Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session L32: Geophysical: General I - Rotating Flows |
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Chair: Jean-Marc Chomaz, LadHyX, CNRS-Ecole Polytechnique Room: 403 |
Monday, November 25, 2013 3:35PM - 3:48PM |
L32.00001: Dynamically Consistent Shallow-Atmosphere Equations with a Complete Coriolis force Marine Tort, Thomas Dubos, Francois Bouchut, Vladimir Zeitlin Atmospheric and oceanic motion are usually modelled within the shallow-fluid approximation, which simplifies the 3D spherical geometry. For dynamical consistency, i.e. to ensure conservation laws for potential vorticity, energy and angular momentum, the horizontal component of the Coriolis force is neglected. Here new equation sets combining consistently a simplified shallow-fluid geometry with a complete Coriolis force are presented. The derivation invokes Hamilton's principle of least action with an approximate Lagrangian capturing the small increase with height of the solid-body entrainment velocity due to planetary rotation. A three-dimensional compressible model and a one-layer shallow-water model are obtained. The latter extends previous work done on the $f$-plane and $\beta$-plane. Preliminary numerical results confirm the accuracy of the 3D model within the range of parameters for which the equations are relevant. These new models could be useful to incorporate a full Coriolis force into existing numerical models and to disentangle the effects of the shallow-atmosphere approximation from those of the traditional approximation. [Preview Abstract] |
Monday, November 25, 2013 3:48PM - 4:01PM |
L32.00002: On the Unexpected Longevity of the Great Red Spot, Oceanic Eddies, and other Baroclinic Vortices Pedram Hassanzadeh, Philip Marcus Vortices in the ocean and atmosphere dissipate via various mechanisms such as wave emission, turbulence, and thermal radiation. However, these vortices are observed to live much longer than the time scales of the dissipation processes. Here we model these processes as either Rayleigh drag or Newtonian cooling with time scale $\tau$, and use simulations of the 3D non-hydrostatic Boussinesq equations. Our results show that vortices in fact do NOT decay at the imposed time scale $\tau$; they decay much slower, sometimes by a factor of 100. The slow decay is due to a meridional circulation, which converts the potential energy to the kinetic energy and vice versa and slows down the decay. In the presence of horizontal shear, the circulation can extract the shear energy and further energize the vortex. We explain the existence of the meridional circulation, the slow decay, and the resulting cyclone-anticyclone asymmetry using the numerical results, a physical model, and simplified equations. Our results suggest that the observed longevity of some vortices can be explained without a forcing mechanism. For very long-lived vortices, such as the Great Red Spot, our results imply that much weaker forcing, compared to what originally thought, is needed to maintain the vortices. [Preview Abstract] |
Monday, November 25, 2013 4:01PM - 4:14PM |
L32.00003: The role of interactions between waves and baroclinic critical layers in zombie vortex self-replication Chung-Hsiang Jiang, Suyang Pei, Pedram Hassanzadeh, Aaron Wienkers, Caleb Levy, Philip Marcus Inertio-gravity waves are triggered from various types of perturbations in numerical simulations of rotating, vertically-stratified and horizontal-shearing flows (Marcus et al. 2013 PRL). The interactions of these waves and baroclinic critical layers can create large vortices when the shear is sufficiently strong. An important feature of these flows is that an instability at one critical layer can excite an instability at its neighboring critical layers and spawn new generations of waves and vortices. Because the self-replication of these vortices in simulations of ``dead zones'' in protoplanetary disks reminds us of zombies multiplying by infecting each other, we call them ``zombie vortices.'' However, not all interactions between waves and critical layers produce zombie vortices. The manner in which one ``infected'' critical layer infects its neighbor is not clear. The interaction of waves and critical layers are sensitive to the local Brunt-Vaisala frequency and to the wavelengths of the waves. Here we discuss how the interactions and formation of vortices depend upon the Brunt-Vaisala frequency (including its change in value as a function of vertical position) and our progress in understanding how the instability passes from a critical layer to its neighbor. [Preview Abstract] |
Monday, November 25, 2013 4:14PM - 4:27PM |
L32.00004: On the Effects of Viscosity and Nonlinearity on Baroclinic Critical Layers Meng Wang, Chung-Hsiang Jiang, Pedram Hassanzadeh, Philip Marcus A new family of baroclinic critical layers in rotating, stably-stratified flows plays a significant role in de-stabilizing shear flows and, in particular, is important in star formation in Keplerian disks (Marcus et al. PRL, 2013). These critical layers are characterized by singularities in their vertical velocities. To understand the critical layers, especially their thicknesses, and to help design future lab experiments that contain these layers, we use matched asymptotic expansions to obtain analytical solutions of the viscous flow in and around the baroclinic critical layers. To verify our solutions and to study the effect of nonlinearity, we also numerically simulate the critical layers produced by tilted vortices in strongly stratified fluids (no rotation, no imposed shear other than that induced by the vortex itself). This problem has been previously studied by Boulanger et al. (2008 JFM) and provides a framework to explore the physics of baroclinic critical layers before adding the complexity of rotation and strong shear. [Preview Abstract] |
Monday, November 25, 2013 4:27PM - 4:40PM |
L32.00005: Evolution of a turbulence cloud under rotation Avishek Ranjan, P.A. Davidson Localized regions of turbulence frequently occur in the geophysical environment and are governed by inhomogeneous dynamics. A direct numerical simulation study of such a region of turbulence (a ``turbulence cloud'') under external rotation is conducted at Rossby number of 0.1. The initial condition is generated using a spatial filter on a pre-run of fully developed homogeneous turbulence in a 512$^{3}$ periodic box. Lagrangian particle tracking is used to track turbulent diffusion. In the velocity iso-surfaces, columnar flow structures are seen to emerge from the turbulence cloud and grow linearly with time. These are created by inertial waves sustained by the Coriolis force in the rotating reference frame and propagate on a faster time scale compared to turbulence. Helicity is used as a diagnostic to confirm that columnar structures are indeed inertial waves.\footnote{Ranjan, A, Davidson, PA (2013) \textit{Evolution of a turbulence cloud under rotation}, JFM (in preparation)} The observations conform with the evolution of a single Gaussian eddy under rotation for which analytical solution is available in literature. [Preview Abstract] |
Monday, November 25, 2013 4:40PM - 4:53PM |
L32.00006: Laboratory Scale Simulating of Spiral Plumes in the Mantle Albert Sharifulin, Anatoly Poludnitsin On the basis of laboratory simulation a mechanism is established for the formation of the mantle convection spiral plumes from a core hot point in the presence of a roll-type large-scale convective flow. Experiment are close to fulfilling Golitsin's requirements [1] to laboratory models of mantle convection. We experimentally simulated the appearance of a plume from the local heat source generated by beam of green laser and study its interaction with cellular flow, simulating beneath the plates shear flow. It is shown that the presence of convective motion may lead to the formation of a strange spiral convective plume. Experimentally showed that the presence of cellular convective motion (simulating the large-scale shear flow exists beneath the plates) the plume from a point source of heat (core hot point) can acquire a spiral shape with horizontal sections needed to launch the mechanism of formation of chains of volcanic islands [2]. It is shown that possible existence of spiral plumes in mantle can help to interpret of last decade mantle tomography results. \\[4pt] [1] Golitsin GS (1979) Simple theoretical and experimental study of convection with some geophysical applications and analogies. J Fluid Mech 95: 567.\\[0pt] [2] Skilbeck, JN, Whitehead JA (1978) Formation of discrete islands in linear chains. \textit{Nature} 272: 499. [Preview Abstract] |
Monday, November 25, 2013 4:53PM - 5:06PM |
L32.00007: Direct numerical simulation of Coriolis effects on cylindrical gravity currents Mariano Cantero, Jorge Salinas, Thomas Bonometti, Enzo Dari Gravity currents are generated by the action of gravity (or other volumetric force) on changes in fluid density. When they appear in turbulent regime, gravity currents are of a non-linear nature and have a wide range of temporal and spatial scales. In these systems there is a strong coupling between turbulence and stratification effects, with important consequences in the exchange of mass, momentum and energy. At geophysical scale, the analysis of these type of flows is further complicated by the influence of rotation effects by the Coriolis forces originated by earth's rotation. In this work we address the rotational effects in gravity currents with cylindrical initial condition by means of direct numerical simulations (DNS). We report results on five three dimensional DNS with grid resolutions up to 166-million points, with different boundary conditions, Reynolds numbers (Re=4000 and Re=8000), and different conditions of rotation. The results focus mainly on the distance of propagation of the fronts, frequency of the successive outward fronts, and the turbulent structures present in the currents and their influence in flow dynamics. [Preview Abstract] |
Monday, November 25, 2013 5:06PM - 5:19PM |
L32.00008: Spontaneous bending of a columnar vortex in stratified-rotating fluids Eunok Yim, Paul Billant In a stably stratified and rotating fluids, an isolated asymmetric vortex can be unstable to a long-wavelength instability with an azimuthal wavenumber $m=1$ which is different from classical instabilities. This instability bends the vortex and leads to the formation of pancake vortices. It can be the most dangerous instability when the background rotation and the stratification are strong. In order to better characterize this bending instability, numerical and asymptotic analyses have been performed for wide range of Froude and Rossby numbers and various velocity profiles. The maximum growth rate increases with the Rossby numbers but is independent of the Froude number when it is below unity. When the Froude number is above unity, the growth rate decays abruptly because of critical layers. By means of an asymptotic stability analysis for long-wavelength, we show that necessary instability conditions for any Froude and Rossby numbers are that there exists a critical radius $r_c$ where the angular velocity is equal to the frequency $\Omega(r_c)=\omega$ and the vorticity gradient at the critical radius is positive $\zeta'(r_c) > 0$. These conditions are identical to those of the shear instability. Numerical results supporting these conditions will be presented. [Preview Abstract] |
Monday, November 25, 2013 5:19PM - 5:32PM |
L32.00009: A new regime of instability for the stably stratified Taylor-Couette flow Paul Billant, Junho Park We show that the stably stratified Taylor-Couette flow is unstable when the angular velocity $\Omega(r)$ increases along the radial direction, a regime never explored before. The instability is different from the centrifugal instability: it is highly non-axisymmetric and involves the resonance of two families of inertia-gravity waves like for the strato-rotational instability. The growth rate is maximum when only the outer cylinder is rotating and goes to zero when $\Omega(r)$ is constant. The sufficient condition for linear, inviscid instability derived previously: $d\Omega^{2}/dr<0$ is therefore extended to $d\Omega^{2}/dr\neq0$, meaning that only the regime of solid-body rotation is stable in stratified fluids. A WKBJ analysis in the inviscid limit, confirmed by the numerical results, shows that the instability occurs only when the Froude number is below a critical value and only for a particular band of azimuthal wavenumbers. The physical mechanism of the instability will be explained in terms of wave over-reflection.\\[4pt] References: Park J. \& Billant P., {\it J. Fluid Mech.}, \textbf{725}, 262-280 (2013); Yavneh, I., McWilliams, J. C. \& Molemaker, M. J.,{\it J. Fluid Mech.} \textbf{448}, 1-21 (2001). [Preview Abstract] |
Monday, November 25, 2013 5:32PM - 5:45PM |
L32.00010: Laboratory Observation of Stratorotational Instability with a Large Density Gradient Bruce Rodenborn, Ruy Ibanez, Harry L. Swinney In 2001 a new class of instabilities in vertically stratified Taylor-Couette flows was predicted by Molemaker et al. (J. Fluid. Mech. {\bf 448}, 1). Dubrulle et al. (Astron. Astrophys. {\bf 429}, 1, 2005) then showed that this phenomenon, which they named stratorotational instability (SRI), could be a source of turbulence-producing angular momentum transport in an astrophysical accretion disk. Recently Shtemler et al. (Mon. Not. R. Astron. Soc. {\bf 406}, 517, 2010) showed that the SRI is unlikely to be a primary source of turbulence, but could well be an important secondary source. We use a Couette-Taylor system to study the SRI outside of the Boussinesq limit, i.e., with large axial density gradients, as exist in accretion disks. Our measurements of torque and the spatiotemporal structure of the flow as a function of the density profile and Froude number indicate that the SRI is robust outside of the Boussinesq limit, a minimum condition for relevance to accretion disks. [Preview Abstract] |
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