Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session BL: Geophysical: General I |
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Chair: H.J.S. Fernando, Arizona State University Room: Salt Palace Convention Center 250 F |
Sunday, November 18, 2007 10:34AM - 10:47AM |
BL.00001: Schmidt number and non-Boussinesq effects on the propagation of density currents. Thomas Bonometti, S. Balachandar The results of a numerical study of density currents are described. Two complementary approaches are used, namely a high-resolution spectral method and a finite-volume interface capturing method. They allow to describe density currents for a wide range of Schmidt number (Sc), density contrast and Reynolds number (Re). First we establish that Sc only weakly affects the dynamics of density currents provided Re is large. The patterns of lobes and clefts are observed to be independent of Sc while the formation of vortex structures at the interface is sensitive to Sc. A criterion is proposed for the stability of the interface, and is found to be in agreement with present computed results and available experimental and numerical data. Effects of wall friction are then considered. They are shown to play a significant role on the propagation of density currents. When slip (resp. no-slip) conditions are imposed at walls, agreement (resp. discrepancy) is observed between computed front velocities and shallow water theories. A simple model is proposed in order to take into account resistive effects at boundaries and good agreement is found for the whole range of density contrast. [Preview Abstract] |
Sunday, November 18, 2007 10:47AM - 11:00AM |
BL.00002: Turbulent oscillating channel flow subjected to wind stress W. Kramer, H.J.H. Clercx, V. Armenio The Westerschelde estuary in the Netherlands is characterized by a strong tidal driven flow with typical velocities in the range of 0.2 to 1 m/s. In addition to the tides the wind (5 m/s) exerts a stress at the free surface driving the upper fluid layers. To investigate this flow we performed resolved Large Eddy Simulations for a generic configuration: a periodic 3D channel domain with an oscillating pressure gradient over the channel length, a fixed wind stress at the flat free-surface and no-slip conditions at the bottom boundary. The wind stress drives a unidirectional flow, which in combination with the oscillating (tidal) part generates a strong shear-layer near the free surface. In this shear layer and in the shear layer near the no-slip bottom turbulence is strongly enhanced. Subsequently, the turbulence is spreading over a larger part of the domain, where it has a large influence on the dispersion of particles. The study is extended by including the effects of rotation and stratification. [Preview Abstract] |
Sunday, November 18, 2007 11:00AM - 11:13AM |
BL.00003: Stratified turbulence: a possible interpretation of some geophysical turbulence measurements James Riley, Erik Lindborg For stably-stratified regions of both the atmosphere and the oceans, several existing sets of smaller-scale data, with horizontal length scales ranging from the Ozmidov scale $\ell_o = \sqrt{\epsilon/N^3}$ to several hundred times $\ell_o$, appear to display Kolmogorov-Obukov-Corrsin inertial ranges in horizontal spectra. For both the atmospheric and oceanic data, this corresponds to horizontal length scales of roughly 1 to at least several hundred meters. Based upon results from numerical simulations$^{1,3}$ and theoretical arguments$^{1,2}$ it is argued that these data are inconsistent with the assumptions for these inertial range theories. Instead, it is hypothesized that the dynamics of stratified turbulence$^{4}$ explain these data. In stratified turbulence a strong downscale transfer of energy exists in the horizontal, and with this the development of a horizontal (but not vertical) spectral inertial range above $\ell_o$. This downscale transfer of energy can then lead to smaller-scale instabilities and turbulence, providing new `pathways' to turbulence in geophysical flows. $^1$E.Lindborg,2005,{\it Geophys.Res.Ltrs.},{\bf 32},L01809. \\ $^2$E.Lindborg,2006,{\it J.Fluid Mech.},{\bf 550},207. \\ $^3$J.J.Riley,S.M.deBruynKops,2003,{\it Phys.Fluids},{\bf 15},2047. \\ $^4$D.K.Lilly, 1983,{\it J.Atmos.Sci.},{\bf 40},749. [Preview Abstract] |
Sunday, November 18, 2007 11:13AM - 11:26AM |
BL.00004: Dynamics of Decaying Turbulence in Stably Stratified Flows David Hebert, Stephen de Bruyn Kops In natural settings it is common for flows with a large initial Froude number to form and subsequently decay from the lack of an energy source. As the flow decays the Froude number will become order 1 and the effects of density stratification become important. If the Reynolds number is sufficiently high the flow will become both turbulent and strongly stratified. In this talk, simulated turbulent flows subject to strong stratification are analyzed from high resolution direct numerical simulations (DNS) generated from two different initial conditions: 1) Taylor-Green vorticies and 2) an idealized momentumless wake. Based on an autocorrelation length scale, the Froude number of the simulations ranged from 1.2-3.4, while the Reynolds number ranged from 15000-38000. When using DNS one has the ability to quantify each term in the kinetic and potential energy transport equations. For the simulated flows in this study, the terms describing the amount of energy converted from kinetic to available potential energy via buoyancy flux, the amount of energy converted between the horizontal and vertical contributions to kinetic energy, and the amount of energy dissipated to heat, $\epsilon$, and to background potential energy, $\chi$, are quantified. Also, the length scale of terms in the energy equation are shown via spectral analysis. Finally, the mixing efficiency, $\Gamma = \chi/\epsilon$, is shown to be similar for all simulations despite the differing initial conditions. [Preview Abstract] |
Sunday, November 18, 2007 11:26AM - 11:39AM |
BL.00005: Diffusive Layering in Large and Small Aspect-Ratio Containers S.U. Pol, H.J.S. Fernando, S. Webb The diffusive interface of double-diffusive staircases is investigated using laboratory experiments and theoretical modeling. Heat/salt and petrochemical (stimulant oil)/heat mixtures are considered, with applications to oceanographic and engineering (e.g. Strategic Petroleum Reserves) flows. The goals were to study how the convective layers above the first layer can be scaled for large aspect ratio (width/height) configurations; delineate conditions under which adjoining convective layers merge; and propose scaling for layer heights for small aspect ratio cases. In the experiments a stable solute gradient is heated from below, forming multiple convective layers separated by diffusive interfaces, and the evolution of temperature and density profiles as well as velocity fields are measured. The theoretical layer heights are derived based on the argument that convective layers grow until their vertical growth is inhibited by a balance between the vertical inertia forces of convective eddies and stable buoyancy forces of diffusive interfaces. Comparisons of experimental and theoretical results are made. [Preview Abstract] |
Sunday, November 18, 2007 11:39AM - 11:52AM |
BL.00006: Absence of small-scale fluctuations of high-Pr buoyant scalars in stratified turbulence Hideshi Hanazaki, Takehiro Miyao Diffusion of scalars in turbulent flows, such as heat and salt, is important in geophysical systems since it indirectly but definitely determines the circulation of the atmosphere and ocean. It has often been assumed that fluctuations of scalars with small molecular diffusivities (Prandtl number $Pr>1$) can survive at length scales smaller than the Kolmogorov scale. This is indeed true to passive scalars whose distribution does not affect the fluid motion. However, we demonstrate here that it would not be true to buoyant/active scalars such as heat and salt, whose distribution affects the fluid motion. Results of direct numerical simulations for a double-diffusive system, i.e., a system with two active scalars which constitute density stratification, show that the fluctuations of active scalars with high Prandtl number disappear at the Kolmogorov scale. This implies that the fluctuations of heat ($Pr=6$) and salt ($Pr=600$) in the ocean, would disappear at much larger scales than have been considered. This suggests also the possibility of realizing numerical simulations with much coarser computational grids than have ever been thought. Similar results would be applied to other active scalars controlled by external restoring forces, such as electric or magnetic forces. [Preview Abstract] |
Sunday, November 18, 2007 11:52AM - 12:05PM |
BL.00007: Evolution of a Turbulent Shear Layer when One Layer is Uniformly Stratified Hieu Pham, Sutanu Sarkar, Kyle Brucker Direct Numerical Simulation of a turbulent shear layer between an upper unstratified region and a linearly stratified bottom region is performed. A pycnocline is found to develop at the bottom of the shear layer. The unsteady turbulent shear layer excites an internal gravity wave field over a broad range of frequencies. The waves travel away at angles in the range of 30-60 degrees to the vertical. Fluctuating velocities and density are transported into the bottom region. At late time, the turbulent kinetic energy in the bottom region is higher than in the shear layer. The internal wave flux is approximately 10\% of the integrated production rate, and 40\% of the integrated buoyancy flux. The balance of turbulent kinetic energy is compared to a corresponding case with a density jump but without a stratified bottom region. The turbulent production, dissipation and buoyancy flux are reduced with respect to the latter case. The growth rate of the shear layer thickness is also reduced. [Preview Abstract] |
Sunday, November 18, 2007 12:05PM - 12:18PM |
BL.00008: Direct Numerical Simulations of a Stratified Self-Propelled Wake Kyle Brucker, Sutanu Sarkar Direct Numerical Simulations (DNS) of a self-propelled wake
subject to stratification are utilized to study the
characteristics of the
mean flow and turbulence fluctuations in the wake.
Results include wake height, wake width, peak defect velocity,
r.m.s. velocity fluctuations and turbulent fluxes, $\left< u_i
u_j \right>$ and $\left |
Sunday, November 18, 2007 12:18PM - 12:31PM |
BL.00009: Experimental studies of MHD flow in a rapidly rotating system Douglas H. Kelley, Daniel S. Zimmerman, Santiago Andres Triana, Daniel P. Lathrop We present experimental studies of fluid flow in a spherical vessel with either shear- or propeller-driven flows. Our work is motivated by the numerical results of Dudley and James (1989), who found dynamo action in flows of this geometry (so-called S$_1$T$_1$ flow). Using liquid sodium as a test fluid, we apply an external magnetic field (up to 400~G) and image the induced field with an array of Hall probes near the surface of the vessel. A rich variety of dynamics occur at various rotation rates, including oscillatory behaviors, likely to be indicative of inertial waves in shear-driven flow or magnetocoriolis (MC) waves in propeller-driven flow. The detailed characteristics and dynamics of these waves, as well as their interaction with a turbulent (Re $\sim 10^7$) background flow, are the subject of ongoing research. Our work has implications for dynamo action, thought to produce the magnetic fields of stars, accretion disks, and planets, including Earth. [Preview Abstract] |
Sunday, November 18, 2007 12:31PM - 12:44PM |
BL.00010: Rapid Gravitational Adjustment of a Horizontal Shear Layer Karl Helfrich, Brian White Shallow coastal ocean flows frequently involve strong horizontal shear layers in combination with a horizontal density gradient. Examples include estuarine outflows and separating flows around headlands and islands. The stability and evolution of the shear layer formed from the initial state of two co-flowing streams with laterally-varying, but depth independent, velocity and density is explored through three-dimensional nonhydrostatic numerical calculations. In the absence of the density contrast, the shear layer undergoes the classic instability including roll-up of the vertical vorticity into well-defined vortices. The addition of the density gradient results in a lateral gravity-driven flow resembling a lock-exchange. The lateral adjustment leads to tilting (from vertical) and stretching of the emerging shear layer vortices, greatly amplifying vorticity in the vortex cores. This converts horizontal shear into vertical shear and ultimately the rapid break-down of the vortices, large density overturns, and vertical mixing. The work is guided by a simple scaling argument that compares the timescale for growth of the linearly most unstable wave on a pure shear layer to the timescale for the transverse gravitational adjustment. For large values of this ratio the gravitational adjustment dominates and inhibits the shear instability. As this ratio decreases, the shear and gravity-driven flows become increasingly coupled, producing strong mixing. [Preview Abstract] |
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