Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session F35: Geophysical Fluid Dynamics: Stratified Flows I |
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Chair: Alberto Scotti, University of North Carolina at Chapel Hill Room: Georgia World Congress Center B407 |
Monday, November 19, 2018 8:00AM - 8:13AM |
F35.00001: Laboratory experiments of mixing at oceanographic scales Alberto Scotti, Pierre-Yves Passaggia A quantitative description of the efficiency of mixing in stratified flows has remained an elusive goal. A recent review (Gregg et al., 2018) suggests that, in oceanographic situations, a constant value of 0.2 (the canonical value) is a reasonable choice. Deviations from the canonical value have been suggested to depend on the buoyancy Reynolds number (Shih et al., 2005). Monismith et al. (2018) considering a large collection of efficiency measured in the field show that, despite a large scatter, the canonical value is probably an appropriate value, though deviations may be expected at very large values of the buoyancy Reynolds number. In this talk, we revisit the issue with the aid of an experimental dataset acquired in the UNC Joint Fluid Lab. In a large tank, we generate shear-driven turbulent mixing that spans a significant range of the parameter space encountered in the ocean, including values of the buoyancy Reynolds number that are much larger than what can be obtained in numerical simulations. Rather than focusing on the buoyancy Reynolds number, we show that that an appropriately defined Richardson number is a much better predictor for the efficiency. We discuss the implication for the interpretation of the field data. |
Monday, November 19, 2018 8:13AM - 8:26AM |
F35.00002: Self-organized criticality of turbulence in strongly stratified mixing layers W Richard Peltier, Hesam Salehipour, C. P. Caulfield We investigate the evolution of stratified shear flows for which the stratification is sufficiently 'strong' that the flow is primarily susceptible to Holmboe wave instability (HWI) and turbulent collapse at high Reynolds number. Our DNS-based findings demonstrate the emergence of self-organised criticality (SOC) that is manifest as an adjustment of the horizontally-averaged mean flow of the turbulence towards a critical state with a gradient Richardson number of Ri_g ~ 1/4. This self-organization occurs through a continuously reinforced localisation of turbulent 'avalanches' that are found to exhibit the expected scale invariant characteristics. From an energetics perspective, the emergence of SOC is expressed in the form of a long-lived turbulent flow that remains in a `quasi-equilibrium' state for an extended period of time, corroborating the original physical arguments of Turner (1973) associated with self-regulation of stratified turbulent flows as involving a 'kind of equilibrium'. Most importantly, the irreversible mixing that results from such self-organised behavior appears to be characterized generically by a universal cumulative turbulent flux coefficient of Γ_c ~ 0.2 only for turbulent flows engendered by HWI. |
Monday, November 19, 2018 8:26AM - 8:39AM |
F35.00003: Influence of bottom boundary conditions on flow past a three-dimensional hill Pranav Puthan, Masoud Jalalibidgoli, Karu Chongsiripinyo, Jose Luis Ortiz-Tarin, Sutanu Sarkar Three-dimensional (3D) obstacles on the ocean bottom are common sites for turbulence and mixing. Simulations are conducted for a conical hill, a canonical example of 3D obstacles. Motivated by the use of slip boundary condition (BC) in the literature on geophysical wakes, we examine the sensitivity of the flow to BCs (slip instead of no-slip) on the flat wall and on the obstacle surface. When the bottom is modeled entirely with the free-slip BC, vorticity generation is purely due to the curvature of the obstacle. The no-slip BC allows the formation of a bottom boundary layer which, after separation due to the adverse pressure gradient of curved surfaces, sheds vorticity into the wake. Significant changes occur in the structure of lee vortices and wake turbulence when the BC is changed. For instance, the boundary layer on the flat bottom suppresses the unsteady oscillatory behavior of the separated boundary layer behind the hill so as to delay the formation of coherent lee vortices to locations that are further downstream. The characteristics of the downslope jet formed as part of the hydraulic response in stratified flow and the internal wave field are also altered by the choice of BC. |
Monday, November 19, 2018 8:39AM - 8:52AM |
F35.00004: Transient Growth of Submesoscale Instabilities Varvara Zemskova, Pierre-Yves Passaggia, Brian White Submesoscale instabilities are analyzed using a transient growth approach to determine the optimal perturbation for a rotating Boussinesq fluid subject to baroclinic and symmetric instabilities. We consider a base flow with uniform shear and stratification and compute the non-normal evolution of linear perturbations over finite-time in an ageostrophic, non-hydrostatic regime. Stone (1966, 1971) showed that the stability of the base flow to normal modes depends on the Rossby and Richardson numbers, with instabilities ranging from baroclinic modes (Ri >1) to symmetric (Ri < 1) and Kelvin-Helmholtz (Ri < 1/4) modes. Non-normal transient growth at short time represents a faster mechanism for the energy growth of perturbations and may provide an energetic link between large-scale geostrophic flows and dissipation via submesoscale instabilities. Here we consider two- and three-dimensional optimal perturbations by means of direct-adjoint iterations of the linearized Boussinesq Navier-Stokes equations to determine the form of the optimal perturbation and the optimal energy gain, and explore the mechanisms that contribute to the difference in energy transfer (horizontal buoyancy flux vs Reynolds stress) between short-term transient growth and long-term modal growth. |
Monday, November 19, 2018 8:52AM - 9:05AM |
F35.00005: The Stability of the Bottom Boundary Layer Under a Model Mode-1 Internal Tide John Segreto, Peter Diamessis The instability properties of the bottom boundary layer (BBL) under a model mode-1 internal tide in linearly stratified finite-depth water are studied, using 2D fully nonlinear and nonhydrostatic direct numerical simulations based on a spectral multidomain penalty method model. Low-mode internal tides are known to transport large amounts of energy throughout the oceans. One possible mechanism, by which the energy of the particular tidal waves can be dissipated, is through wave-BBL interactions, where near-bottom shear layers develop, leading to localized instabilities. In the model problem, the stability response of the time-dependent wave-induced BBL is examined by introducing low-amplitude perturbations near the bed. Ultimately distinct localized near-bed Kelvin Helmholtz billows are observed. The growth rate, σ, of the largest amplitude perturbation is compared to the time, T, that it is subject to a local Richardson number less than 1/4, resulting in a nondimensional criterion for instability, σT. A stability boundary is then constructed as a function of the nondimensional parameters that characterize the flow, wave steepness, aspect ratio and Reynolds number. It is shown that the nondimensional growth rate can be written as a function of these parameters, σT = F(Re,st,AR). |
Monday, November 19, 2018 9:05AM - 9:18AM |
F35.00006: Rough critical topography intensifies internal wave beams Saranraj Gururaj, Anirban Guha Oceanic internal gravity waves are often generated due to the interaction between barotropic tidal flow with submarine topography. These waves play key roles in ocean mixing and nutrient transport. To understand and estimate the amount of energy converted from barotropic tide to internal gravity waves, previous studies have mainly focused on spatially uniform oscillatory mean flow over smooth, idealized topographies. Subsequently, the dependence of internal wave generation with parameters like criticality, topography height, etc. were investigated. However, the smooth topography assumption may not be very realistic since the ocean's bottom surface is expected to be rough or undulated. Some researchers have reported that the resolution of topography in numerical experiments can impact the generation process and affect the conversion rates. Thus, to study the effects of roughness, we superimpose various small amplitude, sinusoidal wave-like structures on idealized topographies, and quantify the effect of roughness on conversion rates. For example, on superimposing a sinusoidal wave on a model continental shelf with a linear critical slope, the maximum baroclinic horizontal velocity of the internal wave beam was 40% more than the case where undulations were absent. |
Monday, November 19, 2018 9:18AM - 9:31AM |
F35.00007: Simulations of motion in the bottom boundary layer induced by an internal standing wave Andrew P Grace, Marek Stastna Internal standing waves are a common feature in lakes where one dimension of the lake is significantly longer than the other. Barring effects of rotation of the Earth, the response to prolonged wind stress at the surface of the lake is a tilting of the thermocline which induces oscillation when the wind stress ceases. It is well known than the resulting oscillation can degenerate into non--linear wave trains which can facilitate vertical transport of material across the bottom boundary layer upwards into the water column. The literature is rich in experimental studies and numerical simulations showing the effects that passing solitary waves have on this process, but nothing to our knowledge has been done in the processes by which cross boundary layer transport occurs due to the presences of a seiche and the resulting wave motion induced by the seiche. Through the use of high resolution pseudo--spectral simulations in 2 and 3D, the vertical transport of a tracer in the presence of a seiche is quantified. The vertical transport is compared against existing data from numerical simulations of passing solitary waves. |
Monday, November 19, 2018 9:31AM - 9:44AM |
F35.00008: Turbulence in Forced Stratified Exchange Flows Katherine Smith, John R. Taylor Continuously forced, stratified exchange flows occur in many geophysical systems, such as through channels between ocean basins, between coastal shelves and the deep ocean, and at the mouth of rivers and estuaries. These exchange flows can be unstable to various instabilities that can promote the growth of turbulence and increase mixing between the two differing flows. While these mixing processes are assumed to be important to global ocean budgets, they are unresolved within Earth system models and therefore must be fully understood in order to accurately include through sub- grid scale parameterization. In this talk, we present results from three-dimensional direct numerical simulations of stratified exchange flows that are continuously forced by weakly damping the buoyancy and streamwise velocity back to their initial mean profiles. We explore a range of large and small values of the bulk Richardson number and, after an initial ‘spin-up’ period, a turbulent steady state is observed which is dependent on the bulk Richardson number. Both turbulence and mixing are characterized in each case and the implications for parameterization are discussed. |
Monday, November 19, 2018 9:44AM - 9:57AM |
F35.00009: The Interaction of Dense Gravity Currents with Internal Waves Yukinobu Tanimoto, Nicholas Ouellette, Jeffrey R Koseff Shoaling and breaking internal waves along a pycnocline may lead to mixing and dilution of dense gravity currents, such as brine effluent from desalination plants in near-coastal environments. A series of laboratory experiments was performed in which a shelf-slope gravity current passes through a two-layer stratification interface. A range of interfacial conditions is examined including no approaching waves at the interface (zero Froude number), and waves of varying Froude number. The characteristics of the gravity current are varied over a range of Richardson numbers. We examine the characteristics of the interaction between the gravity current and oncoming internal waves, the mixing at the interface, and the nature of the interfacial waves produced at the interface by the penetrating gravity current over a wide range of Froude and Richardson numbers using dye-based flow visualization, Planar Laser-Induced Fluorescence (PLIF), and measurements with a profiling conductivity-temperature-density (CTD) probe. |
Monday, November 19, 2018 9:57AM - 10:10AM |
F35.00010: Some insights to infer turbulent diapycnal mixing in geophysical flows Amrapalli Garanaik, Subhas Karan Venayagamoorthy In this study, some new insights for inferring diapycnal diffusivity K_{ρ} in stably stratified flows are provided based on physical scaling arguments and tested using high resolution direct numerical simulation (DNS) data. It is shown that for weakly stratified flows where buoyancy effects are not dominant, the eddy diffusivity K_{ρ}∼ w' L_{E. }Here L_{E} is the Ellison length scale that represents the outer scale of turbulence and w' is the vertical turbulent velocity scale. For the strongly stratified regime, this scaling overpredicts the true diapycnal diffusivity due to internal wave induced adiabatic motions. In order to infer K_{ρ} in the limit of strong stratification, a new formulation for K_{ρ} is provided using w', L_{E} and turbulent Froude number Fr=ε/Nk, wherein N is the buoyancy frequency, k is the turbulent kinetic energy and ε is the rate of dissipation of turbulent kinetic energy, respectively. The comparison between the proposed formulation and exact diffusivities using DNS data is remarkable and highlights the strength of the proposed new parameterization in its ability to predict turbulent mixing in stably stratified geophysical flows. |
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