrophic Secondary Circulation at a Submesoscale Front and the Formation of Gravity Currents

AbstractLarge-eddy simulations are performed to investigate the development of the ageostrophic secondary circulation (ASC) and associated transport in a submesoscale front. Based on the observatio...

Seasonality of Deep Cycle Turbulence in the Eastern Equatorial Pacific

AbstractThe 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 leve...