Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session M7: Geophysical: General V |
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Chair: Hieu Pham, University of California, San Diego Room: 24C |
Tuesday, November 20, 2012 8:00AM - 8:13AM |
M7.00001: Buoyancy effects in the spatially-evolving wake of a sphere at Re=3,700 Matthew de Stadler, Sutanu Sarkar Direct numerical simulation is used to simulate spatially-evolving flow past a sphere in a stratified fluid. A Cartesian grid is used along with an immersed boundary method to represent the sphere inside the domain. The Reynolds number of 3,700 is chosen so that the wake behind the sphere is turbulent. The emphasis of the present study is on the near to intermediate wake as buoyancy effects become dominant. A comparison is made between an unstratified wake and a wake at a Froude number of 3. Statistics of interest include the defect velocity, wake dimensions, turbulence intensities, mean kinetic energy, turbulent kinetic energy and associated budgets. Visualizations of the vortical structures in the wake and the internal wave field will also be provided and discussed. [Preview Abstract] |
Tuesday, November 20, 2012 8:13AM - 8:26AM |
M7.00002: The Lagrangian energetics of stably stratified turbulence in the Boussinesq approximation with non-linear equation of state Seungbum Jo, Keiko Nomura, James Rottman There has been a recent resurgence of interest in determining the consistency of the Boussinesq approximation to describe the coupling of the dynamics and thermodynamics of turbulent stratified flows. In particular, there is some debate over how energy is converted from internal to mechanical energy in this approximation. Moreover, the effect of the non-linear equation of state and the strength of stratification on the internal energy is still unclear. To gain some insight into these issues, we derive the evolution equations of the different forms of energy for Boussinesq stratified flows with variable volumetric expansion coefficient in the Lagrangian frame. This analysis allows us better physical insight into these issues and allows us to show explicitly how energy is converted between internal and mechanical energy and how significant the internal energy is under these conditions. The physical significance of these results will be discussed. [Preview Abstract] |
Tuesday, November 20, 2012 8:26AM - 8:39AM |
M7.00003: A zero-equation closure model for wall-bounded stably stratified flows Farid Karimpour, Subhas Karan Venayagamoorthy In this study, we propose a parameterization for the turbulent Prandtl number (\textit{Pr}$_{t})$ for stably stratified wall-bounded flows. To date, most of the widely used parameterizations for \textit{Pr}$_{t}$ for stably stratified flows are based on data from homogeneous flows and are usually formulated as functions of the gradient Richardson number (\textit{Ri}$_{g})$. The effect of the wall boundary is completely neglected. We introduce a modified parameterization for \textit{Pr}$_{t}$ that takes into account the inhomogeneity caused by the wall coupled with the effects of density stratification. We show that in wall-bounded flows, the turbulent Prandtl number has a different behavior from homogeneous flows. We evaluate the new parameterization by using a zero-equation turbulence model for the eddy viscosity that was proposed by Munk and Anderson in 1948 to simulate a one-dimensional stably stratified channel flow. Comparison of the one-dimensional simulation results with direct numerical simulation of stably stratified channel flow results show remarkable agreement. We also compare other commonly used parameterizations of \textit{Pr}$_{t}$ for homogeneous flows to highlight their shortcomings in predicting both momentum and scalar mixing correctly in wall-bounded flows. [Preview Abstract] |
Tuesday, November 20, 2012 8:39AM - 8:52AM |
M7.00004: Pathways to dissipation in strongly rotating and stratified turbulent systems Enrico Deusebio, Erik Lindborg Geophysical flows are strongly affected by rotation and stratification at very large scales ($\approx 10^3$ km). As the flow scale is reduced, first rotation (at $\approx 10^2$ km) and then also stratification (at $\approx 1$ km) become of secondary importance. Understanding the transitions between different regimes is crucial in order to evaluate the global circulating models which nowadays start to resolve them. We mainly focus on how energy is transferred from the large scales, at which it is injected, to the small-scales, where it is dissipated, in strongly rotating and stratified systems by means of numerical simulations of the Boussinesq equations. The large resolution employed, $N_x=N_y=N_z=1024$, allows us to resolve more than one dynamical regime. Large scale dynamic closely resembles quasi-geostrophic dynamics. However, departure from a quasi-geostrophic regime may also be recognized. We show the presence of a leakage of energy which starts from the largest scales and it is entirely supported by a non-geostrophic dynamics, which is possibly stratified turbulence. Despite the idealized set considered in the study, the results surprisingly agree with observations in the atmosphere, suggesting that the presented mechanism may play a crucial role in geophysical dynamics. [Preview Abstract] |
Tuesday, November 20, 2012 8:52AM - 9:05AM |
M7.00005: A model for turbulence in moderately stratified flows Jennifer Jefferson, Chris Rehmann Models based on the Reynolds-averaged Navier-Stokes (RANS) equations have successfully predicted turbulence in weakly stratified flows, but they require adjustment in more strongly stratified flows to account for the interaction between turbulence and internal waves. In contrast, rapid distortion theory (RDT), which strictly applies for infinite Richardson number, captures many features of the wave mode of strongly stratified flows. To develop a model for turbulence in the moderate stratification observed in many environmental flows, we incorporated aspects of RANS models into RDT and attempted to predict the results of laboratory experiments of homogeneous turbulence in a stratified flow. Using a turbulent viscosity and diffusivity computed from length and velocity scales of the turbulence did not reproduce the timing of the oscillations of the vertical density flux. The inadequacy of the turbulent viscosity approach suggests including nonlinear interactions in the model by following the approach of Kevlahan and Hunt (1997). [Preview Abstract] |
Tuesday, November 20, 2012 9:05AM - 9:18AM |
M7.00006: Evolution of deep-cycle turbulence in an Equatorial Undercurrent Model Hieu Pham, Sutanu Sarkar, Kraig Winters Large-Eddy Simulation is used to investigate the relationship between the near-$N$ oscillations and the deep-cycle turbulence in the Equatorial Undercurrent. The profiles of velocity and density in the model are similar to those observed in the field. A constant wind stress and a diurnal heat flux are applied at the surface. The model is simulated for a 2-day duration. During the day time, the wind accelerates the surface water increasing the surface shear but the turbulence intensity is low due to heating. In the evening, when the heat flux becomes neutral, shear instabilities develop in the surface layer and generate turbulence. At night time, convection due to surface cooling creates a well-mixed layer. Later at night when the convection subsides, shear instabilities grow at the base of the mixed-layer where the local gradient Richardson number falls below the critical value of $0.25$. The evolution of the shear instabilities includes the temporal fluctuations of the isopycnals as well as turbulent mixing due to coherent eddies. The turbulence extends well below the surface mixed layer and lasts for a few hours. Result from our model suggests that the oscillations and the deep-cycle turbulence are related to a shear instability local to the base of the mixed layer. [Preview Abstract] |
Tuesday, November 20, 2012 9:18AM - 9:31AM |
M7.00007: Parameterization of turbulent diffusivity in stratified flows using microstructure observations and DNS Benjamin Mater, Subhas Venayagamoorthy In oceanic flows, the eddy diffusivity of density, $K_{d}$, is commonly approximated using the Osborn-Cox model with a constant mixing efficiency, $\Gamma$. Many have sought to improve upon the accuracy of this approach by parameterizing the variability in $\Gamma$ using the buoyancy Reynolds number (\textit{Re}$_{B}$=$\varepsilon$/$\nu N^{2})$. In this study, we point out that \textit{Re}$_{B}$=$Fr^{2}$\textit{Re}$_{L}$ (where \textit{Fr=$\varepsilon$/ kN} and \textit{Re}$_{L}=k^{2}$/$\varepsilon \nu$) and is, thus, a mixed parameter that obscures explicit dependencies on the more fundamental parameters involving turbulent kinetic energy, $k$. Using microstructure observations, we demonstrate this non-uniqueness of \textit{Re}$_{B}$ and explore the independent effects of \textit{Fr} and \textit{Re}$_{L}$. Because $k$ is not readily available from microstructure measurements, however, we investigate alternative methods to infer its value from measured Thorpe scales, $L_{T}$. Through physical reasoning, we argue that $L_{T}$ should scale with a length scale dependent on $k$ and not solely on dissipation $\varepsilon$. We test this reasoning using DNS of decaying grid turbulence. [Preview Abstract] |
Tuesday, November 20, 2012 9:31AM - 9:44AM |
M7.00008: Turbulent Viscosity in Ekman Flow Cedrick Ansorge, Juan Pedro Mellado Direct numerical simulation of neutrally stratified turbulent Ekman flow is carried out at different Reynolds numbers in the range $200 < \mathbf{Re} = \delta^+ < 700$ where $\delta^+$ is the boundary layer (BL) thickness expressed in wall units. Even if no logarithmic layer is found yet, the data suggest that in this intermediate range of $\mathbf{Re}$ certain measures of the flow approach Re-independency. The fully resolved three-dimensional fields of the turbulent flow are used to extract vertical profiles of the reynolds stresses and vertical shear. The assumption of a constant eddy viscosity over a wide range of the turbulent portion of the BL is valid with only small deviations. On the contrary, the data show that on a rotating plane (f-plane) the vectors of shear and vertical stress flux are not aligned. Hence, the assumption that the eddy viscosity is a linear function of the shear is not valid. It turns out that up to small deviations the directional offset of the shear and stress vectors is constant with height and, if varying at all, a function of $\mathbf{Re}$. This makes it possible to account for the directional offset between stress and shear in turbulence closures. [Preview Abstract] |
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