Session X28: Geophysical Fluid Dynamics: Stratified Flows II

Internal wave dissipation and scattering by low-amplitude rough topography

The propagation of internal waves plays an important role in the propagation of energy and momentum throughout the ocean. Generated from underlying topographic features or by storms, these waves can take the form of low-mode waves propagating large distances and high-mode internal wave beams. Topographic generation has been studied focusing on finite-size features that produce wave beams that eventually breakdown to the low mode waves that propagate large distances. For both low-mode and wave beams, reflection studies have typically focused on smooth topography and low amplitude waves, which provide a strong theoretical framework for understanding reflection and propagation. However, fine scale roughness of the underlying topography impacts the generation of backscatter and harmonics. Using numerical simulations, we investigate the impact of both periodic and random fine-scale topographic roughness on the reflection and propagation of internal waves over an otherwise flat topography.   

Vortex pairing in asymmetric stratified shear instabilities

Stratified turbulent mixing events play a key role in setting the distribution of heat, momentum, and nutrients in the ocean. Vortex pairing, an important process observed in experiments and simulations of stratified shear flows, can enhance the amount and details of turbulent mixing in the flows. Prior research has explored the effects and sensitivity of the pairing process in vertically-symmetric stratified shear flows; however, there is a relative lack of work connecting asymmetry in background flow profiles and their influence on pairing evolution. Using direct numerical simulations in both single- and double-wavelength domains, we investigate the role of pairing in two different flow configurations, the asymmetric Kelvin-Helmholtz and Holmboe instabilities. We observe that the greater offset of the initial background velocity profile facilitates the generation of pairing and mixing behaviors. Additionally, the different flow setups and parameters are compared using detailed energetics and mixing analyses, allowing us to quantify the importance of the pairing process for modelling turbulent fluxes in oceanic mixing events.   

Horizontal convection in stratified systems

Overturning circulation due to horizontal density gradients, also known as horizontal convection (HC), is a ubiquitous natural process observed in lakes, oceans, and

atmospheres. HC often occurs in stratified systems, leading to a competition between the stabilizing effect of background stratification and the destabilizing effects of baroclinic adjustment. This competition ultimately determines the fluid dynamics of the stratified HC (SHC) system. We theoretically derived the intrinsic length scale of SHC, the entrainment depth of the overturning circulation, based on the available potential energy of the system. We performed laboratory-scale experiments of SHC to demonstrate the significance of this length scale. Furthermore, the fluid dynamics of SHC, including flow structures, fluid transports, and mechanical energy partitions, is discussed with and without the influence of basin-topography is discussed.   

Experimental investigation of the instabilities of a pair of vortex lines in a stably density-stratified environment

A pair of parallel counter-rotating vortices represents one of the most elementary flow configurations found in the far wake of any lifting devices. When a single vortex line remains isolated, it can persist over a long distance in the absence of instability. However, when two counter-rotating vortex lines are in close proximity, their mutually induced flows can trigger a range of complex three-dimensional instabilities, from short-wavelength elliptic instability to long-wavelength Crow instability that eventually leads to the demise of the vortex lines. These instabilities can potentially be modulated by the density-stratified environment. In this work, to understand the interaction between buoyancy and flow instability, we designed a high-speed volumetric scanning system capable of performing stereoscopic particle image velocimetry (stereo PIV) and planar laser-induced fluorescence (PLIF). This allows us to measure the three-dimensional fluid velocity field and density field simultaneously. By systematically varying the density stratification (the Froude number) and the inertia of the vortex pair (the Reynolds number), we investigated various instabilities in a controlled way and generated a unique dataset that helps us study the parametric dependence of the routes to turbulence originating from these different instabilities.   

Coherent vortex structures in stratified rotating flow past a three-dimensional hill

Large eddy simulations of flow past an isolated conical obstacle in a stratified, rotating fluid are performed. The Reynolds number Re_D=U_∞D/ν = 10 000, the Froude number Fr=U_∞/(Nh)=0.15, and the case-dependent Rossby number Ro=U_∞/(Df_c) are the controlling parameters. Here U_∞ is the freestream velocity, ν is the kinematic viscosity, N and f_c are the buoyancy and rotating frequencies, and D is the base diameter and h is the height of the hill. Three cases corresponding to non-rotating (Ro=∞), submesoscale (Ro=0.75), and mesoscale (Ro=0.15) topography are simulated. Large-scale coherent vortices emerge from the wakes in all cases, and are shown to be the dominant global modes using spectral proper orthogonal decomposition (SPOD). Increasing rotation frequency (decreasing Ro) changes the spatial organization of the structures from slanted ‘sheets’ to tall ‘columns’, but has little influence on the global mode frequency. The center of the wake vortices, identified with a mean-shift clustering algorithm, advect at close to the local mean 〈U〉(x, y, z), independent of rotation. The structural cyclonic/anticyclonic asymmetry in the wake vortices is examined. Turbulence and fine-scale structure in the wake is also quantified.   

Flow past a disk under different levels of stratification

The wave field of a horizontally-moving circular disk in a stratified fluid is studied using large eddy simulations. Five levels of stratification (body Froude numbers of Fr = 0.5, 1, 1.5, 2 and 5) are studied at Reynolds number of 5000. The wavelength and amplitude of steady lee waves are compared with linear-theory analysis. Good agreement is found if an 'equivalent body' that includes the separation region is employed for the linear theory. Unsteady wake generated waves in a stationary-body frame are linked to the vortex shedding frequency. Study of these waves in a stationary-ambient frame, along with the linear dispersion relationship, helps understand their propagation angle. The partition between steady and unsteady components of the wave flux is found to depend on Fr. Spectral Proper Orthogonal Decomposition (SPOD), when applied to the wake, shows the suppression of the natural vortex shedding frequency of the disk at Fr < O(1). A new parameter is introduced to identify the critical Fr for the onset of this suppression.   

Lineraly Stratified Flow Past Rotating 2D Ellipses

Direct Numerical Simulations (DNS) of linearly stratified flow past rotating 2D ellipses have been performed, to quantify the effect of rotation, shape, and stratification on the flow. 

Drag and lift on the rotating body, and the induced flow structures were quantified. Simulations were conducted using high-order Schwarz- spectral element method (Schwarz-SEM),

which facilitates high-fidelity simulations for rotating bodies. Simulations were conducted for Reynolds number = 120, Densimetric Froude number (Fr²) in the range 1000-0.01, theree aspect raptios of the ellipse, and one rate of rotation. This is the first instance in which Schwarz-SEM was being used for simulating stratified flows, thus comparision was conducted against literature and mono-domain simulations. Hilbert tranformation and DMD analysis was also conducted to understand and quantify the internal gravity wave (IGW) formed at higher stratification. These are some of the first high-fidelity simulation of moving bodies in stratified flow.    

Experimental study of the penetrative convection in gases

We present an experimental study of penetrative convection in gases, which allows reaching a lower Prandtl number Pr = 0.7 than classical water experiments. A heavy gas (SF6) fills the bottom of a meter size rectangular tank. Diffusion of SF6 in air establishes a stratified vertical profile in part of the domain. Electric resistors heat the bottom plate of the tank up to a chosen temperature while water circulation fixes the top plate temperature at room temperature. After a short transient, the SF6-rich lower layer convects and progressively invades the upper stably-stratified layer while exciting propagating internal gravity waves. Density and PIV measurements are performed, allowing to follow the growth of the convective region as well as the characteristics of the internal waves and convective fields. While mixing at the interface is often modelled in classical penetrative convection with an eddy diffusivity, we find that the convective layer growths here quadratically in time, which contradicts a stationary and homogeneous turbulent diffusion. The analysis of the wave spectra in the stratified domain reveals a peak frequency at the buoyancy frequency, with a clear cut-off above. Running PIV in both layers simultaneously allows us to compute the kinetic energy transfer from the convective zone into the stratified one, which amounts to about 4%. We also define a new scaling law for the erosion rate as a function of the Froude number.   

The near-wake of an inclined 6:1 prolate spheroid in a stratified fluid

A slender body can produce a range of distinct wake geometries, arising from complex 3D flow separations that vary with incidence angle and Reynolds number. Little is known on the effects of background stratification, and how buoyancy affects the near- and intermediate wake. Here, an experiment is conducted on the wake of a 6:1 spheroid in both uniform and stratified backgrounds. The inclination angle is varied from 0° - 20°. Reynolds numbers, Re_D = {0.5, 1, 2} × 10⁴ and Froude numbers, Fr ={16, 32, 64, ∞ } are tested. Both stereo-PIV (2D3C) and tomo-PIV (3D3C) are used to visualize the flow. When the body is at incidence, the wake is formed from a combination of the usual drag wake together with coherent streamwise vortices, and this wake geometry can evolve in ways that are measurably different from the zero incidence case. In the presence of density stratification, the inclined wake itself generates large-scale internal wave undulations, even at relatively weak background stratification.   

Measuring the Reflection Coefficient When Internal Wave Beams Reflect from Rough Surfaces

Internal waves may be important in the redistribution of tidal energy within the ocean and cause the erosion of continental shelves to the critical angle of tidally generated waves. We analyze this problem using the reflection coefficient of internal waves defined as the ratio of outgoing propagating energy to the incoming wave beam energy. Our experiments use particle image velocimetry to determine the velocity field of internal wave beams, and the Hilbert Transform method created by Mercier et al. (Phys. Fluids, 2008) to select for wave beams based on frequency and propagation direction. The energy flux of the internal waves is derived from the velocity field using the method of Lee et al. (Phys. Fluids, 2014). Our experiments focus on determining the dependence of the reflection coefficient on different types of boundaries: a smooth boundary with angles ranging from horizontal to critical, and various horizontal boundaries with sinusoidal roughness. We compare our results to the theory of Baines et al. (J. Fluid Mech, 1971) for internal waves and find good agreement. We have found that a rough boundary greatly alters the values of the reflection coefficient, which may have implications for internal wave beams in the ocean.    

Marangoni effects on oil droplets rising in a stratified fluid

When a droplet of lower density rises through a stratified ambient fluid, it will often get trapped in regions of high density gradient. This phenomena is observed in many environments, for example, during smoke plume dispersal in thermal inversions or trapping of oil plumes in ocean density gradients due to varying salt concentration and temperature.  Such changes may also affect interfacial tension, in which case Marangoni effects will produce additional flows which affect the droplet trapping. Recent studies indicate that these effects may be significant in some regimes. We conducted experiments at the intermediate Reynolds regime to quantify how interfacial tension gradients affect the motion of a single oil droplet rising through a stratified ambient fluid.   

Stratified drift

Vertical migration of zooplankton has been suggested as a major contributor to ocean mixing. The original hypothesis is based on estimates of the Darwinian drift of fluid parcels due to the motion of passive particles in a viscous stably stratified ambient. This suggestion is highly debated, however, with there being subsequent suggestions to the contrary. In this study, we attempt to quantify the drift volume associated with a sphere moving vertically in a viscous stably stratified ambient. For the case where viscous and buoyancy forces are in balance, we first describe the flow field around the particle, emphasizing the existence of non-trivial features on length scales much larger than the primary screening length. Next, we trace the pathlines of individual fluid elements, in an initial material plane surrounding the sphere, over a range of viscous Richardson numbers. We show that the drift volume, for long times, is finite, unexpectedly small in relation to naive scaling estimates, and has a negative sign due to the Lagrangian reflux of parcels induced by the ambient stratification. We then examine both the flow field and drift volume for the oceanically more relevant scenario where inertial and buoyancy forces are of comparable magnitude.