Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session L30: Geophysical Fluid Dynamics: Stratified Turbulence |
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Chair: Colm-Cille Caulfield, University of Cambridge Room: 311 |
Monday, November 23, 2015 4:05PM - 4:18PM |
L30.00001: Instability of Stratified Shear Flow: Intermittency and Length Scales Robert Ecke, Philippe Odier The stability of stratified shear flows which occur in oceanic overflows, wind-driven thermoclines, and atmospheric inversion layers is governed by the Richardson Number $Ri$, a non-dimensional balance between stabilizing stratification and destabilizing shear. For a shear flow with velocity difference $U$, density difference $\Delta \rho$ and characteristic length $H$, one has $Ri = g (\Delta \rho/\rho) H/U^2$. A more precise definition is the gradient Richardson Number $Ri_g = N^2/S^2$ where the buoyancy frequency $N = \sqrt{(g/\rho) \partial \rho/\partial z}$, the mean strain $S = \partial U/\partial z$ with $z$ parallel to gravity and with ensemble or time averages defining the gradients. We explore the stability and mixing properties of a wall-bounded shear flow for $0.1 < Ri_g < 1$ using simultaneous measurements of density and velocity fields. The flow, confined from the top by a horizontal boundary, is a lighter alcohol-water mixture injected from a nozzle into quiescent heavier salt-water fluid. The injected flow is turbulent with Taylor Reynolds number about 75. We compare a set of length scales that characterize the mixing properties of our turbulent stratified shear flow including Thorpe Length $L_T$, Ozmidov Length $L_O$, and Ellison Length $L_E$. [Preview Abstract] |
Monday, November 23, 2015 4:18PM - 4:31PM |
L30.00002: Baroclinic Critical Layers and the Zombie Vortex Instability (ZVI) in Stratified, Rotating Shear Flows: Where They Form and Why Meng Wang, Patrick Huerre, Chung-Hsiang Jiang, Suyang Pei, Maryann Rui, Philip Marcus It has been found recently that baroclinic critical layers are responsible for a new finite-amplitude instability, called the Zombie Vortex Instability (ZVI), in stratified (with Brunt--V\"{a}is\"{a}l\"{a} frequency N) flows, rotating with angular velocity $\Omega $ and shear $\sigma $. ZVI occurs via baroclinic critical layers that create linearly unstable vortex layers, which roll-up into vortices. Those vortices excite new baroclinic critical layers, which form new generations of vortices, resulting in ``vortex self-replication'' that fills the fluid with turbulent vortices. To understand the role of baroclinic critical layers in ZVI, we analyze their structures with matched asymptotic expansions, assuming viscosity determines the magnitude and thickness of the critical layer. We verify our analytically obtained leading order inner and outer layer solutions with numerical simulations. In addition, maps of the control parameter space (Reynolds number, N/$\Omega $ and $\sigma $/$\Omega )$ are presented that show two regimes where ZVI occurs, and the physics that determines the boundaries of the two regimes is interpreted. The parameter map and its underlying physics provide guidance for designing practical laboratory experiments in which ZVI could be observed. [Preview Abstract] |
Monday, November 23, 2015 4:31PM - 4:44PM |
L30.00003: Spontaneous layer formation dynamics in stratified Taylor--Couette flow Colin Leclercq, Jamie L. Partridge, Pierre Augier, C.P. Caulfield, Paul F. Linden, Stuart B. Dalziel The spontaneous formation of horizontal layers is a common feature of strongly and stably stratified flows and plays a major role in the dynamics of geophysical flows. However, little is known about the physical mechanism setting the depth of the layers spontaneously emerging in ``stratified Taylor--Couette flow'' in the annulus between a rotating inner cylinder and a fixed outer cylinder, initially filled with stably, axially and linearly stratified fluid. Using linear stability analysis, direct numerical simulations and experiments, we investigate the relative importance of primary linear instability and secondary nonlinear processes in the transient dynamics leading to the experimentally and numerically observed step-like density profile in this flow. We explore the effects of the particular form of the spin-up of the inner cylinder and initial conditions on the transient dynamics and nonlinear attractor of the flow. By better understanding the dynamics of layer formation, we are able to identify the approriate scaling laws relating layer depth to rotation rate, initial stratification, gap width and radius ratio. [Preview Abstract] |
Monday, November 23, 2015 4:44PM - 4:57PM |
L30.00004: Energy and water vapor transport in a turbulent stratified environment Luca Gallana, francesca de santi, michele iovieno, renzo richiardone, Daniela Tordella We present direct numerical simulations about the transport of kinetic energy and unsaturated water vapor across a thin layer which separates two decaying turbulent flows with different energy. This interface lies in a shearless stratified environment modeled by means of Boussinesq's approximation. Water vapor is treated as a passive scalar (Kumar et al. 2014). Initial conditions have $Fr^2$ between 0.64 and 64 (stable case) and between -3.2 and -19 (unstable case) and $Re_\lambda = 250$. Dry air is in the lower half of the domain and has a higher turbulent energy, seven times higher than the energy of moist air in the upper half. In the early stage of evolution, as long as $|Fr^2|>1$, stratification plays a minor role and the flows follows closely neutral stratification mixing. As the buoyancy terms grows, $Fr^2 \sim O(1)$, the mixing process deeply changes. A stable stratification generates a separation layer which blocks the entrainment of dry air into the moist one, characterized by a relative increment of the turbulent dissipation rate compared to the local turbulent energy. On the contrary, an unstable stratification sligthy enhances the entrainment. Growth-decay of energy and mixing layer thichness are discussed and compared with laboratory and numerical experiments. [Preview Abstract] |
(Author Not Attending)
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L30.00005: Layering from anticyclonic vortices in a rotating stratified medium with combined salinity and temperature effects Joel Sommeria, Michael Burin, Samuel Viboud We generate anticyclonic vortices by a fluid source in a rotating and uniformly stratified medium, a laboratory model of long lived vortex lenses in the ocean. Experiments are performed in the large ‘Coriolis’ rotating platform at Grenoble, 13 m in diameter, providing previously unaccessible turbulent regimes. The other novelty is to combine temperature and salinity effects, like in ‘meddies’, vortices formed by intrusion in the Atlantic ocean of warm and salty water from the Mediterranean Sea. For both heated an unheated cases, we observe shear driven instability at the vortex periphery, leading to the emission of material filament from a large-scale m=2 instability. Heated vortices behave much the same way but with two key additions. One, prominent at early times, is that the vortex edge appears serrated around most of its circumference in the upper part of the lens. Two, clearer for later times, a staircase density profile develops above the eddy. We explain this small scale turbulence as thermal convection in the statically unstable density profile resulting from selective vertical diffusion of temperature (while salinity is less diffusive). The resulting turbulent mixing generates horizontal intrusions at the upper part of the vortex, unlike the double-diffusive instability. [Preview Abstract] |
Monday, November 23, 2015 5:10PM - 5:23PM |
L30.00006: Turbulent mixing due to Holmboe wave instability in stratified shear flows at high Reynolds numbers Hesam Salehipour, Colm-cille Caulfield, W. Richard Peltier We consider numerically the transition to turbulence and associated mixing in parallel stratified shear flows with hyperbolic tangent initial velocity and density distributions. When the characteristic length scale of density variation is sufficiently sharper than that of the velocity variation, this flow is primarily susceptible to Holmboe wave instability (HWI) which perturbs the interface to exhibit characteristic cusped interfacial waves. Unlike previous low-$Re$ experimental and numerical studies, in the high-$Re$ regime in which our DNS analyses are performed, the primary HWI triggers a vigorous yet markedly more long-lived turbulent event compared to its better known relative, the Kelvin-Helmholtz instability (KHI). HWI `scours' the primary density interface, leading to substantial irreversible mixing and vertical transport of density displaced above and below the (robust) primary density interface which is comparable in both absolute terms and relative efficiency to the mixing associated with an equivalent KHI. Our results establish categorically that, provided the Reynolds number is high enough, shear layers with sharp density interfaces and associated locally high values of the gradient Richardson number are sites of substantial and efficient irreversible mixing. [Preview Abstract] |
Monday, November 23, 2015 5:23PM - 5:36PM |
L30.00007: Mixing efficiency dependence on overturning and turbulence intensity in stratified shear layers C. P. Caulfield, Ali Mashayek, W. R. Peltier It is well-known that both the total amount of irreversible mixing and its efficiency in stratified shear flows are strongly time-dependent. We consider shear layers that are susceptible to primary Kelvin-Helmholtz instabilities, developing relatively large billow overturnings that in turn are subject to various secondary instabilities which trigger turbulence transition. Valuable insights can be gained by considering the time-dependence of three characteristic length scales of the flows: the overturning Thorpe scale $L_T$; the largest turbulence scale unaffected by stratification known as the Ozmidov scale $L_O=\sqrt{\epsilon/N^3}$; and the Kolmogorov scale $L_K=(\nu^3/\epsilon)^{1/4}$, where $\epsilon$ is the kinetic energy dissipation rate, $\nu$ is the kinematic viscosity, and $N$ is the buoyancy frequency. Provided $L_O/L_K$ is sufficiently large, we show that $L_T$ first grows as the primary billow develops, but then falls rapidly as the turbulence onsets and $L_O$ increases in turn and then decays more slowly, leading to a typical monotonic increase in the ratio $L_O/L_T$ with time. Both the most efficient and the most vigorous mixing occurs when $L_T \simeq L_O$, which has important implications for the interpretation and modelling of real oceanic mixing events. [Preview Abstract] |
Monday, November 23, 2015 5:36PM - 5:49PM |
L30.00008: Biases in Thorpe scale estimates of turbulence dissipation Alberto Scotti The Thorpe-scale method is widely used to estimate dissipation and mixing rates in environmental stratified turbulent flows from density measurements along vertical profiles. We show that the relevant displacement scale in general is not the rms value of the Thorpe displacement. Rather, the displacement field must be Reynolds decomposed to separate the mean from the turbulent component, and it is the turbulent component than ought to be used to diagnose mixing and dissipation. In shear-driven flows, the rms of the Thorpe displacement, known as the Thorpe scale is shown to be equivalent to the turbulent component of the displacements, and we show that the Thorpe scale approximates the Ozmidov scale, or, which is the same, the Thorpe scale is the appropriate scale to diagnose mixing and dissipation. However, when mixing is driven by the available potential energy of the mean flow (convective-driven mixing), we show that the Thorpe scale is (much) larger than the Ozmidov scale. [Preview Abstract] |
Monday, November 23, 2015 5:49PM - 6:02PM |
L30.00009: An analysis of diapycnal mixing efficiency in stably stratified turbulent flows Amrapalli Garanaik, Subhas Karan Venayagamoorthy, Derek Stretch In order to estimate turbulent diapycnal mixing in stably stratified flows such as in oceanic flows, two key quantities are required namely the diapycnal mixing efficiency $R_f^*$ and the dissipation rate of turbulent kinetic energy $\epsilon$. The focus of this study is to investigate the variability of $R_f^*$ by considering oceanic turbulence data obtained from microstructure profiles in conjunction with data from laboratory experiments and DNS. The analysis of the field data was performed on turbulent patches which were identified using the Thorpe sorting method for potential temperature. The turbulent kinetic energy $k$ contained within a turbulent patch was inferred based on the flow regime following the methodology proposed by Mater and Venayagamoorthy (Physics of Fluids, 26, 036601, 2014). The analysis shows that high mixing efficiency can persist at high buoyancy Reynolds numbers ($Re_b=\epsilon/\nu N^2$, where $N$ is buoyancy frequency and $\nu$ is the kinematic viscosity), contrary to the notion that mixing efficiency decreases in a universal manner beyond $Re_b > 100$. These findings clearly show that $Re_b$ based parameterizations that are obtained from low-Reynolds number experimental/DNS studies are not universal and/or appropriate for geophysical flows. [Preview Abstract] |
Monday, November 23, 2015 6:02PM - 6:15PM |
L30.00010: The Efficiency of Deep and Abyssal Ocean Turbulent Mixing Ali Mashayek, Colm Caulfield, Raffaele Ferrari, Maxim Nikurashin, Richard Peltier \\ Turbulent mixing produced by breaking of internal waves in the deep ocean plays a primary role in the climate through exerting a control upon the upwelling of deep dense waters formed at high latitudes, thereby driving the global ocean overturning circulation. A key parameter used to characterize turbulent mixing in observations, climate models, and global energy budgets, is the `efficiency' of mixing, here defined as the ratio of the portion of the tide and wind energy input into the deep ocean that is invested in mixing, to the portion viscously dissipated into heat. Efficiency is conventionally assumed to be a constant of approximately twenty percent. Here we show that it varies significantly in the abyssal ocean, and that mixing is predicted to be most efficient, reaching values as high as fifty percent near topographic features which host vigorous wave generation and breaking. This result suggests a more accurate closure of the bulk ocean energy budget, a goal lying at the heart of understanding the role of the ocean circulation in climate and one towards which the oceanographic community has been striving for decades. [Preview Abstract] |
Monday, November 23, 2015 6:15PM - 6:28PM |
L30.00011: Plankton dynamics in thermally-stratified free-surface turbulence Salvatore Lovecchio, Alfredo Soldati Thermal stratification induced by solar heating near the ocean-atmosphere interface influences the transfer fluxes of heat, momentum and chemical species across the interface. Due to thermal stratification, a region of large temperature gradients (thermocline) may form with strong consequences for the marine ecosystem. In particular, the thermocline is believed to prevent phytoplankton from reaching the well-lit surface layer, where they can grow through the process of photosynthesis. In this paper, we use a DNS-based Eulerian-Lagrangian approach to examine the role of stratification on phytoplankton dynamics in thermally-stratified free-surface turbulence. We focus on gyrotactic self-propelled phytoplankton cells, considering different stratification levels (quantified by the Richardson number) and different gyro tactic re-orientation times. We show that the modulation of turbulent fluctuations induced by stable stratification has a strong effect on the orientation and distribution of phytoplankton, possibly leading to trapping of some species within the thermocline. Specifically, we observe the appearance of a depletion layer just below the free-surface as stratification increases, accompanied by a reduction in the vertical stability of phytoplankton cells. [Preview Abstract] |
Monday, November 23, 2015 6:28PM - 6:41PM |
L30.00012: An affordable and accurate conductivity probe for density measurements in stratified flows Marco Carminati, Paolo Luzzatto-Fegiz In stratified flow experiments, conductivity (combined with temperature) is often used to measure density. The probes typically used can provide very fine spatial scales, but can be fragile, expensive to replace, and sensitive to environmental noise. A complementary instrument, comprising a low-cost conductivity probe, would prove valuable in a wide range of applications where resolving extremely small spatial scales is not needed. We propose using micro-USB cables as the actual conductivity sensors. By removing the metallic shield from a micro-B connector, 5 gold-plated microelectrodes are exposed and available for 4-wire measurements. These have a cell constant $\sim $550m$^{-1}$, an intrinsic thermal noise of at most 30pA/Hz$^{1/2}$, as well as sub-millisecond time response, making them highly suitable for many stratified flow measurements. In addition, we present the design of a custom electronic board (Arduino-based and Matlab-controlled) for simultaneous acquisition from 4 sensors, with resolution (in conductivity, and resulting density) exceeding the performance of typical existing probes. We illustrate the use of our conductivity-measuring system through stratified flow experiments, and describe plans to release simple instructions to construct our complete system for around {\$}200. [Preview Abstract] |
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