Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session JL: Geophysical: General II |
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Chair: P. Marcus, University of California, Berkeley Room: Salt Palace Convention Center 250 F |
Monday, November 19, 2007 3:35PM - 3:48PM |
JL.00001: Lagrangian coherent structures in geophysical flows Philip Du Toit In aperiodic flows, particle trajectories may appear to be chaotic and unstructured. However, using finite time Lyapunov exponents we are able to detect sharp separatrices that determine the underlying structure of the flow. These separatrices are barriers to transport and form the boundaries of almost invariant regions. Computing these Lagrangian Coherent Structures (LCS) for oceanic and atmospheric flows in two and three dimensions allows us to visualize the mixing processes and elucidates the underlying mechanisms by which particle transport and mixing occur. We will show that the LCS reveal many of the familiar elements from classical geometric dynamics including hyperbolic points, intersections of stable and unstable manifolds, homoclinic tangles, and transport via lobe dynamics. These methods have broad application to many geophysical flows. In particular, we observe that mixing in hurricanes and tropical storms is dominated by transport via lobe dynamics. Identifying the LCS allows us to quantify material entrainment and detrainment from the storm center. Precisely the same transport mechanism is also observed in flows surrounding ocean eddies. [Preview Abstract] |
Monday, November 19, 2007 3:48PM - 4:01PM |
JL.00002: ABSTRACT WITHDRAWN |
Monday, November 19, 2007 4:01PM - 4:14PM |
JL.00003: Effects of Dispersion on Vortical and Wave Modes in 3D Rotating Stratified Flows Leslie Smith, Jai Sukhatme We study the growth and spectra of energy in the vortical and wave modes of a forced, 3D rotating stratified fluid as a function of $\epsilon = f/N$, where $f, N$ are the Coriolis parameter and Brunt-Vaisala frequency. The Froude and Rossby numbers are comparable and much less than one. The inquiry is motivated by analytical work suggesting asymmetry about $\epsilon =1$. For $\epsilon \le 1$ the wave mode energy saturates and the ensuing forward cascade is an efficient means of dissipating ageostrophic energy. As $\epsilon$ decreases, the wave spectra steepen from $k^{-1}$ to $k^{-5/3}$. When $\epsilon > 1$ the wave mode energy never saturates and eventually dominates the total energy. With regard to the vortical modes, for $\epsilon \le 1$, the signatures of 3D quasi-geostrophy are clearly evident. In contrast, for $\epsilon > 1$ and increasing, the vortical modes contain a progressively smaller fraction of the total energy and the 3D quasi-geostrophic subsystem disappears. [Preview Abstract] |
Monday, November 19, 2007 4:14PM - 4:27PM |
JL.00004: The Rossby Wave Extra Invariant in the Physical Space Alexander Balk, Toshio Yoshikawa We investigate {\it the extra invariant} for the Rossby wave dynamics. This invariant has been connected to {\it zonal jets}. We find an explicit expression of this invariant in the physical (or coordinate) space and show that the invariant is indeed physically important. [Preview Abstract] |
Monday, November 19, 2007 4:27PM - 4:40PM |
JL.00005: New Intermediate Models for Rotating Shallow Water and Boussinesq Flows Mark Remmel, Leslie Smith We derive new intermediate models to include physics beyond quasi-geostrophic (QG) dynamics in the context of rotating shallow water (RSW) flow. It is known that the 2D QG reduced model results from restricting the nonlinear interactions to include only the vortical eigenmodes of the linearized equations. Our new models are constructed by progressively adding more nonlinear interactions involving gravity waves. The simplest new model, denoted PPG, adds all interactions involving only one gravity wave. Whereas 2D QG has cyclone/ anticyclone symmetry, the PPG model quantitatively captures anticyclone dominance observed in full RSW decay. New intermediate models are also derived to move beyond 3D QG in the context of the Boussinesq equations. Our approach is non-perturbative. [Preview Abstract] |
Monday, November 19, 2007 4:40PM - 4:53PM |
JL.00006: Stability, cyclone-anticyclone asymmetry and frequency selection in rotating shallow-water wakes Thomas Dubos, Gaele Perret, Alexandre Stegner, Jean-Marc Chomaz, Marie Farge Atmospheric and oceanic wakes past islands or mountains present, or not, similarities with the von-Karman vortex street. Observations amd rotating-tank experiments show that cyclone-anticyclone asymmetry may occur, and that shedding frequencies (Strouhal numbers) may differ. Using direct numerical simulation and linear stability analysis, we explain and interpret these observations and characterize the dynamics of a single shallow layer of rotating fluid downstream a cylindrical obstacle. Especially, we show that while the wake is symmetric in the quasi-geostrophic (QG) regime, the frontal-geostrophic (FG) regime favors the emergence of anticyclones. This selection takes place at the linear stage and is exacerbated in subsequent, nonlinear stages. Furthermore we find that the wake emerges from a genuine, global instability only in a certain region of the parameter space, including the QG regime. Outside of this region, and especially in the FG regime, the wake emerges only as a response to upstream noise. However very low levels of upstream noise are sufficient to trigger a fully nonlinear wake with a well-defined shedding frequency. [Preview Abstract] |
Monday, November 19, 2007 4:53PM - 5:06PM |
JL.00007: Planetesimal Formation: Trapping Dust in 3D Vortices Xylar Asay-Davis, Joseph Barranco, Philip Marcus Scenarios of planetesimal formation have been plagued by a difficult puzzle: micron-sized dust grains that accompany the gas around a new star at extraordinarily low density ($\sim $10$^{-10}$ g/cm$^{3})$ must somehow clump together to form kilometer-sized objects and eventually planets. At such low densities, direct interaction between grains is negligible and the kinetic energy of grains is always too large to allow gravitational collapse to occur. Although gravity pulls dust grains toward the mid-plane of the protoplanetary disk, our numerical simulations show that shear instabilities disrupt the dust layer before a Goldreich-Ward gravitational instability could occur. However, 3D, long-lived vortices provide just the kind of environment required to concentrate dust enough for agglomeration or gravitation to create planetesimals. Our numerical simulations have shown that 3D vortices exist as stable, long-lived solutions to the equations of motion of the gas in the disk around a star. These simulations indicate that 3D vortices form from breaking internal gravity waves that are generated by turbulent motion of the gas or by the interaction of existing 3D vortices. The simulations also show that 3D vortices are stable attractors of dust grains, even when the vortices occur off the mid-plane of the disk, where the ``downward'' pull of gravity must be counterbalanced by ``upward'' gas drag. [Preview Abstract] |
Monday, November 19, 2007 5:06PM - 5:19PM |
JL.00008: Length of a lava tube Miranda Holmes, John Whitehead Motivated by the existence of long lava tubes in certain types of volcanic flows, we study the question of a viscous melted substance flowing in a cold circular tube. As the fluid flows it cools and solidifies at the tube radius and we investigate the question ``how far can the fluid flow and remain liquid?'' A theoretical solution is derived for the liquid radius and the temperature profiles in liquid and solid. It is shown that if fluid is maintained at constant flux the distance can be infinite, but if the fluid is maintained at constant pressure difference across the length of the tube, then a there is a maximum length which depends on the Peclet number and a dimensionless temperature. Conditions are derived for which the radius is unstable. These predictions are investigated with numerical and laboratory experiments. [Preview Abstract] |
Monday, November 19, 2007 5:19PM - 5:32PM |
JL.00009: ABSTRACT WITHDRAWN |
Monday, November 19, 2007 5:32PM - 5:45PM |
JL.00010: Chevrons formation in laminar erosion Olivier Devauchelle, Christophe Josserand, Pierre-Yves Lagree, Stephane Zaleski, Khanh-Dang Nguyen, Luce Malverti, Eric Lajeunesse When eroded by laminar free-surface flows, granular substrates may generate a rich variety of natural patterns. Among them are dunes, similar to the ones observed by Charru and Hinch in a Couette cell (Charru F, Hinch EJ ; Ripple formation on a particle bed sheared by a viscous liquid. Part 1. Steady flow ; JOURNAL OF FLUID MECHANICS 550: 111-121 MAR 10 2006). Chevron-shaped instabilities as those found on the sea-shore, can also be observed, sometimes in competition against dunes formation. These were first pointed out by Daerr et al. when pulling a plate covered with granular material out of a bath of water (Daerr A, Lee P, Lanuza J, et al. ; Erosion patterns in a sediment layer ; PHYSICAL REVIEW E 67 (6): Art. No. 065201 Part 2 JUN 2003). Both instabilities can grow in laminar open-channel flows, an experimental set-up which is more easily controlled. The mechanisms leading to the formation of these patterns are investigated and compared. Whereas dunes formation requires vertical inertia effects, we show that chevrons may result from the non-linear evolution of bars instability, which may grow even in purely viscous flows. [Preview Abstract] |
Monday, November 19, 2007 5:45PM - 5:58PM |
JL.00011: Level set simulation of precipitation and dissolution of flow-transported reactive solutes in porous media Xiaoyi Li, Hai Huang, Paul Meakin The coupled process of flow, transport and precipitation/dissolution of reactive solutes in porous media is important in a large variety of scientific and engineering areas. Examples include evolution of geological fractures, acid stimulation in petroleum recovery, and retardation of contaminant transport in groundwater. In this work, we develop an innovative numerical tool to simulate reactive flow and structure evolution at the pore scale. Convection, diffusion, and chemical reaction resulting in changes in the pore space geometry are treated simultaneously by solving coupled momentum and solute transport equations. The reaction-induced evolution of solid grain surface is captured using a level set method. We obtain a more elegant sub-grid representation of the interface using a level set approach, instead of the pixel-based representation of the interface used in most lattice-Boltzman and cellular-automata methods. The model is validated against analytical solutions for simplified geometries. The patterns of precipitation/dissolution in a simple throat as well as a random porous matrix are discussed. The quantitative relationships among hydraulic properties (e.g. permeability and porosity) of the porous media are obtained from simulation. The results elucidate the underlying mechanism of the reaction-induced property changes in porous media. [Preview Abstract] |
Monday, November 19, 2007 5:58PM - 6:11PM |
JL.00012: Combined Infrared and Hyperspectral Imagery in the Riverine Environment Geoffrey B. Smith, W. Joseph Rhea, George O. Marmorino Results from a recent NRL field experiment will be discussed. The program was focused on the Pearl River, a fairly slow, meandering river, located in Mississippi, which empties into the Gulf of Mexico. Data from airborne infrared (IR) and hyperspectral imagers will be presented. The IR sensor is sensitive to radiation in the 3 - 5 $\mu$m band; when imaging water, radiation in this band comes only from approximately the top 30$\mu$m of the water column. This means that the imagery can be thought of as a temperature map of the water surface. The imager used is sensitive to temperature fluctuations of the order of 0.02K. This enables the visualization of very small disturbances to the water surface. The hyperspectral imager operates in the visible bands, and in the case of clear water can therefore see deeper into the water column. In this presentation the primary focus will be on using the color imagery to aid in interpretation of the IR data. Effects of look angle in the IR data will also be presented and discussed. [Preview Abstract] |
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