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 LH: GFD: General I |
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Chair: Paul Linden, University of Cambridge Room: Long Beach Convention Center 103C |
Monday, November 22, 2010 3:35PM - 3:48PM |
LH.00001: Absolute instability of gravity waves Madiha Ahmed, Jean-Marc Chomaz Although large-scale internal gravity waves of finite amplitude are known to be unstable, they are frequently observed in the lee of topography. We propose an explanation for this paradox by showing that the instability of these waves is convective and not absolute. Hence, in the frame of the mountain, a localized initial perturbation gives rise to a wave packet that grows but is entrained downstream, eventually leaving the flow undisturbed. The evolution of one such localized perturbation of a uniform finite-amplitude gravity wave is computed using direct numerical simulation of the Navier-Stokes equation under the Boussinesq approximation. The wave packet's edge velocity is determined by analyzing the amplitude of the response on spatio-temporal rays. This generic technique allows discrimination between the absolute and convective nature of the instability and suggests that transition to turbulence might occur due to the nonlinear evolution of absolute instability. [Preview Abstract] |
Monday, November 22, 2010 3:48PM - 4:01PM |
LH.00002: Transient growth on horizontal shear with vertical stratification Cristobal Arratia, Jean-Marc Chomaz, Sabine Ortiz We report an investigation of the three-dimensional stability of an horizontal shear flow, the hyperbolic tangent velocity profile, in an inviscid, stably stratified fluid. A previous work by Deloncle et al.(2007) shows that the most unstable mode for this flow is two-dimensional. However, for strong stratification, the range of unstable vertical wavenumbers widens proportionally to the inverse of the Froude number. This means that the stronger the stratification, the smaller the vertical scales that can be destabilized. This is consistent with the self-similarity found by Billant and Chomaz (2001). Here we extend that previous result by computing the optimal perturbations that maximize the energy growth up to a time horizon T as a function of the streamwise and spanwise wavenumbers. We concentrate on short optimization times in the strong stratification limit, where the Billant and Chomaz self-similarity is verified to hold. The gravity wave components of the perturbations are obtained by means of a Craya-Herring decomposition which, in the absence of shear, corresponds to an exact separation between gravity waves and vortical modes for the linear dynamics. Intense excitation of gravity waves due to transient growth of perturbations is found in a broad region of the wavevector plane, gravity waves being eventually emitted away from the shear layer. [Preview Abstract] |
Monday, November 22, 2010 4:01PM - 4:14PM |
LH.00003: Internal bores: An improved model via a detailed analysis of the energy budget Zachary Borden, Tilman Koblitz, Eckart Meiburg Internal bores, or hydraulic jumps, arise in many atmospheric and oceanographic phenomena. The classic single-layer hydraulic jump model accurately predicts a bore's behavior when the density difference between the expanding and contracting layer is large (i.e. water and air), but fails in the Boussinesq limit. A two-layer model, where mass is conserved separately in each layer and momentum is conserved globally, does a much better job but requires for closure an assumption about the loss of energy across a bore. Through the use of 2D direct numerical simulations, we show that there is a transfer of energy from the contracting to the expanding layer due to viscous stresses at the interface. Based on the simulation results, we propose a two-layer model that provides an accurate bore velocity as function of all geometrical parameters, as well as the Reynolds and Schmidt numbers. We also extend our analysis to non-Boussinesq internal bores to bridge the gap between the single and two-layer models. [Preview Abstract] |
Monday, November 22, 2010 4:14PM - 4:27PM |
LH.00004: Stability of isolated Barchan dunes Antoine Fourri\`ere, Fran\c{c}ois Charru When sand grains are entrained by an air flow over a non-erodible ground, or with limited sediment supply from the bed, they form isolated dunes showing a remarkable crescentic shape with horns pointing downstream. These dunes, known as Barchan dunes, are commonly observed in deserts, with height of a few meters and velocity of a few meters per year (Bagnold 1941). These dunes also exist under water, at a much smaller, centimetric size (Franklin \& Charru 2010). Their striking stability properties are not well understood yet. Two phenomena are likely to be involved in this stability: (i) relaxation effects of the sand flux which increases from the dune foot up to the crest, related to grain inertia or deposition, and (ii) a small transverse sand flux due to slope effects and the divergence of the streamlines of the fluid flow. We reproduced aqueous Barchan dunes in a channel, and studied their geometrical and dynamic properties (in particular their shape, velocity, minimum size, and rate of erosion). Using coloured glass beads (see the figure), we were then able to measure the particle flux over the whole dune surface. We will discuss the stability of these dunes in the light of our measurements. [Preview Abstract] |
Monday, November 22, 2010 4:27PM - 4:40PM |
LH.00005: A Lagrangian description of the energetics of stably stratified turbulence Seungbum Jo, Keiko Nomura, James Rottman The general equations describing the energetics of stratifed flows have been derived previously for a fixed volume in the Eulerian frame. Here we consider the energetics of a fluid particle in a homogeneous flow and develop appropriate equations in the Lagrangian frame. Comparison with Eulerian analysis is discussed. We then illustrate our results using Lagrangian statistics from DNS of homogeneous stably stratified shear flows which include decaying, stationary, and growing turbulence conditions. [Preview Abstract] |
Monday, November 22, 2010 4:40PM - 4:53PM |
LH.00006: Regimes of Turbulent Rotating COnvection Eric King, Jonathan Aurnou Heat transport by thermal turbulence has been of interest to the fluid dynamics community for decades. Furthermore, turbulent convective motions are responsible for many of the observed features of planets and stars, such as magnetic field generation and atmospheric jet formation. In these flows, the influence of background rotation through the Coriolis force is thought to be paramount. We present an examination of the importance of rotation in turbulent Rayleigh-B\'enard convection through heat transfer measurements in a collaborative suite of laboratory experiments and numerical simulations. There exist two separate heat transfer regimes: rapidly rotating and non-rotating. We argue that the dynamical regime of a given convection system is determined by the competition between the thermal boundary layer and the Ekman boundary layer. This boundary layer control hypothesis permits the formulation of a predictive scaling of the transition between heat transfer regimes, and reconciles a broad array of previously disparate convection studies. The experimental results are also shown to apply to numerical models of planetary dynamos. [Preview Abstract] |
Monday, November 22, 2010 4:53PM - 5:06PM |
LH.00007: The Role of Viscosity Contrast on the Plume Structure and Dynamics in High Rayleigh Number Convection Sreenivas KR, Vivek N. Prakash, Jaywant H. Arakeri We study the plume structure in high Rayleigh number convection in the limit of large Prandtl numbers. This regime is relevant in Mantle convection, where the plume dynamics is not well understood due to complex rheology and chemical composition. We use analogue laboratory experiments to mimic mantle convection. Our focus in this paper is to understand the role of viscosity ratio, U, between the plume fluid and the ambient fluid on the structure and dynamics of the plumes. The PLIF technique has been used to visualize the structures of plumes rising from a planar source of compositional buoyancy at different regimes of U (1/300 to 2500). In the near-wall planform when U is one, a well-known dendritic line plume structure is observed. As U increases (U $>$ 1; mantle hot spots), there is a morphological transition from line plumes to discrete spherical blobs, accompanied by an increase in the plume spacing and thickness. In vertical sections, as U increases (U $>$ 1), the plume head shape changes from a mushroom-like structure to a ``spherical-blob.'' When the U is decreased below one, (U$<$1; subduction regime), the formation of cellular patterns is favoured with sheet plumes. Both velocity and mixing efficiency are maximum when U is one, and decreases for extreme values of U. We quantify the morphological changes, dynamics and mixing variations of the plumes from experiments at different regimes. [Preview Abstract] |
Monday, November 22, 2010 5:06PM - 5:19PM |
LH.00008: Tidal instability and magnetic field generation Patrice Le Gal, David C\'ebron, Wietze Herreman, Michael Le Bars, St\'ephane Le Diz\`es We are interested in the interaction of the elliptical instability and magnetic fields in liquid metal flows both on laboratory and planetary scales. We first discuss an experimental set-up that realizes an elliptical flow of Galinstan under an imposed field. The presence of a magnetic field is here of double interest. Elliptically excited flows are monitored through the magnetic fields they induce and the instability may be controlled by Joule damping. This study provides some new insight in the nonlinear stages of the elliptical instability. In a planetary context, it is likely that elliptical instability under imposed field occurs in the tidally deformed moon Io of Jupiter. We show how tidally excited flows may significantly deform the imposed field of Jupiter through an induction process. Finally, we also study whether tidally driven flows can be capable of generating and sustaining magnetic fields through the dynamo effect. We present a first numerical study on the possibility of tidally driven dynamo action in triaxial spheroids. [Preview Abstract] |
Monday, November 22, 2010 5:19PM - 5:32PM |
LH.00009: Tidal instability in exoplanetary systems David Cebron, Rim Fares, Pierre Maubert, Claire Moutou, Michael Le Bars, Patrice Le Gal Due to their observational method, many of the discovered exo-planets are massive gas giants called ``hot Jupiters'' orbiting rapidly very close to their stars. Because of this proximity, these celestial bodies (stars and planets) are strongly deformed by gravitational tides. Therefore, a certain number of them must be the site of an hydrodynamic instability, called the tidal instability. Starting from measured astrophysical characteristics of these systems (masses, orbit radius, eccentricity and period, spin velocity...), we show that this instability is, as expected, present in some of the stars when the ratio of the planet orbiting period to the star spinning period is not in a ``forbidden range.'' In this case, the instability should drive strong flows in the different fluid layers of both bodies. These flows must be taken into account to model the bodies interiors and subsequent properties (synchronization, dynamos, zonal winds...). Of particular interest is the possibility of modifying the alignment of the rotation axes of stars and planets by this tidal instability. [Preview Abstract] |
Monday, November 22, 2010 5:32PM - 5:45PM |
LH.00010: Universal scaling law for the aspect ratio of a pancake vortex in a rotating stratified medium Oriane Aubert, Michael Le Bars, Patrice Le Gal, Philip S. Marcus The Great Red Spot of Jupiter and the meddies in the Atlantic Ocean are the most famous and puzzling examples of long-lived pancake like anticyclones that take place in a rotating and stably stratified medium. To reproduce and study these vortices in the laboratory, we inject a volume of isodensity dyed fluid in a rotating linearly stratified layer of salt water. Due to the Coriolis force, the injected fluid rapidly forms a pancake vortex whose long term evolution is quantified using PIV measurements and image processing. Three different phases take place: a fast geostrophic adjustment, an axisymmetrization by viscous coupling with the outside and finally a very slow decrease of the motion while preserving the self-similar shape of the vortex. This last regime can be described using a simplified system of equations based on a geostrophic equilibrium, where the energy source maintaining the long-lived vortex is the density anomaly with the outside: the vortex persists as long as the density anomaly remains, maintained by internal recirculations. The non-diffusive version of the equations gives an analytical solution for the self-similar shape of the vortex and the evolution law for the aspect ratio for small Rossby numbers. These theoretical predictions are verified experimentally and also agree with published measurements for the meddies and Jupiter's Great Red Spot. [Preview Abstract] |
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