Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session D23: Geophysical Fluid Dynamics: Stratified Turbulence II |
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Chair: Robert Ecke, Los Alamos National Laboratory Room: 2001 |
Sunday, November 23, 2014 2:15PM - 2:28PM |
D23.00001: A Sweeping based Kinematic Simulation for the Stably Stratified Surface Layer Aditya Ghate, Sanjiva Lele A Kinematic Simulation (KS) for a statistically stationary and stably stratified surface layer is proposed. The Fourier coefficients are obtained by numerically solving the linearized NS equations with Boussinesq approximation in spectral space, under the assumption of ``rapid'' deformation (RDT) due to combined shear and stratification. The linearization of RDT, which is unrealistic for the surface layer, is rectified using Mann's (JFM, 1994) idea of wavenumber dependent eddy lifetime. The input parameters required by the KS are estimated using either Monin-Obukhov theory, or an appropriate Second Moment Closure. In order to overcome the frozen turbulence hypothesis made in the Mann model, we incorporate inter-scale ``sweeping'' of eddies following the ideas of Fung, et. al. (JFM, 1992), along with temporal decorrelation associated with the natural eddy time scale. The solenoidal velocity field generated by the KS allows inclusion of a wide range of scales with correct space-time correlations, making it ideal to investigate particle dispersion in a stably stratified environment, and can also serve as inflow for the study of Wind Farm-PBL interactions. The effect of varying Obukhov length will be discussed by analyzing the frozen Eulerian spectra and Lagrangian particle dispersion. [Preview Abstract] |
Sunday, November 23, 2014 2:28PM - 2:41PM |
D23.00002: An Immersed Boundary Method for the simulation of turbulent stratified flows over rough topography Narsimha Rapaka, Sutanu Sarkar An Immersed Boundary Method (IBM) is developed to simulate stratified flows over rough topography using a Cartesian grid. The solver is validated in the problem of tidal flow over a laboratory-scale (order of few meters) smoothed triangular ridge. The results including phasing of turbulence, statistics and baroclinic wave flux agree well with the those obtained using in the DNS studies of Rapaka et al. (JFM 2013) and Jalali et al. (JFM 2014) performed with a body-fitted grid. The bottom drag is parameterized using the DNS data and tested for simulations using coarser grids. The beam thickness is increased with the boundary layer being under-resolved but the baroclinic wave flux agree well. Phasing of turbulence is qualitatively similar at both low and high Excursion numbers (Ex). Integrated TKE and dissipation are of the same order as in the DNS. Large Eddy Simulations (LES) are performed on a large scale topography, of the order of few kilometers, with the same Ex and the criticality parameter but significantly larger Reynolds number. The baroclinic response is stronger than the laboratory scale model owing to the larger length of critical slope. The baroclinic flux as well as turbulence energetics and phasing are studied. [Preview Abstract] |
Sunday, November 23, 2014 2:41PM - 2:54PM |
D23.00003: Mixing structures in stratified shear flow: Dependence on gradient Richardson number Robert Ecke, Philippe Odier, Jun Chen We report experimental measurements of velocity and density fields of wall-bounded stratified shear-flow turbulence as a function of shear velocity and density difference. A turbulent channel flow exits a nozzle onto the underside of a flat transparent plate at fixed velocity $4 < U < 8$ cm/s and with a fractional density difference $0.0027 < \Delta \rho/\rho < 0.0054$ between the inflowing fluid and the quiescent fluid in the tank. Simultaneous velocity and density measurements are obtained using PIV and PLIF, respectively (see P. Odier, J. Chen, and R.E. Ecke, J. Fluid Mech. 794, 498 (2014) for experimental details). For a resultant range of gradient Richardson numbers $0.05 < Ri_g < 0.5$, we compute and compare different measures of turbulent mixing obtained from direct measurement of turbulent dissipation, Reynolds stress, buoyancy flux, and density and velocity gradients. In particular, we obtain mixing lengths, Ozmidov and shear lengths, Thorpe lengths, buoyancy Reynold number, flux Richardson number, diapycnal mixing parameter, and intermittency properties of flows as a function of gradient Richardson number. These quantities characterize the transition from shear dominated flow at low $Ri_g$ to stratification dominated behavior at larger $Ri_g$. [Preview Abstract] |
Sunday, November 23, 2014 2:54PM - 3:07PM |
D23.00004: Evaluation of the standard $k$-$\epsilon$ closure scheme for modeling stably stratified wall-bounded turbulence Amrapalli Garanaik, Farid Karimpour, Subhas Venayagamoorthy Reynolds-averaged Navier-Stokes (RANS) turbulence models are widely used for modeling stratified turbulent flows. The focus of this study is to account for the effect of the buoyancy forces in the two-equation standard $k$-$\epsilon$ closure scheme for modeling stably stratified wall-bounded turbulence. The buoyancy parameter ($C_{\epsilon3}$) is analytically revisited and it is found that it can be neglected in the evolution equation of the dissipation rate of the turbulent kinetic energy. Furthermore, we use different propositions for the turbulent Prandtl number ($Pr_t$) to assess their efficacy for modeling stratified wall-bounded flows. Numerical simulations are implemented in a 1-D water column model and the results are compared with data of direct numerical simulation of stably stratified channel flow. [Preview Abstract] |
Sunday, November 23, 2014 3:07PM - 3:20PM |
D23.00005: Porous Sphere in Stratified Environments: Entrainment and Diffusion Roberto Camassa, Claudia Falcon, Shilpa Khatri, Richard McLaughlin A theoretical, experimental, and numerical study of porous spheres falling in stratified fluids will be presented. The systematic justification of asymptotic regimes resulting in asymptotic models with ``heat bath" boundary conditions for salinity are derived in low Reynolds number regimes. Violation of these asymptotic scalings will be discussed in the context of experiments and mathematical modeling. In particular the presence of a salt depletion or enrichment wake left behind by the settling, ab/de-sorbing sphere, and its competition with entrainment, will be presented and highlighted. Experimental results with microporous spheres as well calibrated manufactured drilled spheres will be compared. [Preview Abstract] |
Sunday, November 23, 2014 3:20PM - 3:33PM |
D23.00006: LIF measurements of the flow past a sphere descending in a stratified fluid Shinsaku Akiyama, Shinya Okino, Hideshi Hanazaki When a sphere descends in the stratified salt water, a strong upward jet is often generated above the sphere. In this study, the flow is observed by the laser induced fluorescence (LIF) method, assuming the proportionality between the concentrations of salt and fluorescent dye. In particular, the radius of the jet and the thickness of the density boundary layer on the sphere surface are measured. It is found that the radius of the jet is proportional to both $Fr^{1/2}$ ($Fr$: Froude number) and $Re^{-1/2}$ ($Re$: Reynolds number), in agreement with the simple dimensional analysis. The density boundary layer on the sphere surface also becomes thinner as $Fr$ decreases or $Re$ increases, showing a similar trend. These results are explained by a scenario that the fluid in and near the density boundary layer on the sphere moves up along the sphere surface, changing its density across the isopycnals to finally form a jet above the sphere. [Preview Abstract] |
Sunday, November 23, 2014 3:33PM - 3:46PM |
D23.00007: The near wake of a towed grid in a stratified fluid Xinjiang Xiang, Trystan Madison, Prabu Sellapan, Geoffrey Spedding Though much detailed quantitative information has been assembled to describe the late wakes behind various objects in stably-stratified fluids, much less is known about the early stages when the flow begins to feel the effects of the background density gradient. Here we report on experiments on the early wake of a towed grid, with $Re \in \{2700, 11000\}$, and $Fr \in\{0.6,9.1\}$. Internal waves are found for all $Fr$, originating as the flow turns around the obstacle, with wavelength linearly proportional to $Fr$ and approximately constant amplitude. The mean centerline stream-wise velocity is strongly affected by the lee waves, and so depends on $Fr$. Strong vertical shear is observed at the wake edge, leading to overturning through Kelvin\--Helmholtz instabilities. Stratified turbulence develops up to $Nt \approx 10$ (except at the lowest $Fr$), with buoyancy Reynolds number independent of $Fr$ at higher $Nt$. Developing anisotropy in the horizontal and vertical directions in the early wake is described for both mean and fluctuating quantities. The data and their variation with $Re$ and $Fr$ comprise a start towards making a generally available database for detailed comparisons with numerical experiment. [Preview Abstract] |
Sunday, November 23, 2014 3:46PM - 3:59PM |
D23.00008: ABSTRACT WITHDRAWN |
Sunday, November 23, 2014 3:59PM - 4:12PM |
D23.00009: Mixing Efficiency in Stratified Turbulent Jets Chung-Nan Tzou, Roberto Camassa, Sian Lewis-Bevan, Richard McLaughlin, Nathan Perreau Building upon prior results of the authors establishing rigorously the optimal mixing profile of a turbulent buoyant jet in a special class of stratified environments, a substantial expansion to a broader family of background stratifications is considered both experimentally and analytically with some surprising observations. [Preview Abstract] |
Sunday, November 23, 2014 4:12PM - 4:25PM |
D23.00010: Mixing efficiency in shear-driven and convective turbulent stratified flows Alberto Scotti, Brian White DNS of steady-state and time-evolving mixing layers are used to calculate the mixing efficiency under different forcing conditions. Two basic mechanisms to sustain turbulence are considered: shear acting against a stably stratified background, and zero-shear, but convectively unstable regions embedded in a stratified fluid. When turbulence is produced by shear the mixing efficiency can be collapsed in terms of the buoyancy Reynolds number for values of the latter less than 20, whether the flow is steady or time evolving. For higher values, no such collapse exists. The efficiency of time-evolving shear-driven mixing layers approaches a constant value during the turbulent phase of about 0.15. In steady-state flows, on the contrary, the mixing efficiency is controlled to leading order by the externally imposed Richardson number. We show that the difference is due to the different way in which buoyancy and momentum are fed into the mixing layer. In overturning mixing layers we observe larger values of the mixing efficiency, approaching 1/2. The results suggests that the practice of adopting a constant mixing efficiency in parameterizing shear-driven episodic mixing events is justified in environmental flows. [Preview Abstract] |
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