Research Projects

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    Shear instabilities, internal waves and turbulent mixing in the Equatorial Undercurrents

    Hieu T. Pham

    My current research focuses on small-scale processes in the Pacific Equatorial Undercurrent (EUC). The EUC is a subsurface jet-like eastward-flowing current below a westward surface current driven by the trade wind. Vertical mixing in the EUC is believed to influence the sea surface temperature and the depth of the thermocline, and therefore, can play an important role in the predictability of an El Nino/La Nina event. There have been many observational campaigns focusing on the mixing process, and the data indicates intermittent bursts of turbulence during night time at depth well below the surfaced mixed layer, the so-called deep-cycle turbulence. The dissipation rate inside the bursts can be up to three orders of magnitude larger than the background value. Observational data further indicates that the deep-cycle turbulence is accompanied with the near-N oscillations in the isotherms. A strong correlation between the two phenomena infers that the deep-cycle turbulence results from the breakdown of the oscillations; however, the origin of the oscillations is still debatable among oceanographers. There are two main hypotheses: (1) the oscillations are internal waves that are generated at the base of the mixed layer and propagate downward, or (2) they are signatures of a shear instability local to the EUC.

    Our research objective is to understand the mixing processes in which the oscillations lead to the deep-cycle turbulence under different background scenarios. We use numerical models such as DNS and LES to simulate various flow conditions. In one model, we observe a Holmboe shear instability emerges at the base of the surface mixed layer. The growth of the Holmboe instability causes near-N oscillations in the isopycnals in the EUC. Kelvin-Helmholtz billows, formed on the crests of the Holmboe instability, break down and generate significant turbulent mixing. In many occasions, vortices associated with the billows are ejected downward, stretched into horseshoe vortices by the EUC shear, and subsequently create intermittent patches of turbulence in the EUC. Our model results qualitatively agree with recent observational data collected in 2008.


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    Density profile showing the Holmboe instability.
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    Comparison of our computational model with data from Moum et al., JPO (2011).
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    Internal wave field during a tidal flow over a sloping topography

    Bishakhdatta Gayen.

    The objective of the present study, based on four phases, is to employ DNS and LES to further understand and quantify the dynamical processes underlying turbulenceduring the generation of an internal wave beam and its subsequent interaction with arealistically-stratified upper ocean. In the first phase, a study of a stratified non-sloping bottom boundary layer under an oscillating tide has been completed and published by Gayen et al. JFM (2010). Here, we observed that stratification decreases phase lag with respect to free stream velocity for various boundary layer properties over the course of the cycle. Turbulence generated internal waves are observed to propagate external to boundary layer. Phase angle of IW changes over tidal cycle. The frequency spectrum of the propagating wave is found to span a narrow band of frequencies corresponding to clustering around 45o.

    In second phase, three-dimensional DNS has been performed of generation by a laboratory-scale slope in the regime of excursion number, Ex ≪ 1, and criticality, e ≃ 1, that shows transition to turbulence. The transition is found to be initiated by a convective instability which is closely followed by shear instability. Turbulence is present along the entire extent of the near-critical region of the slope. The wave energy exhibits a temporal cascade to higher harmonics, subharmonics and inter harmonics. Recently, this work has been published in Gayen & Sarkar, Phys. Rev. Lett.(2010). The work of Gayen & Sarkar, JFM (2011) extends the previous work by examining internal wave energetics as well as the energetics of turbulence in the bottom boundary layer.The peak value of the near-bottom velocity is found to increase with increasing length of the critical region of the topography. The scaling law that is observed to link the near-bottom peak velocity to slope length is explained by an analytical boundary layer solution that incorporates an empirically obtained turbulent viscosity. The slope length is also found to have a strong impact on quantities such as the wave energy flux, turbulent production and turbulent dissipation. These sets of numerical experiments that explain and characterize turbulence during the generation of internal waves from tide-topography interaction at near-critical environment constitute the second phase of work.

    Our main goal in the third phase is to scale up the computational domain which has been used in second phase, from O(10)m to O(1) km in order to reproduce the large scale overturns observed in the ocean and compare the wave energetics, turbulent statistics etc. with the available measured data. Here, we have taken a beam of 60 m width and amplitude of 0.125 m/s to study the mixing dynamics over a sloping topography under near critical environment. Large value of tke as well as large values of of positive buoyancy flux at elevated level is observed during the flow reversal from downslope to upslope motion (Ref. Gayen & Sarkar, Geophys. Res. Lett. (2011))

    The objective of the forth phase is to understand the interaction process between internal tidal beam and realistic upper ocean stratification and to characterize the role turbulence.

    Pase I: Turbulence and internal waves at non-sloping bottom under an oscillating tide

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    Slice of ∂w/∂z in the x–z plane for the case with Ri=500 at different tidal phases: (a) φ =−5, (b) φ =90 and (c) φ =180. Each part is divided into three panels: top panel shows the waves in the far-field, z=35−86; middle panel shows the turbulent source and near-field waves; bottom panel shows the streamwise velocity profile with black and light grey indicating positive and negative signs of the velocity relative to the free steam. The O symbols on the velocity profiles show the location of ∂θ(z, t )/∂z=0.1 to demarcate the mixed layer.

    Pase II: Turbulence and internal waves at sloping bottom under an oscillating tide

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    Internal wave field visualized by a slice of dw/dz field in x-z plane.

    Pase III: Boundary mixing by density overturns in an internal tidal beam

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    Bottom panel shows vertical x-z slice of the density field (after subtracting 1000 kg m −3) at 4 different times (phases) in a tidal cycle. Top panel shows spanwise-averaged streamwise velocities, u(z, t) m/s and density profiles, ρ(z, t, x = 0) at corresponding phases. Background linear density (dashed blue line) profile is also shown. Note that u, x are horizontal while z is vertical. Parts (a) and (e) correspond to maximum downward boundary flow, parts (b) and (f) correspond to flow reversal from down to up, parts (c) and (g) correspond to peak up-slope velocity and, finally, parts (d) and (e) correspond to flow reversal from up to down. The four different times are indicated by the four red color circles in Figure 4a that follows. Here, arrows are pointing the ow structures.

    Pase IV: Interaction of IW beam with pycnocline and turbulence

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    Preliminary results show an upward wave beam incident on realistic upper ocean stratification (buoyancy frequency profile is the green curve on the left). The phase of the barotropic tidal currents (white sine curve) is shown by the red dot. This figure is taken from ongoing work performed by Gayen and Sarkar.
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    The turbulent wake behind a bluff body in a stratified fluid

    Anikesh Pal, Karu Chongsiripinyo, and Alexandra Vandine

    While the turbulent wake behind a moving body is a fundamental problem in turbulence and has been studied for hundreds of years, even the wake behind relatively simple shapes such as spheres still lacks a complete description. The reason for this is that the wake is highy nonlinear which makes it difficult to study analytically. The presence of a density gradient significantly complicates matters as it destroys the symmetry of the problem and introduces a complex coupling between kinetic and potential energy.

    For studying the wake behind a bluff body there are two configurations that are commonly used: a towed body and a self-propelled body. The wake profiles for the two configurations are qualitatively different. The wake of a towed body consists solely of a drag lobe whereas the wake of a self-propelled body consists of both a drag lobel and a thrust lobe. For a self-propelled body moving at constant speed, the drag and thrust balance which produces a wake with zero net momentum. If a self-propelled body is accelerating then it will have a wake with excess momentum. The presence of a density gradient disrupts the balance of momentum in the wake of a self-propelled body moving at constant speed by inhibiting motion in the vertical direction and allowing the presence of internal gravity waves which carry energy away from the wake to the surroundings.

    All stratified turbulent wakes follow a qualitatively similar evolution. First there is a near wake region where the wake evolves as thought it was unstratified. The next region is termed the Non-Equilibrium regime where the wake feels the effect of buoyancy. During this time the wake slowly collapses in the vertical direction and expands in the horizontal direction. The collapse generates internal gravity waves which propagate energy from the wake to the background. At late time, the Q2D regime, the flow is quasi-horizontal and decays until the wake relaminarizes. Large pancake eddies form in the Q2D regime.

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    Wake evolution in the vertical, x3, and horizontal, x2, directions. Wavy arrows show the time when wake generated internal gravity waves are significant and pancake eddies are shown in the late wake.
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    The mean velocity in the wake behind a body moving to the left. (a) Towed body. (b) Self-propelled body with zero net momentum. (c) propelled body with excess momentum.
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    Unstratified flow past a sphere at Re = 3700. Picture shows isosurface of vortical structure captured by Q-criterion at Q = 1. Vortical structures appear to be tube-like, so called "vortex tube".
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    Barotropic instability in the submesoscale regime

    Eric Arobone

    Isolated horizontal shear is a feature of boundary currents, flow near river deltas, and wakes of topographical features. The picture below shows a shear layer resulting from separation of a boundary current. Mixing and transport induced by vertical shear in a stably stratified fluid has been explored far more extensively than that case of horizontal shear. We are interested in the effects of stratification strength and rotation rate on flow dynamics. When stratification is strong, vertical gradients can dominate the flow and new instability mechanisms such as the zigzag instability emerge. The zigzag instability is shown below along with a vortex taken from a simulation of a stratified horizontal shear layer. The effects of rotation are non-negligible when length scales are of order 1 kilometer. Rotation can either stabilize or destabilize a flow field, depending on rotation rate and orientation.

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    Horizontal shear layer in a river.
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    Zigzag instability. (left image) Experiment. (right image) Simulation.
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    Baroclinic energy conversion across topographically rough straits with application to Luzon Strait

    Narsimha Rapaka

    The project is focused, via numerical experiments, on the conversion of barotropic tides into internal tides and the effect of turbulence generated near the topography on the conversion. The Navier-Stokes equations are solved using a mixed RK3-ADI time integration scheme. Immersed Boundary Method module is developed to include the effect of three dimensional rough topography on a cartesian grid. At the initial phase of the project, direct and large eddy simulations are performed to study tidal flow over a model ridge. The Navier-Stokes equations are solved in generalized coordinates using a mixed spectral-finite difference algorithm. The effect of criticality parameter on the tidal conversion is studied in the laminar flow regime. Nonlinear processes become important at critical slope of the topography even for low excursion numbers. The effect of turbulence on tidal conversion is studied under near-critical flow conditions. Physical quantities of interest include the kinetic energy, power spectra, vertical turbulence intensity and buoyancy flux.

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    Comparison between the subcritical, critical and supercritical flows at Res=30.
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    urms near the topography for critical flow at Res=30.
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    Internal wave reflection on near critical slopes

    Vamsi Chalamalla

    Direct numerical simulation is performed to study the internal gravity wave reflection on a sloping boundary, considering near critical slope angles. Our objective is to understand the role of near critical slopes in mixing near the boundaries during internal wave reflection. The wave field includes only the reflected wave, this is done by imposing velocity and density boundary conditions for the reflected wave at the sloping bottom. Two different scenarios have been considered, first by keeping slope angle constant and studying the effect of Froude number, second by keeping Froude number constant and varying the slope angle. With increasing Froude number, the reflection process becomes increasingly nonlinear with the formation of higher harmonics and subsequently fine scale turbulence. At a critical value of Froude number, turbulence is initiated via convective instability. Also, turbulent intensities are more pronounced for somewhat off-critical reflection compared to exactly critical reflection. As the Froude number increases, the near wall shear plays a dominant role in critical reflection by enhancing turbulence compared to off-critical reflection. For a fixed slope angle, as the Froude number increases the fraction of the input energy converted into the turbulent kinetic energy increases and saturates at higher Froude numbers.

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    Contour of turbulent kinetic energy.
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    Contour of along slope velocity.