Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session MH: GFD: General II |
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Chair: Sawan Suman, Texas A&M University Room: Long Beach Convention Center 103C |
Tuesday, November 23, 2010 8:00AM - 8:13AM |
MH.00001: Non-cohesive, unimodal sediment transport in non-hydrostatic dam-break flow Patricio Bohorquez The mixture equations for non-cohesive, unimodal sediment transport in turbulent free-surface flow are derived from the conditionally averaged Navier-Stokes equations. The mathematical similarity between the sediment volumetric concentration $\beta$ and the water phase indicator function $\gamma$ is highlighted in the present model. We take advantage of this fact to formulate an explicit Finite Volume Method in which the pressure equation is formulated as the Schur complement in a segregated pressure-based solver. The numerical scheme was implemented into OpenFOAM\textregistered, an open source software tailored for Computational Continuum Mechanics. The capabitities to account for non-buoyant sediment transport in shallow-water flows is illustrated by computing an erosional dam-break flow. This benchmark depicts the capabilities of the present model to account for erosional processes, as well as to model the boundary between the traction carpet (or bed load layer) and the intermittently suspended sediment, which cannot be sharply defined in hyperconcentrated flows. [Preview Abstract] |
Tuesday, November 23, 2010 8:13AM - 8:26AM |
MH.00002: Gravity currents in stratified fluids Paul Linden This paper discusses the application of a model for the speed of a gravity current in an unstratified ambient fluid to the case where the ambient fluid is stratified with a constant vertical density gradient. The model is based on the fact, first noted by Ungarish \& Huppert (2002), that away from the front of the current the flow is hydrostatic so that the driving pressure difference can be determined from a vertical integral of the density field. An energy-conserving model derived by Shin et al. (2004) for a gravity current in an unstratified fluid is modified to take account of the changed pressure difference. This modified model is compared with lock-release laboratory experiments of Maxworthy et al. (2002) and numerical simulations by Maxworthy et al. (2002), Birman et al. (2007) and White \& Helfrich (2008). Excellent agreement between the predicted and observed current speeds is found for supercritical currents for a wide ratio of dimensionless lock-depths. Subcritical currents, on the other hand, are observed to travel faster than predicted by this model. The reasons for these behaviours are discussed and the roles of the internal waves generated in the ambient stratification are evaluated. [Preview Abstract] |
Tuesday, November 23, 2010 8:26AM - 8:39AM |
MH.00003: Initial lock ratio effects on the dynamics of constant-volume density currents Thomas Bonometti, Marius Ungarish, S. Balachandar The behaviour of non-Boussinesq constant-volume density currents of density \textit{$\rho $}$_{c}$, released from a lock of height $h_{0}$ and length $x_{0}$ into a ambient of height $H$ and density \textit{$\rho $}$_{a}$, are considered. Two-dimensional Navier-Stokes simulations are used to cover a wide range of density ratio 10$^{-2}<$\textit{$\rho $}$_{c}$/\textit{$\rho $}$_{a}<$10$^{2}$ and initial lock ratio 0.5$\le $\textit{$\lambda $}$\le $18.75. The Navier-Stokes results are compared with predictions of a shallow-water model. In particular, we derive novel insights on the influence of the lock aspect ratio \textit{$\lambda $}=$x_{0}$/$h_{0}$ on the shape and motion of the current in the slumping stage. It is shown that a critical value exists, \textit{$\lambda $}$_{crit}$; the dynamics of the current is significantly influenced by \textit{$\lambda $} if below \textit{$\lambda $}$_{crit}$. We conjecture that this critical lock ratio depends on two characteristic time scales, namely the slumping time and the time of formation of the current's head. Comparison with space-time diagrams obtained from the Navier-Stokes simulations show a good agreement. We present a simple analytical model which support the observation that for a light current the speed of propagation is proportional to \textit{$\lambda $}$^{1/4}$ when \textit{$\lambda $}$<$\textit{$\lambda $}$_{crit}$. [Preview Abstract] |
Tuesday, November 23, 2010 8:39AM - 8:52AM |
MH.00004: The dam-break of non-Boussinesq gravity currents of various fractional depth: two-layer shallow-water results Marius Ungarish The dam-break initial stage of propagation of a gravity current released from a lock of length $x_0$ and height $h_0$ into an ambient fluid in a channel of height $H^\ast$ is considered. The system contains heavy and light fluids, of density $\rho_H$ and $\rho_L$, respectively. When the Reynolds number is large, the resulting flow is governed by the parameters $R= \rho_L/\rho_H$ and $H = H^\ast/h_0$. We focus attention on non-Boussinesq effects, when the parameter $R$ is not close to $1$; in this case significant differences appear between the ``light'' (top) current and the ``heavy'' (bottom) current. Using a shallow-water two-layer formulations, we obtain ``exact'' analytical solutions for the thickness and speed of the current and ambient by the method of characteristics. We shown that a jump (instead of a rarefaction wave) propagates into the reservoir when $H < H_{crit}(R)$, and that propagation with critical speed occurs for some combinations of $H,R$. The theory is applied to the full-depth lock exchange $H=1$ problem, and also to more general cases $H >1$. Comparisons to previously published results are discussed. This is a significant extension of the Boussinesq problem (which is recovered by the present solution for $R = 1$), which elucidates the non- Boussinesq effects during the first stage of propagation of lock-released gravity currents. [Preview Abstract] |
Tuesday, November 23, 2010 8:52AM - 9:05AM |
MH.00005: Turbulent Mixing in Gravity Currents with Transverse Shear Brian White, Karl Helfrich, Alberto Scotti A parallel flow with horizontal shear and horizontal density gradient undergoes an intensification of the shear by gravitational tilting and stretching, rapidly breaking down into turbulence. Such flows have the potential for substantial mixing in estuaries and the coastal ocean. We present high-resolution numerical results for the mixing efficiency of these flows, which can be viewed as gravity currents with transverse shear, and contrast them with the well-studied case of stably stratified, homogeneous turbulence (uniform vertical density and velocity gradients). For a sheared gravity current, the buoyancy flux, turbulent Reynolds stress, and dissipation are well out of equilibrium. The total kinetic energy first increases as potential energy is transferred to the gravity current, but rapidly decays once turbulence sets in. Despite the non-equilibrium character, mixing efficiencies are slightly higher but qualitatively similar to homogeneous stratified turbulence. Efficiency decreases in the highly energetic regime where the dissipation rate is large compared with viscosity and stratification, $\varepsilon/(\nu N^2)>100$, further declining as turbulence decays and kinetic energy dissipation dominates the buoyancy flux. In general, the mixing rate, parameterized by a turbulent eddy diffusivity, increases with the strength of the transverse shear. [Preview Abstract] |
Tuesday, November 23, 2010 9:05AM - 9:18AM |
MH.00006: Numerical Simulations of Two-layer Bores Laura Brandt, Kyle Brucker, James Rottman, Doug Dommermuth Implicit LES is used for a systematic study of the energetics of upstream-propagating bores generated by trans-critical flow of two density layers over two-dimensional and three-dimensional topography. The results of these simulations are compared with solutions of the MCC equations for weakly nonlinear two-layer bores, to establish the range of validity of this approximation, and are used to improve classical hydraulic theories for two-layer bores. [Preview Abstract] |
Tuesday, November 23, 2010 9:18AM - 9:31AM |
MH.00007: Numerical Prediction of Wave Forces on a Breakwater under Tsunami Loading Kyle A. Brucker, Mary Beth Oshnack, Thomas T. O'Shea, Dan Cox, Douglas G. Dommermuth Numerical Flow Analysis (NFA) predictions of wave propagation and wave- impact loading are compared to the Oregon State University (OSU) O.H. Hinsdale Wave Research Laboratories Tsunami experiments (Oshnack, et al. 2009). The simulations were designed to replicate the experiments such that a soliton is sent down a wave flume, runs up a small beach, and impacts with a breakwater. The soliton is 1.2m high in a water depth of 2.29m and travels over 61m before hitting the breakwater. The NFA predictions are compared to laboratory measurements of a) free-surface elevation at several locations down the flume and b) impact pressure at the base of the breakwater. The free-surface elevations as predicted by NFA are in excellent agreement with the experimental measurements. This shows that NFA can simulate the propagation of waves over long distances with minimal amplitude and dispersion errors. Pressures that are induced by the jet are important because in certain coastal areas buildings must be designed to sustain Tsunami loads. The pressure predictions over the duration of breaking agree very well with laboratory measurements. The peak pressures predicted by NFA are in excellent agreement with experiments. [Preview Abstract] |
Tuesday, November 23, 2010 9:31AM - 9:44AM |
MH.00008: Alternative analysis of the temperature distribution in the interior ocean Sheng-Qi Zhou, Kai Li, Ling Qu In the interior ocean(below the thermocline), temperature variation is less influenced by the wind Ekman upwelling and the surface heating, and it is mainly dominated by the balance between the downward mixing of heat by turbulence and the upward transport of heat by the vertical current. In 1966, Munk proposed one-dimension advective-diffusive model, and he found that the temperature and the depth has an exponential relationship when the upward velocity and the the vertical eddy diffusivity are assumed to be constant. We have analyzed the global ocean potential temperature in 2008 from the ARGO delay model temperature dataset. It has been found that the exponential relationship between potential temperature and depth can be found only in some regions, such as in the Indian Ocean. The power law relationship has been found in other regions, such as in the North Pacific Ocean. The different relationships may suggest that the vertical eddy diffusivity has different dependencies on the depth, which may be useful to the global ocean models. [Preview Abstract] |
Tuesday, November 23, 2010 9:44AM - 9:57AM |
MH.00009: Energy spectra of stably stratified turbulence Yoshifumi Kimura, Jackson Herring We investigate energy spectra of stably stratified turbulence using direct numerical simulations (DNS) at a resolution of $1024^3$. 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 decomposed into the vortex mode and the wave mode. In general, both the wave and vortex spectra are consistent with a Kolgomorov--like $k^{-5/3}$ range at sufficiently large k. At large scales, and for sufficiently strong stratification the wave spectrum is a steaper $k_{\perp}^{-2}$, while that for the vortex component is consistent with $ k_{\perp}^{-3}$. Here $k_{\perp}$ is the horizontally gathered wave numbers. In contrast to the horizontal wave number spectra, the vertical wave number spectra show very different features. We can observe clear $k_z^{-3}$ dependence for small scales while the large scales show rather flat spectra. We link these spectra to the 2nd order structure functions of the velocity correlations in the horizontal and vertical directions. Finally we study the inviscid limit in which the highest wave-numbers are progressively thermalized, leaving the smaller wave numbers to adjust to their internal dynamics {\it sans} dissipation. In this case, we see--for the non-thermalized components--similar dynamics as that for the finite Reynolds case. [Preview Abstract] |
Tuesday, November 23, 2010 9:57AM - 10:10AM |
MH.00010: Numerical simulations of the transport of passive scalars around obstacles in tidal flows Hyeyun Ku, Subhas Venayagamoorthy This research is centered on understanding the mixing and transport of passive scalars around obstacles with and without drag in tidal flows. High-resolution two- and three-dimensional numerical simulations were performed of a passive scalar in an idealized domain to study the effects of drag and different flow conditions (tides and currents) on the evolution of a passive scalar. The horizontal dispersion coefficient is quantified as a function of three non-dimensional parameters namely: the drag coefficient, $C_{d}$ (imparted by the obstacle); the ratio of the tidal to mean flow velocity amplitudes, $U_{T}/U_{M}$; and an oscillatory tidal excursion length parameter, $2U_{T}/{\omega}D$, where $\omega$ is the frequency and $D$ is the diameter of an obstacle.The drag exerted by a porous obstacle blocks the flow partially and causes the deceleration of the flow, the shedding of vortices and the formation of a downstream wake. Results of the scalar field with and without drag for both uni-directional and oscillatory flow fields are presented. The simulation results highlight the complex dispersion patterns around submerged obstacles and provide an understanding on pollutant dispersion in the atmosphere such as urban cities and in water bodies such as the coastal ocean where vegetation tends to obstruct flow. [Preview Abstract] |
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