Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session PS: Geophysical: General II - Stratified Fluids and Turbulence |
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Chair: Peter Diamessis, Cornell University Room: 200G |
Tuesday, November 24, 2009 11:40AM - 11:53AM |
PS.00001: Energetics of vertical fluid particle dispersion in stably stratified turbulence Seungbum Jo, Keiko Nomura, James Rottman The vertical dispersion of fluid particles in stably stratified turbulence is investigated. We present an analysis framework which describes the associated flow energetics in the Lagrangian frame. The total potential energy of a marked fluid particle is considered in terms of the available potential energy, associated with the nonequilibrium displacement, and the equilibrium (minimum) potential energy, associated with the change in particle equilibrium height. The corresponding evolution equations elucidate the key sequence of processes and clarify previous interpretations of the transport mechanisms. The analysis shows that in the case of stationary flow, the rate of mean square displacement is equal to the rate of mean square equilibrium displacement which is given by the scalar dissipation rate. The analysis is demonstrated using direct numerical simulations of stationary sheared turbulence. A dispersion model is developed and compared with previous models. [Preview Abstract] |
Tuesday, November 24, 2009 11:53AM - 12:06PM |
PS.00002: On spectral energy transfer in strongly stratified flows James Riley, Vishal Vasan, Oscar Flores, P.K. Yeung The fluid dynamics of many regions of the atmosphere and oceans are characterized by being strongly affected by stable density stratification, but weakly affected by the earth's rotation. This is typical of the open ocean, e.g., on horizontal scales from a few meters up to hundreds of meters. One approach to understanding and predicting such flows is by examining their nonlinear, spectral energy transfer. At horizontal scales strongly affected by stratification, vertical motion as well as the stretching of vertical vorticity is suppressed. In addition the stable stratification supports the propagation of internal waves. These features impose strong constraints on spectral energy transfer. We will present the results of direct numerical simulations of strongly stratified flows with Taylor-Green initialization. The simulations are performed using highly scalable codes run on massively parallel computers; the computational domains are highly anisotropic with up to 2048 X 2048 X 256 grid points. This allows sufficient resolution to examine both the downscale as well as the upscale transfer of energy, both which are found to be dynamically significant. [Preview Abstract] |
Tuesday, November 24, 2009 12:06PM - 12:19PM |
PS.00003: Energy spectra of stably stratified turbulence Yoshifumi Kimura, Jackson Herring Energy spectra for forced stably stratified turbulence are investigated numerically using the Direct Numerical Simulations (DNS) with $1024^3$ grid points. The calculation is done by solving the 3D Navier-Stokes equations under the Boussinesq approximation pseudo-spectrally. Using toroidal-poloidal decomposition (Craya-Herring decomposition), the velocity field is divided into the vortex mode ($\phi_1$) and the wave mode ($\phi_2$). The $\phi_1$ and $\phi_2$ spectra as a function of horizontal wave numbers, $k_{\perp}$, has the form of \vspace{-0.6cm} \begin{eqnarray} E_{\perp\Phi_1}(k_{\perp}) =\left\{\begin{array}{l} \alpha \eta_{\perp\Phi_1}^{2/3}k_{\perp}^{-3} \quad(k_{\perp}< k_c) \\ C_K\varepsilon_{\perp \Phi_1}^{2/3}k_{\perp}^{-5/3}\quad (k_{\perp}>k_c)\end{array}\right. \;, \nonumber\\ E_{\perp\Phi_2}(k_{\perp}) =\left\{\begin{array}{l} \beta \sqrt{N\varepsilon_{\perp\Phi_2}} k_{\perp}^{-2} \quad(k_{\perp}< k_c) \\ C_K\varepsilon_{\perp\phi_2}^{2/3}k_{\perp}^{- 5/3}\quad(k_{\perp}>k_c)\end{array}\right. \;.\nonumber \end{eqnarray} where $\eta_{\perp\phi_1}$ and $\varepsilon_{\perp\phi_2}$ are the horizontal enstrophy dissipation based on the $\phi_1$ energy and the horizontal energy dissipation based on the $\phi_2$ energy, respectively. For both cases, $C_K\approx 1.2\sim2.0$ is obtained being close to the Kolmogorov constant. To understand the reason for the steeper spectra than the Kolmogorov -5/3 for large scales, inviscid calculations (truncated Euler's equation) without forcing are conducted. We verified that emergence of steeper spectra for large scales and thermalization spectra for small scales. [Preview Abstract] |
Tuesday, November 24, 2009 12:19PM - 12:32PM |
PS.00004: On the turbulent Prandtl number in homogeneous stably stratified turbulence Subhas Venayagamoorthy, Derek Stretch We derive a general relationship for the turbulent Prandtl number $Pr_t$ for homogeneous stably stratified turbulence from the turbulent kinetic energy and scalar variance equations. A formulation for the turbulent Prandtl number $Pr_t$ is developed in terms of a mixing lengthscale $L_M$ and an overturning lengthscale $L_E$, the ratio of the mechanical to scalar time scales $T_L/T_{\rho}=(k/\epsilon)/(\frac{1}{2}\overline{\rho'}^2)/\epsilon_{\rho})$ and the gradient Richardson number $Ri$. We show that our formulation for $Pr_t$ is appropriate even for nonstationary (developing) stratified flows since it does not include the reversible contributions in both the kinetic energy production and buoyancy fluxes that drive the time variations in the flow. Our analysis of direct numerical simulation data of homogeneous sheared turbulence shows that the ratio $L_M/L_E\approx 1$ for weakly stratified flows. We show that in the limit of zero stratification, the turbulent Prandtl number is equal to the inverse of the ratio of the mechanical to scalar time scales, $T_L/T_{\rho}$. We propose a new parameterization for $Pr_t$ in terms of the gradient Richardson number $Ri$ and use data from stably stratified direct numerical simulations to support it. The formulation presented here provides a general framework for calculating $Pr_t$ that will be useful for turbulence closure schemes in numerical models. [Preview Abstract] |
Tuesday, November 24, 2009 12:32PM - 12:45PM |
PS.00005: Double-diffusive convection in narrow-aspect cylinders -- experimental data and CFD simulations Stephen Webb, Reneta Dimitrova, Suhas Pol, H.J.S. Fernando An experimental and numerical investigation has been conducted on the evolution of double-diffusive convection in a narrow-aspect cylinder in the diffusive regime in which the cylinder is subjected to bottom and side-wall heating. The laboratory experiments included filling of a narrow aspect ratio tank with linearly stratified salt-water solution. This fluid of known stratification was heated from the side and the bottom to form multiple mixed layers of fluid separated by diffusive interfaces. A micro conductivity and temperature probe was used to obtain the measurements of salinity and temperature and to discern the location of the interfaces. These results are compared to the case of bottom heating only. The numerical simulations have been performed with the FLUENT computational fluid dynamics (CFD) code. Laminar and turbulent simulations have been conducted for one of the experiments. Comparison of laboratory and numerical results shows reasonable agreement. [Preview Abstract] |
Tuesday, November 24, 2009 12:45PM - 12:58PM |
PS.00006: Parametric study of the spectral characteristics of the internal gravity wave field emitted by a stratified turbulent wake with non-zero net momentum Peter Diamessis, Ammar Abdilghanie The internal wave field emitted by the turbulent wake of a towed sphere in a linearly stratified fluid is studied numerically for a range of sphere-based Reynolds and Froude numbers. The full three-dimensional time-dependent governing equations are solved using a parallel spectral multidomain penalty solver. Hovm\"{o}ller (space-time) diagrams of the horizontal divergence field are constructed in the vertical and lateral directions. Spectral analysis of these diagrams enables the identification of the frequency and wave-number of the most energetic waves. Ensemble averaging at multiple stations in the stream-wise direction is performed to remove the influence of streamwise variability. In agreement with previous studies of wave emission from forced turbulent mixed regions, the spectrum exhibits pronounced peaks in a narrow range of frequencies (and hence angles of propagation) and wave numbers. Finally, the role of intermediate-time secondary instabilities and turbulence inside the wake core on wave radiation is discussed. [Preview Abstract] |
Tuesday, November 24, 2009 12:58PM - 1:11PM |
PS.00007: Wind-driven turbulent oscillating channel flow under a stable stratification Werner Kramer, Herman Clercx, Vinceno Armenio We use large-eddy simulations of a turbulent oscillating channel flow to investigate the effects of wind forcing and stratification. This kind of flow is a model for the tidal driven flows in estuaries. In our studies the wind is aligned with the oscillating tidal flow, leading to a pulsating mean flow. Turbulent fluctuations are enhanced in the shear layers present at the no-slip bottom and below the free-surface boundary. A stable density stratification arises from a constant solar heating of the free surface. We will report on the mixing properties and on the structure of the turbulent flucations of such flows. During phases with high turbulent activity the whole fluid column is well-mixed except for the free-surface layer. When turbulence levels drop the stratification extends over the entire fluid column, but does not penetrate the bottom boundary layer. A stable density stratification suppresses vertical transport. In the unstratified case turbulence generated in top and bottom layer interact. Whether the interaction can be suppressed by a stable density stratification is an interesting point for further investigation. [Preview Abstract] |
Tuesday, November 24, 2009 1:11PM - 1:24PM |
PS.00008: Internal waves in nonuniform stratifications Manikandan Mathur, Brian Doyle, Thomas Peacock Internal waves are propagating disturbances in a stably stratified fluid. Linear internal wave propagation in a stratification with constant Brunt-Vaisala frequency $N$ is well-understood, both theoretically and experimentally. When $N$ varies with the vertical coordinate $z$, however, propagating internal waves bend with respect to the vertical, and can get scattered in a non-trivial manner, depending on the exact profile $N(z)$. Here, we discuss two scenarios, (i) a finite-thickness $N_{2}-$layer sitting atop a semi-infinite $N_{1}-$layer, and (ii) a finite-thickness $N_{2}-$layer sandwiched between two semi-infinite $N_{1}-$layers. The former is shown to support wave beam ducting even in the absence of evanescent layers, and is used to explain the observations of a vanishing wave beam near the upper ocean at the Keana ridge, Hawaii. The latter scenario, in the inviscid limit, is shown to be equivalent to the classical multiple beam light interferometer, and hence results in selective wave transmission based on spatial wavelengths. Results from laboratory experiments and linear viscous theory are presented for both the cases. [Preview Abstract] |
Tuesday, November 24, 2009 1:24PM - 1:37PM |
PS.00009: Slow oscillation of passive scalar fluxes in stratified turbulence Hideshi Hanazaki, Tohru Okamura Scalar fluxes in decaying stratified turbulence are investigated when vertical mean gradients of density and passive scalar coexist. Direct numerical simulations show temporal oscillations of a passive scalar flux which contain a component of double-period oscillation, as predicted by the rapid distortion theory. The slow modes appear always when there are initial density fluctuations. For passive scalars with high Schmidt number (Sc$>$2Pr/(1+Pr), Pr: Prandtl number of the active scalar), the slow modes become dominant at large times, and the turbulent diffusion coefficient of a passive scalar Kc decays more slowly than the turbulent density diffusion coefficient. On the other hand, at low Schmidt numbers (Sc$<$2Pr/(1+Pr)$<$2), slow mode suffers strong initial decay, so that Kc and Krho decay at similar rates. These results illustrate the importance of molecular diffusivity, initial conditions and unsteadiness in strongly stratified turbulence. Applicability of RDT is tested for a range of Reynolds numbers and Froude numbers, showing strong sensitivity to the Froude number but with weak sensitivity to the Reynolds number, in agreement with the scaling analysis. [Preview Abstract] |
Tuesday, November 24, 2009 1:37PM - 1:50PM |
PS.00010: Tangential oscillations of a circular disk in a viscous stratified fluid Stefan Llewellyn Smith, Tony Davis A complete solution is obtained for the wave field generated by the time-harmonic edgewise oscillations of a horizontal circular disk in an incompressible stratified viscous fluid. The linearized equations of viscous internal waves and the no-slip condition on the rigid disk are used to derive sets of dual integral equations for the fluid velocity and vorticity. The dual integral equations are solved by analytic reduction to sets of linear algebraic equations. Asymptotic results confirm that this edgewise motion no longer excites waves in the small-viscosity limit. Broadside oscillations and the effect of density diffusion are also considered. [Preview Abstract] |
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