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 QZ: Rotating Flows II |
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Chair: Herman Clercx, Eindhoven University of Technology Room: Hyatt Regency Long Beach Regency F |
Tuesday, November 23, 2010 12:50PM - 1:03PM |
QZ.00001: Dynamics of a fluid inside a precessing cylinder Romain Lagrange, Patrice Meunier, Christophe Eloy, Francois Nadal The instability of a fluid inside a precessing cylinder is studied theoretically and experimentally. This study is motivated by aeronautics and geophysics applications. Precessional motion forces hydrodynamics waves called Kelvin modes whose structure and amplitude are predicted by a linear inviscid theory. When a forced Kelvin mode is resonant, a viscous and weakly nonlinear theory has been developed to predict its saturated amplitude. We show that this amplitude scales as $Re^{1/2}$ for low Reynolds numbers and as $\theta^{1/3}$ (where $\theta$ is the precessing angle) for high Reynolds numbers. These scalings are confirmed by PIV measurements. For Reynolds numbers sufficiently large, this forced flow becomes unstable. A linear stability analysis based on a triadic resonance between a forced Kelvin mode and two free modes has been carried out. The precessing angle for which the flow becomes unstable is predicted and compared successfully to experimental measurements. A weakly nonlinear theory was developed and allowed to show that the bifurcation of the instability of precession is subcritical. It also showed that, depending on the Reynolds number, the unstable flow can be steady or intermittent. Finally, this weakly nonlinear theory allowed to predict, with a good agreement with experiments, the mean flow in the cylinder; even if it is turbulent. [Preview Abstract] |
Tuesday, November 23, 2010 1:03PM - 1:16PM |
QZ.00002: Inertial waves in the channel turbulence with system rotation Yan-Tao Yang, Jie-Zhi Wu We study inertial waves (IWs) in the turbulent channel flow with system rotation about an axis in either streamwise or spanwise direction (STR or SPR). For the mean channel shear flow, we construct IW solutions by the helical wave functions (eigenfunctions of the curl operator), and show their existence when the basic flow satisfies certain conditions. These theoretical predictions were tested by DNS of the rotating channel flows. We have recently confirmed that the STR channel holds IWs when the rotating rate is high enough, and for different rotating rates the IWs have similar wavenumber and negative polarity (JFM, to appear). As for the SPR cases, the IWs may exist at even higher rotating rates than that needed for STR cases. They locate at the layer where the mean streamwise velocity is largest. It is likely that when a system rotation is applied to a unidirectional shear flow, the IWs may appear at the region where the mean streamwise velocity takes the local maximum. The profiles of the mean velocity are modified by IWs. [Preview Abstract] |
Tuesday, November 23, 2010 1:16PM - 1:29PM |
QZ.00003: The motion and the forces on a cylinder and a sphere in rotating shear flow Yoshiyuki Tagawa, Chao Sun, Tom Mullin, Leen van Wijngaarden, Detlef Lohse The motion and rotation rate of a heavy cylinder and sphere inside a rotating drum were investigated. The drum, filled with distilled water, was rotating around its horizontal axis with varying rotation rates. The cylinder was observed to either co- or counter-rotate with respect to the rotating drum. The motion of the cylinder depends not only on the radius of the cylinder, but also on its length. The flow around the cylinder was measured with particle image velocimetry (PIV). Results on spheres with different radii will also be presented. [Preview Abstract] |
Tuesday, November 23, 2010 1:29PM - 1:42PM |
QZ.00004: Viscous spreading of an inertial wave beam in a rotating fluid Pierre-Philippe Cortet, Cyril Lamriben, Frederic Moisy We report experimental measurements of inertial waves generated by an oscillating cylinder in a rotating fluid. The two-dimensional wave takes place in a stationary cross-shaped wavepacket. Velocity and vorticity fields in a vertical plane normal to the wavemaker are measured by a corotating Particle Image Velocimetry system. The viscous spreading of the wave beam and the associated decay of the velocity and vorticity envelopes are characterized. They are found in good agreement with the similarity solution of a linear viscous theory, derived under a quasi-parallel assumption similar to the classical analysis of Thomas and Stevenson [J. Fluid Mech. {\bf 54} (3), 495--506 (1972)] for internal waves. [Preview Abstract] |
Tuesday, November 23, 2010 1:42PM - 1:55PM |
QZ.00005: Spin-Up and Spin-Down in a Half Cone Michael Patterson, Ligang Li, Keke Zang, Rich Kerswell The spin-up and spin-down flow responses in a rapidly-rotating, fluid-filled, closed half-cone are studied both numerically and experimentally. This unusual set up is of interest because it represents a pathological case for the classical linear theory of Greenspan {\&} Howard (1963) since there are no closed geostrophic contours nor a denumerable set of inertial waves. Yet, the flows observed are surprisingly simple except when the fluid is appreciably spun-down which induces boundary layer separation and complicated spatiotemporal behaviour. Most notably, the linear regime of small increase or decrease in the rotational speed exhibits the familiar ``spin-up'' Ekman boundary layer timescale of O(E$^{-1/2})$ (where E is the Ekman number) for adjustment. [Preview Abstract] |
Tuesday, November 23, 2010 1:55PM - 2:08PM |
QZ.00006: Tilt-over mode in a precessing triaxial ellipsoid David Cebron, Michael Le Bars, Patrice Meunier The tilt-over mode in a precessing triaxial ellipsoid is studied theoretically and numerically. Inviscid and viscous analytical models previously developed for the spheroidal geometry by Poincare (1910) and Busse (1968) are extended to this more complex geometry, which corresponds to a tidally deformed spinning astrophysical body. As confirmed by three-dimensional numerical simulations, the proposed analytical model provides an accurate description of the stationary flow in an arbitrary triaxial ellipsoid, until the appearance at more vigorous forcing of time dependent flows driven by tidal and/or precessional instabilities. [Preview Abstract] |
Tuesday, November 23, 2010 2:08PM - 2:21PM |
QZ.00007: Experimental Determination of Zonal Winds Driven by Tides Cyprien Morize, Michael Le Bars, Patrice Le Gal, Andreas Tilgner We describe a new phenomenon of zonal wind generation by tidal forcing. Following a recent theoretical and numerical analysis [A. Tilgner, Phys. Rev. Lett. 99, 194501 (2007)], we present the first experimental evidence that the nonlinear self-interaction of a tidally forced inertial mode can drive an intense axisymmetric flow in a rotating deformed sphere. Systematic measurements of zonal flows are carried out by an embarked system of particle image velocimetry, allowing the determination of general scaling laws. These results are fully relevant for zonal winds generation in planets and stars, and illustrate a generic mechanism of geostrophic flow generation by periodic forcing. [Preview Abstract] |
Tuesday, November 23, 2010 2:21PM - 2:34PM |
QZ.00008: Lagrangian velocity, acceleration and vorticity autocorrelations in rotating turbulence Herman J.H. Clercx, Lorenzo Del Castello The influence of the Earth background rotation on oceanic and atmospheric currents, as well as the effects of a rapid rotation on the flow inside industrial machineries like mixers, turbines, and compressors, are typical examples of fluid flows affected by rotation. Rotating turbulence has often been studied by means of numerical simulations and analytical models, but the experimental data available is scarce and purely of Eulerian nature. In the present study, experiments on continuously forced turbulence subjected to different background rotation rates are performed by means of 3D Particle Tracking Velocimetry. The data collected is processed in the Lagrangian frame, as well as in the Eulerian one. The background rotation is confirmed to induce 2-dimensionalisation of the velocity field, and the large-scales are dominated by stable counter-rotating vertical tubes of vorticity. The auto- correlation coefficients along particle trajectories of velocity, acceleration and vorticity components have been explored, and in this talk the effects of rotation on the Lagrangian temporal scales of the flow will be discussed. [Preview Abstract] |
Tuesday, November 23, 2010 2:34PM - 2:47PM |
QZ.00009: A closed grid turbulence experiment under rotation: Anisotropic energy transfer and inertial modes inhibition Cyril Lamriben, Pierre-Philippe Cortet, Frederic Moisy We report an experimental study of the free decay of an initially 3D homogeneous and isotropic grid turbulence submitted to a global rotation. Turbulence is generated by rapidly towing a grid in a rotating water tank and velocity fields are measured in a vertical plane parallel to the rotation axis using a corotating Particle Image Velocimetry (PIV) system. We first show that, when a simple grid is used, a significant amount of the kinetic energy is stored in a reproducible mean flow composed of resonant inertial modes and whose spatial structures are extracted. The possible coupling between these modes and turbulence suggests that turbulence cannot be considered as freely decaying. We demonstrate that these inertial modes may be considerably inhibited by adding inner tanks to the grid, yielding, for the first time, an effectively freely decaying rotating turbulence in a confined geometry. We also provide a thorough analysis of the anisotropic energy transfers from the anisotropic third order moment of the velocity increments obtained by PIV. We show that the departure from 3D isotropic energy transfers is stronger for horizontal increments. We also show a direct evidence of an inverse energy cascade of horizontal motions at large scales. [Preview Abstract] |
Tuesday, November 23, 2010 2:47PM - 3:00PM |
QZ.00010: Vortex Induced Flows Involving Fused Cylinder/Sphere Pairs D. Palaniappan The two-dimensional inviscid flow field around an infinitely long circular cylinder induced by a point vortex can be constructed via the famous Milne-Thomson's circle theorem. However, for non-circular configurations such calculations become cumbersome and even the computation of approximate solutions of the Euler equations governing the fluid flow require quite a lot of guess work. Here we show a systematic procedure to derive analytic results for a geometry consisting of two overlapping cylinder/sphere pairs in the limit of inviscid flow. Our simple approach yields the image system, also known as Neumann's Green function, describing the complete flow field induced by a vortex in the presence of a twin-circle configuration. The exact results for the uniform flow-vortex-twin circle combination are obtained via our successive-image theory and are expressed in the form of Hamiltonian/streamfunction for the system. The flow topologies for this system reveal the existence of stagnation points and streamline crossing, a strong indication of chaos. The corresponding analytic solutions for two fused spheres submerged in a flow induced by a three-dimensional vortex are also obtained. The exact solution for the twin-sphere problem is expressed in terms of standard convergent elliptic integrals which can be evaluated numerically. The results of this investigation, in general, illustrate the topography effects and are of fundamental importance in oceanography and other related topics as well. [Preview Abstract] |
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