Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session NN: Geophysical Flows V |
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Chair: Roi Gurka, Johns Hopkins University Room: Hilton Chicago PDR 2 |
Tuesday, November 22, 2005 11:01AM - 11:14AM |
NN.00001: Measuring the mixing in two-layer exchange flow Ross Griffiths, Tjipto Prastowo, Graham Hughes, Andy Hogg We have measured the rates of mixing in two-layer, density-driven exchange flows through a constriction. Laboratory experiments utilised two long reservoirs of fresh and salty water separated by a contraction. The shear between the two counter-flowing layers in the contraction generates stratified turbulence and localized mixing. We focus on the amount of mixing and its influence on the mass fluxes. A mixing efficiency is defined as the difference between the measured decrease of potential energy and the decrease expected if there were no mixing, normalized by the expected potential energy decrease with no mixing. Over a period of steady mean flow before gravity currents reach the end walls of the reservoirs, the efficiency is found to be 11{\%} ($\pm $ 1{\%}) for most of the conditions investigated. Smaller efficiencies are found for very small density differences, where the mixing is intermittent. The mass exchange flux is found to be a constant fraction (82{\%} $\pm $2{\%}) of the predicted maximum in the (non-turbulent, steady, inviscid) hydraulically controlled solution. [Preview Abstract] |
Tuesday, November 22, 2005 11:14AM - 11:27AM |
NN.00002: Shear flow and viscosity in single-layer hydraulics Andrew Hogg, Graham Hughes We calculate solutions for one-layer hydraulically controlled flows with viscosity. Viscosity and bottom drag produce two key modifications to inviscid hydraulic theory: the position of the hydraulic control point is altered, and the solution requires knowledge of the velocity profile over the entire domain. Hence, analytically tractable solutions are not generally possible and a numerical technique is developed to calculate such flows. In this presentation, bottom drag and fluid viscosity are treated as independent parameters, allowing the influence of each parameter on flux, flow dissipation and position of hydraulic control to be quantified. We find that the flow is determined primarily by the bottom drag, and, surprisingly, the largest perturbation from this state occurs for intermediate values of fluid viscosity. These new solutions have implications for the use of hydraulic models in turbulent or viscous geophysical flows. [Preview Abstract] |
Tuesday, November 22, 2005 11:27AM - 11:40AM |
NN.00003: Relationship between vertical shear rate and kinetic energy dissipation rate in stably stratified flows David Hebert, Stephen de Bruyn Kops High resolution direct numerical simulations of strongly stratified turbulence are analyzed in order to investigate the commonly used assumption that vertical shearing of horizontal motions is the dominant cause of kinetic energy dissipation. The relative magnitude of each component of the dissipation rate is examined as a function of the nominal Reynolds number and of the buoyancy Reynolds number. From the simulation results, in conjunction with published laboratory results, it is concluded that (1) the simulation results are consistent with the laboratory data but span a much larger range of buoyancy Reynolds number, (2) the ratio of the square of the vertical shear rate to the dissipation rate is a strong function of buoyancy Reynolds number, and (3) the assumption that vertical shear rate is the dominant cause of energy dissipation rate is only good when the buoyancy Reynolds number is less than order one. [Preview Abstract] |
Tuesday, November 22, 2005 11:40AM - 11:53AM |
NN.00004: Stratified Turbulence in the Pancake Regime Adam Fincham Careful application of new laser scanning velocimetry techniques has allowed for detailed, time-resolved, three-dimensional volumetric measurements of a variety of stratified flows. These measurements have confirmed the persistence of a balanced state between horizontal advection and vertical diffusion, that leads to a self similar evolution of the flow structures for late times. For example, the relatively well known stratified dipole, most of the time assumed to be quasi two dimensional, is revealed to have a complex three dimensional vortex topology arising from its self induced propagation. When the buoyancy scale approaches zero, an effective Reynolds number based on vertical diffusion and horizontal advection governs the evolution. Such dipolar structures are believed to characteristic the vortices of the fully turbulent case. Indeed, moderately high Reynolds number towed grid stratified turbulence experiments show a predominance of dipolar type structures, in agreement with recent numerical works. This \textit{turbulent} case consists of a sea of pancake-like structures separated by highly dissipative horizontal vortex sheets. In the collapsed state, the flow evolves independently of the Froude number and is also governed by the effective Reynolds number. The extent to which viscous effects dominate the laboratory results and their agreement with recent numerical simulations will be emphasized. [Preview Abstract] |
Tuesday, November 22, 2005 11:53AM - 12:06PM |
NN.00005: Structure Formation in stable stratified turbulence Yoshi Kimura, Jack Herring Numerically it is widely observed that horizontally scattered pancake vortices are dominant structures in stably stratified turbulence. One of the fundamental properties of pancake vortices is that these strong enstrophy regions correspond to strong vertical shear regions. In this paper, we will propose a possible scenario for producing pancakes from random initial conditions. Our starting point is existence of vortex shear layers extended horizontally in stratified turbulence. Fincham {\it et.al} conjectured the so-called vortex network among the vortex layers in stably-stratified turbulence, and proposed the several ways of connections of vortex lines. One typical case observed numerically is that in which vortex lines go back and forth between a positive and a negative vorticitiy regions making loops. These loops are repeated several times as if they formed a ``coil of vortex lines'' which may be similar to an assembly of vortex rings. we have proposed that coiling vortex lines induces a strong jet penetrating the coil$^{[1]}$. Because of such jets, we could expect that a strong local horizontal velocity exists which pulls and drives the parts of nearby vortex sheets. In our recent stratified turbulence simulations ($512^3$), we observed many dynamically active double-decker pancakes in the flow, which supports the above scenario. \\ {\small [1] Y. Kimura \& J.R. Herring: Diffusion in stably stratified turbulence, {\it J. Fluid Mech.}, {\bf 328} (1996) 253--269.} [Preview Abstract] |
Tuesday, November 22, 2005 12:06PM - 12:19PM |
NN.00006: Passive scalar diffusion in stratified sheared turbulence Hideshi Hanazaki Differential diffusion of a passive scalar and an active scalar/density in stratified shear flow is considered when both the density and the passive scalar have a mean vertical gradient. Using the solution by rapid distortion theory for stratified sheared turbulence (Hanazaki {\&} Hunt, 2004), vertical diffusion of the passive scalar and its difference from the vertical density flux could be obtained. For inviscid and non-diffusive flow, the results show dependence on initial conditions similar to the unsheared flow. Namely, passive scalar flux has a `slow mode' oscillating at a nearly half frequency of the density flux only if there are some initial correlations between density and passive scalar or if there are some initial potential energy due to the density fluctuations. For the special but typical case of Pr=Sc=1, which is often used in direct numerical simulations, analytical expressions for the turbulent fluxes could be obtained and we note again the similar dependence on initial conditions which would persist as long as the turbulence do not forget the initial conditions due to strong nonlinearity. We will show how the molecular diffusion and the initial conditions affect the subsequent time development of the turbulent fluxes, in particular the difference between the passive and active scalars. [Preview Abstract] |
Tuesday, November 22, 2005 12:19PM - 12:32PM |
NN.00007: Statistical evolution of a stratified flow with horizontal shear Kyle Brucker, Sankar Basak, Sutanu Sarkar When subject to large $N$, a shear layer with horizontal shear develops a lattice of dislocated columns of vertical vorticity. Visualizations of the vorticity and buoyancy fields have helped explain the formation of vortex cores and their subsequent dislocations by a buoyancy-related instability. The impact of the coherent dynamics on the flow statistics will be discussed. The velocity fluctuations become more anisotropic, and vertical gradients dominate the dissipation rate of both kinetic and potential energy. The mixing efficiency is significantly larger than in flows with mean vertical shear and similar Richardson number. All scales of motion are affected by buoyancy and the consequent effects on velocity and density spectra will be reported. [Preview Abstract] |
Tuesday, November 22, 2005 12:32PM - 12:45PM |
NN.00008: LES of a stratified bottom boundary layer Sutanu Sarkar, John Taylor The response of a bottom boundary layer (BBL) to stratification imposed from above is studied using LES. The effect on near-wall turbulence is found to be weaker than that in stable atmospheric boundary layers. The entrainment decreases with increasing values of external $N$. Outer layer properties are modified. The effect of $N$ on mean flow and turbulence properties will be quantified in the talk. The possibility of using the gradient Richardson number to parameterize momentum and buoyancy transport will be examined. [Preview Abstract] |
Tuesday, November 22, 2005 12:45PM - 12:58PM |
NN.00009: Density evolution of fresh water above salt with homogeneous mixing John Whitehead, Ian Stevenson A two-layer density-stratified fluid was turbulently mixed with a horizontally moving vertical rod. The rod ran throughout the fluid to create homogenous turbulence, and we observed the evolution of the density profiles as mixing occurred. In the highly-turbulent regime in which this study was conducted, where Reynolds Number Re $>$ 600 and Richardson Number Ri $<$ 0.4, step-formation does not occur. The density profile of the fluid evolved smoothly from a single step to a constant density profile in the fully mixed state. The density flux and buoyancy frequency evolve in rough agreement with that predicted by Posmentier (1977), but in the low Ri regime this data is far from conclusive. Examination of the amount of turbulent kinetic energy going into mixing agrees with previous results (Holford and Linden 1999) with a maximum of 5{\%} of the kinetic energy contributing to the change in potential energy. Finally, we propose a theoretical expression for the buoyancy flux due to turbulent mixing. Using this expression, the solutions to the equation for conservation of density collapse when a similarity variable is used. We verify this collapse experimentally for a range of Reynolds and Richardson Numbers. [Preview Abstract] |
Tuesday, November 22, 2005 12:58PM - 1:11PM |
NN.00010: Pairing in stratified fluid, one step to turbulence Pantxika Otheguy, Jean-Marc Chomaz, Yoshifumi Kimura, Paul Billant In order to understand the difference between strongly stratified turbulence and two-dimensional turbulence, we investigate the effect of stratification on the merging of two vertical vortices by a direct numerical simulation. The merging is accelerated compared to a two-dimensional merging and is fully three-dimensional because of a zigzag instability. It does not occur simultaneously along the vertical. In the linear stage, the zigzag instability translates the vortices closer together and farther apart alternatively every half a wavelength on the vertical. In the layer where the vortices initially moved closer the vortices merge rapidly. In the layer where the vortices initially moved apart, the nonlinear development of the instability brings them back together resulting also in an accelerated pairing. In this nonlinear stage, the flow is seen to nearly recorrelate in each layer, high vertical shear being expulsed in between these layers. This surprising observation suggests that stratified flow should be organized into layers vertically coherent on the buoyancy lengthscale separated by thin viscous layers. [Preview Abstract] |
Tuesday, November 22, 2005 1:11PM - 1:24PM |
NN.00011: Zigzag instability of vortex arrays in a stratified fluid Paul Billant, Axel Deloncle, Jean-Marc Chomaz We investigate the three-dimensional linear stability of classical vortex configurations (Von Karman street, double symmetric row) in a strongly stratified fluid. By means of an asymptotic theory in the limit of long-vertical wavelength and well-separated vortices, we demonstrate that both the Von Karman street and a double symmetric row of columnar vertical vortices are unstable to the zigzag instability. This instability corresponds to a bending of the vortices with almost no internal deformation and ultimately slices the flow into horizontal layers. The most unstable wavelength is found to be proportional to $bF_h$, where $b$ is the separation distance between the vortices and $F_h$ the horizontal Froude number ($Fh=\Gamma/\pi a^2N$ with $\Gamma$ the circulation of the vortices, $a$ their core radius and $N$ the Brunt-V\"ais\"al\"a frequency). The maximum growth rate is independent of the intensity of the stratification and only proportional to the strain $S = \Gamma/2\pi b^2$. These results may explain the formation of layers observed in stratified turbulence. [Preview Abstract] |
Tuesday, November 22, 2005 1:24PM - 1:37PM |
NN.00012: Numerical Investigation of the Scaling and Structure of Stratified Turbulent Wakes Peter J. Diamessis, J. Andrzej Domaradzki, Geoffrey R. Spedding Large Eddy Simulation based on the subgrid scale (SGS) estimation model and truncated Navier-Stokes dynamics is used to study the stratified turbulent wake of a towed sphere. The efficient and spectrally accurate investigation of a broad range of Reynolds numbers, $Re \in [5 \times 10^3,10^5]$, and Froude numbers, $Fr \in [4,64]$ is made possible through use of a parallelized spectral multidomain penalty method model. The efficacy of the SGS model is assessed through comparison with available laboratory profiles and timeseries of turbulence quantities. Results on non-equilibrium regime duration and late- wake power law exponents are summarized for the full range of governing parameters. Finally, the effect of Reynolds number on the structure of the vorticity and internal wave fields is discussed. [Preview Abstract] |
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