Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session M17: Geophysical Fluid Dynamics: Rotating Flows |
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Chair: Philip Marcus, University of California, Berkeley Room: 2002 |
Tuesday, November 25, 2014 8:00AM - 8:13AM |
M17.00001: On the Surprising Longevity of Jupiter's Centuries-Old Great Red Spot Philip Marcus, Pedram Hassanzadeh Jupiter's Great Red Spot (GRS) has been observed continuously for 100 years and is possibly older than 350 years. However, the area of its cloud cover is quickly shrinking. Although the areas of the clouds and of the potential vorticity of the GRS might not be well correlated, it motivates us to examine the physics that determines the GRS lifetime. When the GRS is in quasi-equilibrium, the ratio of its potential (i.e. thermal) energy to its kinetic energy is $\sim 2/Ro \simeq 6$, where $Ro$ is the Rossby number. Because the atmospheric radiative decay time is 4-5 years, the overall energy and structure of the GRS would be expected to decay in 4-5 years, as it does in our 2D simulations of the GRS (or with an faster decay rate in the low-resolution 3D simulations by others). We show that in high-resolution, 3D calculations, meridional circulations (consisting of vertical and radial velocities) develop spontaneously in the GRS. The vertical velocity sustains the GRS by drawing energy from the ambient atmosphere: this circulation transports mass downward in the ambient atmosphere, thereby decreasing its potential energy. This released energy, along with kinetic energy from the ambient zonal jets, is carried to the GRS by the meridional circulation, sustaining the GRS for centuries. [Preview Abstract] |
Tuesday, November 25, 2014 8:13AM - 8:26AM |
M17.00002: Linear Stability and Nonlinear Evolution of 3D Vortices in Rotating Stratified Flows Mani Mahdinia, Pedram Hassanzadeh, Philip Marcus Axisymmetric Gaussian vortices are widely-used to model oceanic vortices. We study their stability in rotating, stratified flows by using the full Boussinesq equations. We created a stability map as a function of the Burger and Rossby numbers of the vortices. We computed the linear growth rates of the most-unstable eigenmodes and their corresponding eigenmodes. Our map shows a significant cyclone/anti-cyclone asymmetry. The vortices are linearly unstable in most of the parameter space that we studied. However, the anticyclonic vortices, over most of the parameter space, have eigenmodes with only very weak growth rates -- longer than 50 vortex turn-around times. For oceanic vortices, that time corresponds to several months, so we argue that this slow growth rate means that the oceanic anticyclones lifetimes are not determined by linear stability, but by other processes. We also use our full, nonlinear simulations to show an example of an unstable cyclone with a very fast growing linear eigenmodes. However, we show that cyclone quickly redistributes its vorticity and becomes a stable tripole with a large core that is nearly axisymmetric. [Preview Abstract] |
Tuesday, November 25, 2014 8:26AM - 8:39AM |
M17.00003: Dynamics of SQG Vortices Cecily Keppel, Stefan Llewellyn Smith The surface quasi-geostrophic (SQG) equations are a model for low-Rossby number geophysical flows in which the dynamics are governed by potential temperature dynamics on the boundary. The model can be used to explore the transition from two-dimensional to three-dimensional mesoscale geophysical flows. We examine the dynamics of SQG vortices and the resulting flow in the entire fluid including at first order in Rossby number ($O(Ro)$). This requires solving an extension to the usual QG equation to compute the velocity corrections, and we demonstrate this mathematical procedure. As we show, it is simple to obtain the vertical velocity, but difficult to find the $O(Ro)$ horizontal corrections. We then consider the specific case of an exact SQG vortex solution developed by Dritschel (2011). We examine the interaction of two such vortices in both the infinite and doubly periodic domain. [Preview Abstract] |
Tuesday, November 25, 2014 8:39AM - 8:52AM |
M17.00004: The baroclinic instability of an initially stratified fluid layer Patrice Le Gal, Miklos Vincze, Uwe Harlander Our project aims to describe the baroclinic instability that destabilizes an initially stratified layer of fluid. Classically, this instability is studied using pure fluid. Here, the originality of the project comes from the use of a layer of water initially stratified with salt. Before rotation is started, double convection sets in within the stratified layer with a strongly non-homogeneous pattern consisting of a double diffusive staircase at the bottom of the container in the very dense water layers and a shallow convective cell in the top surface layer. As radial motions take place due to the presence of these convective cells, the action of the Coriolis force generates strong zonal flows as soon as rotation is started. Thus, above a rotation rate threshold, the baroclinic instability destabilizes the flow in a shallow layer, generating a ring of pancake vortices. Infrared camera images measure the temperature distributions at the water surface and PIV velocity maps describe the wavy flow pattern and the pancake vortices. Note finally that if we prepare a stratification profile with an inner shallow non-stratified zone, it is possible to confine the baroclinic instability within this confined zone immersed inside the stratified fluid. [Preview Abstract] |
Tuesday, November 25, 2014 8:52AM - 9:05AM |
M17.00005: An experimental study of the spread of buoyant water into a rotating environment Thomas Crawford, Paul Linden We present an experimental study that aims to investigate the spread of buoyant water, released from a finite potential vorticity source, into a rotating environment. The source structure is designed to simulate the discharge of a river into the ocean and as a result the freshwater enters the salt water ambient horizontally and with considerable momentum flux. The finite depth of the source gives rise to a non-zero potential vorticity as seen in the natural environment. We perform a parametric study in which we vary the rotation rate, freshwater volume flux and density difference between the incoming buoyant fluid and the stationary ambient. The parameter values are chosen to match the regimes seen in the River Rhine and River Elbe when entering the North Sea. Persistent features of an anticyclonic outflow vortex and a propagating boundary current can be identified in each experimental run and their properties are quantified. The flow is seen to become unstable for small values of the deformation radius, suggesting it has an important role to play in determining the behaviour of the flow. We also present a finite potential vorticity, geostrophic model that provides theoretical predictions for the current height, width and velocity. These are compared with the experimental data. [Preview Abstract] |
Tuesday, November 25, 2014 9:05AM - 9:18AM |
M17.00006: Experimental observation of steady inertial wave turbulence in deep rotating flows Ehud Yarom, Eran Sharon The theoretical framework that should be used for describing rotating turbulence is the subject of an active debate. It was shown experimentally and numerically that the formalism of 2D turbulence is useful in the description of many aspects of rotating turbulence. On the other hand, theoretical and numerical work suggests that the formalism of wave turbulence should provide a reliable description of the entire 3D flow field. The waves that are suggested as the basis for this turbulence are Coriolis-force-driven inertial waves. Here we present experimental results that suggest the existence of inertial wave turbulence in deep steady rotating turbulence. Our measurements show energy transfer from the injection scale to larger scales, although the energy spectra are concentrated along the dispersion relation of inertial waves. The turbulent fields are, therefore, well described as ensembles of 3D interacting inertial waves. [Preview Abstract] |
Tuesday, November 25, 2014 9:18AM - 9:31AM |
M17.00007: Inertial wave excitation in a rotating annulus with partially librating boundaries Ion Dan Borcia, Uwe Harlander, Christoph Egbers, Abouzar Ghasemi V., Marten Klein, Eberhard Schaller, Torsten Seelig, Andreas Will, Michael V. Kurgansky Inertial waves are excited in a fluid filled rotating annulus by modulating the rotation rate of parts of the vessel boundary. This forcing leads to inertial wave beams emitted from the corner regions of the annulus due to periodic motions in the boundary layers. Firstly we use a meridional symmetrical geometry. When the forcing frequency matches with the eigenfrequency of the rotating annulus the beam pattern amplitude is increasing, the beams broaden and mode structures can be observed. The eigenmodes are compared with analytical solutions of the corresponding inviscid problem. In particular for the pressure field a good agreement can be found. However, shear layers related to the excited wave beams are present for all frequencies. Then, the meridional symmetry is broken by replacing the inner cylinder with a truncated cone (frustum). The geometry is non-separable and exhibits wave focusing and wave attractors. Under the assumption that the inertial waves do not essentially affect the boundary-layer structure, we use classical boundary-layer analysis to study oscillating Ekman layers over a librating wall that is at a non-zero angle to the axis of rotation. [Preview Abstract] |
Tuesday, November 25, 2014 9:31AM - 9:44AM |
M17.00008: Nonlinear flows driven by libration in a rotating half cone Michael Patterson, Rosen Rachev, Ligang Li, Keke Zhang We investigate the problem of nonlinear oscillatory flow of homogeneous fluid with viscosity $\nu$ confined in a half cone that rotates rapidly about a fixed axis with angular velocity ${\Omega}_0 $ and that undergoes weak longitudinal libration with amplitude $\epsilon {\Omega}_0$ and frequency $\hat{\omega} {\Omega}_0$, where $\epsilon$ is the Poincar\'{e} number and $\hat{\omega} $ is dimensionless frequency with $0< \hat{\omega}<2$. Two different methods are employed in this investigation: experimental studies and direct numerical simulation using a finite element method. [Preview Abstract] |
Tuesday, November 25, 2014 9:44AM - 9:57AM |
M17.00009: What is the energy dissipation rate in rotating turbulence? Frederic Moisy, Antoine Campagne, Pierre-Philippe Cortet, Basile Gallet The scaling of the energy dissipation rate $\epsilon$ is one of the most fundamental open issues for rapidly rotating turbulence. For non-rotating 3D turbulence at large Reynolds number, it takes the classical form $\epsilon_{3D}\simeq U^3/L$, with $U$ and $L$ the characteristic velocity and length scales. Here, we propose a simple experiment aiming to probe directly the influence of the background rotation on $\epsilon$: we measure the torque $\Gamma$ acting on a propeller rotating at constant rate $\omega$ in a large volume of fluid rotating at $\Omega$ (the torque measurement being performed in the rotating frame). The normalized torque $K_p=\Gamma/(\rho R^4 H \omega^2)$ (where $R$ and $H$ are the propeller radius and height) provides a direct measure of the normalized dissipation $\epsilon / \epsilon_{3D}$ as a function of the Rossby number $Ro=\omega/\Omega$. For cyclonic propeller rotation ($Ro>0$) we find a transition between $K_p =$constant at large $Ro$ (no rotation) and $K_p\simeq Ro$ at small $Ro$ (large rotation), in agreement with weakly nonlinear rotating turbulence prediction. The situation is more intricate for anticyclonic rotation ($Ro<0$), showing a peak dissipation at intermediate $Ro$, and a decrease at small $Ro$ but with a different scaling. [Preview Abstract] |
Tuesday, November 25, 2014 9:57AM - 10:10AM |
M17.00010: Comparison of Two-Dimensional Turbulence on the Surface of a Sphere with Two-Dimensional Turbulence on a Plane Leila Azadani, Anne Staples Although there are not two-dimensional turbulent flows in nature, there are many applications in which the fluid motion can be described by two-dimensional models. For example large-scale geophysical flows in the atmosphere and ocean can be accurately represented by two-dimensional turbulence models. The combined effects of geometry, stratification and rotation restricts the flow motion in the vertical direction and makes these flows almost two-dimensional. While Cartesian coordinates are usually used to perform these computations, spherical coordinates are more natural and account for the Earth's curvature. Computations of two-dimensional turbulent flows in Cartesian and spherical geometries yield different results. The energy transfer mechanism, the rate of enstrophy transfer to higher wave numbers and the behavior of coherent structures in spherical coordinates are different from those in Cartesian coordinates. Here, we compare two-dimensional turbulence on a plane with two-dimensional turbulence on the surface of a sphere is spectral space and explain the differences in Cartesian and spherical geometries. [Preview Abstract] |
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