Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session E13: Geophysical: General III |
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Chair: James Rottman, University of California, San Diego Room: 27A |
Sunday, November 18, 2012 4:45PM - 4:58PM |
E13.00001: Trapped subsurface oil plumes and critical escape phenomena Chung-Nan Tzou, Roberto Camassa, Zhi Lin, Rich McLaughlin, Keith Mertens, Brian White A critical phenomenon concerning the escape/trap of buoyant miscible plumes rising through strongly stratified fluids is presented experimentally and theoretically. The criticality is determined by the distance between plume release height and depth of ambient density transition. For fluid released closer to the background density transition than this critical distance, the buoyant fluid escapes and rises indefinitely. For fluid released further than this critical distance, the buoyant fluid is forever trapped within the fluid. Two new mathematically exact formulas will be presented for the cases of linear and sharp ambient stratification and they show quantitative agreement with experiments. The new solution for linear stratification is analyzed in the limit of vanishing transition layer thickness. The analytic solution for sharp stratification is shown to accurately estimate the depth at which subsurface plumes trapped during the Deepwater Horizon oil disaster. Also, a dimensional analysis argument is presented which captures the essential physics to provide a simple understanding of this phenomenon. [Preview Abstract] |
Sunday, November 18, 2012 4:58PM - 5:11PM |
E13.00002: Numerical simulation of jets generated by a sphere moving vertically in stratified fluids Hideshi Hanazaki, Shota Nakamura Numerical studies are performed on the flow past a sphere moving vertically at constant speeds in a stratified fluid. Initial unsteady development of the flow shows that violation of density conservation due to diffusive effects on the sphere surface is the key process for the generation of jets observed in the experiments, since the fluid which was originally at dragged downward would indefinitely long distance unless the isopycnal surface is not teared off. Initially, when the diffusion is negligible, the density is conserved so that the density contours are simply pulled down by the sphere. As the diffusion becomes larger, fluid of unconserved density generates a jet. The violation of density conservation on the sphere surface occurs first near the equator of the sphere where the diffusion is large, and the diffusion becomes larger poleward to finally become effective at the rear/upper stagnation point. [Preview Abstract] |
Sunday, November 18, 2012 5:11PM - 5:24PM |
E13.00003: On the validity of Kraichnan scalings for forced two-dimensional turbulence Jerome Fontane, David Dritschel, Richard Scott We examine the validity of the scaling laws derived by Kraichnan (1967) for forced two-dimensional turbulence. We use a new numerical technique (Dritschel \& Fontane 2010) to reach higher Reynolds number than previously accessible with classical pseudo-spectral methods. No large scale friction or hypo-diffusion is used in order to avoid any distortion of the inverse cascade and to be in agreement with the theoretical framework of Kraichnan. Both spectral and spatial forcing are considered and statistical convergence is obtained through large simulation ensembles. A steeper energy spectrum proportional to $k^{-2}$ is observed for the inverse cascade in place of the classical $k^{-5/3}$ prediction. This steepening is shown to be associated with a faster growth of energy at large scales, scaling like $t^{-1}$ rather than Kraichnan's prediction of $t^{-3/2}$. The deviation from Kraichnan's theory is related to the emergence of a vortex population dominating the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum. [Preview Abstract] |
Sunday, November 18, 2012 5:24PM - 5:37PM |
E13.00004: Perturbations from 2D Navier-Stokes: rapidly rotating and weakly stratified Boussinesq flow Jared Whitehead, Beth Wingate Relying on the derivation of ``slow'' equations in the limit of rapid rotation (Rossby number 0) and weak stratification (Froude number 1), we demonstrate that the 3D Boussinesq equations (for any Rossby and Froude numbers) can be written as 2D Navier-Stokes plus a Reynolds stress, and two passive advection equations (with additional active Reynolds stresses). The impact this formulation has on the exchange of horizontal and vertical kinetic energy with potential energy is discussed, as well as the breakdown of the potential enstrophy into components relative to a passive density stratification. These results are elucidated with direct numerical simulations that consider rapid rotation (small but finite Rossby number) with weak stratification. [Preview Abstract] |
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