Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session EG: Geophysical Fluid Dynamics II |
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Chair: S. Balachandar, University of Florida Room: Tampa Marriott Waterside Hotel and Marina Florida Salon 5 |
Sunday, November 19, 2006 4:15PM - 4:28PM |
EG.00001: Energy dissipation in shallow-water models for high-Re gravity currents Marius Ungarish The motion of a 2D gravity current, released from a lock in a horizontal channel is considered. Attention is focused on the energy transfers (between forms and fluids) and dissipation. The analysis uses the two-layer inviscid shallow-water (SW) formulation (with nose Froude numbers, Fr, given by Benjamin's and other formulas) and is backed by numerical Navier-Stokes results. We show that the current performs significant work on the ambient. In general, the increase of kinetic energy of the inviscid SW (or similar two-layer vertically-averaged) system cannot fully recover the decay of potential energy. This imbalance reproduces the classical dissipation predicted by Benjamin's steady-state analysis. We call this ``averaged flow dissipation''. This dissipation typically increases with the depth ratio of ambient to lock, and hence all deep SW currents (in particular the one-layer SW model predictions) with finite positive Fr are dissipative. However, the link between the ``averaged flow dissipation'' and the irreversible loss of energy in a real gravity current is missing. The implications on the validity of the SW predictions are discussed. [Preview Abstract] |
Sunday, November 19, 2006 4:28PM - 4:41PM |
EG.00002: Gravity currents in an ambient flow Anja Slim, Herbert Huppert Gravity currents occur whenever fluid of one density flows, predominantly horizontally, into fluid of a different density. In natural and man-made situations they are frequently generated in the presence of a flowing ambient. For example, both volcanic ash clouds and toxic gas releases are affected by atmospheric winds, while river plumes and pollutant releases in the sea are affected by marine currents. We theoretically study the canonical problem of a homogeneous, high Reynolds number gravity current generated by a constant source in a uniform ambient flow. In order to model it we employ a shallow-water formulation and present both numerical and asymptotic solutions. Of interest is how the current evolves and its dimensions, particularly its maximum upstream extent. We also briefly describe unusual features of gravity currents generated by a slowly sedimenting particle load. [Preview Abstract] |
Sunday, November 19, 2006 4:41PM - 4:54PM |
EG.00003: Turbulent structures on gravity currents fronts Mariano Cantero, S. Balachandar, Marcelo Garcia Gravity currents are flows driven by horizontal pressure gradients generated due to the action of gravity over two fluids with density difference. This work presents highly resolved simulations of planar and cylindrical gravity currents for Reynolds numbers ranging from about 1000 to about 10000. Soon after release the interface between light and heavy fluids rolls up forming Kelvin-Helmholtz vortices. This process continues only during the slumping and inertial phases. The coherent Kelvin-Helmholtz vortices undergo spanwise or azimuthal instabilities and eventually breakdown into small scale turbulence. In the case of planar currents this turbulent region extends over the entire body of the current and it is populated with hairpin vortices. Also during the early stage of the flow development, incipient lobes and clefts start to form at the lower frontal region. These instabilities grow in size and extend to the upper part of the front. Lobes and clefts continuously merge and split and, thus result in a complex pattern that dynamically evolves. In this work we show the relation between the flow structures mentioned above and the local flow patterns and bottom shear stress patterns. For the case of the cylindrical current, laboratory experiments have been performed at the higher Reynolds numbers and the results have been compared to the simulation results. The agreement between numerical results and experimental observations is good. [Preview Abstract] |
Sunday, November 19, 2006 4:54PM - 5:07PM |
EG.00004: Gravity Current - Submarine Structure Interaction: Hazard Analysis via High-Resolution Flow Simulations Esteban Gonzales-Juez, George Constantinescu, Eckart Meiburg Two-dimensional large eddy simulations of a compositional lock-release gravity-current interacting with a submerged square cylinder are performed in order to investigate the governing physical mechanisms. The effect of the Reynolds and Schmidt numbers, and of the gap separating the floor and the cylinder, are investigated for both full- and partial-depth release gravity currents. The results are validated with available experimental measurements. The transient forces during the initial impact stage are seen to be several times higher than the forces encountered during the later quasi-steady stage. The density stratification, which is time dependent and can be stable or unstable, has a clear influence on the flow structures that develop. Such flow structures are described in detail and related to the time variation of flow forces and floor shear stresses. The latter are discussed in the context of potential erosional patterns near the structure. [Preview Abstract] |
Sunday, November 19, 2006 5:07PM - 5:20PM |
EG.00005: Gravity Currents and Internal Waves in a Stratified Fluid Brian L. White, Karl R. Helfrich Properties of a gravity current of uniform density $\rho_c$, propagating into a stratified ambient with a general density profile, $\rho(z)$, are studied numerically and theoretically. For a gravity current of height $h$, the isopycnal displacement and steady propagation speed, $U_c$, can be calculated using Long's equation and a flow force balance (c.f., Ungarish 2006). However, such methods neglect unsteady internal waves. Solutions do exist for internal solitary waves with a trapped core of stagnant fluid, which reach a finite amplitude limit unique to each $\rho(z)$, known as the conjugate state (c.f., Lamb and Wilkie 2004). We show that the conjugate state is equivalent to the energy-preserving gravity current solution. Numerical simulations of the dam-break initial value problem using a two-dimensional non-hydrostatic model verify that the gravity current can excite large amplitude internal waves. The interaction between the waves and the current depends on the Froude number, $Fr = U_c / U_{cs}$, where $U_{cs}$ is the conjugate state wave speed. When the available potential energy (APE) of the dammed fluid is comparable to or larger than the total energy of the conjugate state, we find that $Fr\rightarrow1$, and the current speed is well-predicted by the energy-preserving theory. However, when the APE is smaller, the gravity current is subcritical ($Fr<1$), and internal waves are present ahead of the current. The results illustrate the connection between the gravity current and the wave-guide characteristics of the ambient stratification. [Preview Abstract] |
Sunday, November 19, 2006 5:20PM - 5:33PM |
EG.00006: Measurement of Entrainment from an Oceanic Overflow Facility Jun Chen, Philippe Odier, Michael Rivera, Robert Ecke The mixing and entrainment process existing in oceanic overflow, e.g. Denmark Strait Overflow (DSO), affects the global thermohaline circulation. Due to limited spatial resolution in global climate prediction simulations, the small-scale dynamics of oceanic mixing must be properly modeled. A laboratory oceanic overflow simulation facility is built to investigate the fine structure of the entrainment and mixing. Inside a water tank, a flow injection is introduced along an inclined plate into a denser environment. Simultaneous PIV and PLIF measurements are conducted to visualize and quantify the flow structure. The obtained data is used to examine the entrainment assumption and the relevant entrainment constant. [Preview Abstract] |
Sunday, November 19, 2006 5:33PM - 5:46PM |
EG.00007: Decaying Turbulence with Non-uniform Density Stratification David Hebert, Stephen de Bruyn Kops Density stratification in environmental flows is often non-uniform in height (e.g. thermohaline staircase, atmospheric layer transition). The description of these flows, however, is often considered in terms of the average density change with height, and in numerical simulations this simplification is almost always made because it greatly simplifies the calculations. In this presentation, high resolution direct numerical simulations of an idealized turbulent late wake with non-uniform density stratification are analyzed to understand the consequences of assuming linear stratification. The simulations are initialized with a vortex street, each vortex having a vertical mean velocity profile $\mathrm{sech}^2(z/\delta_U)$. An ambient density $\overline{\rho}=\mathrm{tanh}(z/\delta_\rho)$ and stratification profile $d\overline{\rho}/dz = \mathrm{sech}^2(z/\delta_\rho)$ are imposed on the flow. The vertical scale of $d\overline{\rho}/dz$ is varied by changing $\delta_\rho$ while holding $\delta_U$ constant. An analysis of flow behavior for several ratios $DR=\delta_\rho / \delta_U$ will be presented, including methodology for calculating potential energy for non-uniform density stratification. [Preview Abstract] |
Sunday, November 19, 2006 5:46PM - 5:59PM |
EG.00008: ABSTRACT WITHDRAWN |
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