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 MZ: Rotating Flows I |
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Chair: Hussein Aluie, Los Alamos National Laboratory Room: Hyatt Regency Long Beach Regency F |
Tuesday, November 23, 2010 8:00AM - 8:13AM |
MZ.00001: Joint Baroclinic and Convective Instability Keith Julien, Geoff Vasil The existence of balanced geostrophic dynamics for nonhydrostatic flows has been recently demonstrated.\footnote{Julien, Knobloch, Milliff and Werne, J. Fluid Mech. 555 (2006)} The NonHydrostatic Balanced Geostrophic Equations that result are appropriate for columnar motions with significant unbalanced ageostrophic vertical motions. The NHBGE have successfully been applied to the case of rapidly rotating Rayleigh-Benard convection.\footnote{Sprague, Julien, Knobloch, and Werne, J. Fluid Mech. 551(2006)} However, geophysical and astrophysical systems are fundamentally multiscale in nature, and when viewed on scales much greater than the convective eddies the forcing is fundamentally inhomegeneous in the lateral directions. Consequently, baroclinic instabililties may arise that both interact and compete with convectively driven motions. In this study, the NHBGE are extended to include large-scale inhomogeneous dynamics. The PDE's contains the classical problem of Eady (Tellus,1, 1949) for baroclinic instability. We show that Eady instability persists for an unstably-stratified fluid layer and competes with convective instability. We discuss criteria dominance of the baroclinic instability and present some results in the strongly nonlinear regime. [Preview Abstract] |
Tuesday, November 23, 2010 8:13AM - 8:26AM |
MZ.00002: Rapidly Rotating Wall Mode Convection Geoffrey Vasil, Keith Julien In a rapidly rotating finite-aspect ratio system the onset of Rayleigh-Benard convection can occur either via a set of slowly oscillating modes supported in the bulk interior of the domain, or via a set of faster modes that exist in a thin boundary layer attached to side of the container. If the background rotation rate is sufficiently large, then these wall-localized modes are always the preferred pattern of instability. However, extreme wall localization is not the entire picture; wall mode convection is actually a fundamentally multiscale phenomenon. Outside an asymptotically thin boundary layer, the convective modes connect to a dynamical interior that maintains scales set by the geometry of the domain. In the rapidly rotating limit, we derive a new balanced set of reduced PDE's that govern the strongly nonlinear development of the wall-mode instability in the interior of a general container. Furthermore, the small-scale dynamics within the boundary layer are linearly and diagnostically determined in terms of the bulk interior dynamics. The boundary layers then feedback on the interior via a nonlinear lateral heat-flux boundary condition. These new PDE's clearly contain the results from previous linear instability theory. We will also discuss some results in a strongly supercritical regime. [Preview Abstract] |
Tuesday, November 23, 2010 8:26AM - 8:39AM |
MZ.00003: An asymptotic model for rotationally-constrained non-penetrative thermal convection Antonio Rubio, Keith Julien Unsteady non-penetrative convection is found when a stable layer of fluid is sandwiched between an insulating thermal boundary condition and an adverse thermal boundary condition.\footnote{Adrian, Ferreira and Boberg, Exp. Fluids. 4, 121-141 (1986)}$^,$\footnote{Fernando, Boyer and Chen, J. Fluid Mech. 228, 513-547 (1991)} Unsteady non-penetrative convection is a canonical setup for a deepening mixed layer in which the effects of entrainment are either negligible or ignored for simplicity. Of particular interest is deep ocean convection in which the flow within the convective layer is rotationally-constrained and exhibits weak entrainment.\footnote{Julien, Legg, McWilliams and Werne, Dyn. Oc. Atm. 26, 259-262 (2001)} Non-penetrative convection is investigated using a straight-forward extension to an existing class of non-hydrostatic balanced geostropic equations (NHBGE)\footnote{Julien, Knobloch, Milliff and Werne, JFM. 555, 233-274 (2006)} valid in the low Rossby number limit. After a brief discussion of the model we show the results of the linear stability analysis, nonlinear single mode solutions as well as preliminary direct numerical solutions of the modified NHBGE. [Preview Abstract] |
Tuesday, November 23, 2010 8:39AM - 8:52AM |
MZ.00004: The dynamics of mercury flow in a curved pipe Yan Zhan, Foluso Ladeinde, Harold G. Kirk, Kirk T. McDonald Mercury has been investigated as a potential high-Z target for the Moun Collider Accelerator project. Preliminary design of the target delivery system involves pipe curvature and axially-dependent pipe radius. The investigation of the dynamics of mercury flow under these conditions is undertaken with the goal of obtaining the proper nozzle design for this application. Depending on the Dean number, rotational body force modes are observed, with dynamics that are considerably different from these in a straight pipe of constant radius. [Preview Abstract] |
Tuesday, November 23, 2010 8:52AM - 9:05AM |
MZ.00005: Influence of the surface tension and the viscosity on irregular surface switching of rotating fluids Yuji Tasaka, Makoto Iima We have investigated the influence of the surface tension and the viscosity of the fluids on temporally-irregular surface switching, which is a recently discovered phenomenon of rotating fluids accompanied by a free surface deformation (see Suzuki {\it et al.}, {\it Phys. Fluids}, 2006 and Tasaka \& Iima, {\it J. Fluid Mech.}, 2009). Tap water, liquid Gallium, 1 cSt and 10 cSt Silicone oils were used to change the viscosity and the surface tension; oils have smaller surface tension than water and liquid gallium larger one than water. Variations of the magnitude of the velocity fluctuation with respect to the speed of the disk rotation were obtained for the fluids without liquid gallium as the bifurcation diagram. Comparison of the diagram between the fluids indicates that the smaller surface tension enhances the surface deformation but prevents the appearance of the surface switching. Surface motion recorded by a digital video camera shows that the surface of the rotating oil(1 cSt) has sloshing motion ($n = 1$) ahead of the surface switching instead of the intermittent deformation of the surface shape ($n = 2$) which was observed in water; here $n$ means the mode of axisymmetry breaking on the free surface. [Preview Abstract] |
Tuesday, November 23, 2010 9:05AM - 9:18AM |
MZ.00006: Studies of Rossby waves and hydrodynamic turbulence in a Taylor-Couette device Eric Edlund, E. Schartman, E. Spence, A. Roach, P. Sloboda, H. Ji We present the design of a new experiment at the Princeton Plasma Physics Laboratory with the mission of studying angular momentum transport in rotating incompressible fluids at Re $>10^6$. This hydrodynamic experiment supports and complements a similar device, the Princeton MRI experiment, which uses a liquid metal to study MHD effects [1]. The inner and outer cylinders may be separately driven; differentially rotating rings on the top and bottom boundaries between the cylinders allow the Ekman circulation to be greatly diminished while maintaining shear in the azimuthal flow close to the Rayleigh criterion. The top, fluid-facing boundary of the device can be outfitted with various surfaces or operated with a free surface to modify the Rossby wave characteristics. A set of ultrasonic transducers is used to measure the $v_r$ and $v_\phi$ profiles at three distinct heights. A two component LDV system provides measurements of the local $v_r$ and $v_\phi$ which will further constrain measurements of the turbulent angular momentum transport reported previously [2].\\[4pt] [1] E. Schartman {\it et al.}, RSI {\bf 80}, 024501 (2009).\\[0pt] [2] H. Ji {\it et al.}, Nature {\bf 444}, 343 (2006). [Preview Abstract] |
Tuesday, November 23, 2010 9:18AM - 9:31AM |
MZ.00007: A Stereo-PIV Study of the Taylor-Column Generated by a Rotating Disk Jozef H.A. Vlaskamp, Peter J. Thomas, Rainer Hollerbach, Robert M. Kerr The formation of Taylor-Columns is one of the familiar phenomena observed in flows where strong background rotation is present. The current investigation considers the Taylor-Column generated by a rotating disc in a rotating fluid, a geometry similar to the classic Stewartson-layer problem. Experimental work is performed on the large turntable at the University of Warwick (overall height 5.7m and 1.4m diameter). The facility offers a water depth of 2m below the disk, allowing for a much longer Taylor-Column to be observed than in previous experimental work. A fully automated, traverse-mounted Stereo-PIV system has been developed to visualize the flow, allowing data-acquisition at different heights of the Taylor-Column without the need for recalibration. The experimental results show a z-dependence of the angular velocity profile in the Taylor-Column, which contradicts the Taylor-Proudman theorem. Additional numerical simulation is being performed and compared with the experimental results. [Preview Abstract] |
Tuesday, November 23, 2010 9:31AM - 9:44AM |
MZ.00008: Velocity profile measurements in high Reynolds number Taylor-Couette flow for pure outer-cylinder rotation Sander Huisman, Dennis van Gils, Chao Sun, GertJan van Heijst, Detlef Lohse Using Laser Doppler Anemometry, we measured azimuthal and axial velocity profiles inside the gap of a Taylor-Couette apparatus, spinning only the outer cylinder at a varying Reynolds number from $1.4 \times 10^5$ to $1.4 \times 10^6$. The system has a radius ratio of 0.716 and an aspect ratio of 11.68, and the end plates are attached to the outer cylinder. The azimuthal profiles were found to be notably different from the laminar velocity profile due to the influence of the end plates. We analyzed the end effects by studying the Ekman and Stewartson boundary layer dynamics in Taylor-Couette flow. [Preview Abstract] |
Tuesday, November 23, 2010 9:44AM - 9:57AM |
MZ.00009: Statistics of velocity fluctuations in turbulent Couette-Taylor flow Chao Sun, Sander Huisman, Dennis van Gils, Detlef Lohse Azimuthal and axial velocity fluctuations between concentric cylinders were measured using Laser Doppler Anemometry in a turbulent Taylor-Couette apparatus. We measured the velocity fluctuations in the middle of the gap and near the outer wall, for pure inner cylinder and counter-rotating cylinders at a fixed Reynolds number of $2 \times 10^6$. The velocity structure functions calculated using extended self-similarity exhibit clear power-law scaling. The transverse and longitude structure function exponents have been compared in two measurement positions. [Preview Abstract] |
Tuesday, November 23, 2010 9:57AM - 10:10AM |
MZ.00010: Torque scaling between independently rotating cylinders in turbulent Taylor-Couette flow Dennis van Gils, Daniela Narezo, Sander Huisman, Chao Sun, Detlef Lohse The Twente Turbulent Taylor-Couette (T$^{3}$C) system allows for a 20 Hz rotation rate of the inner cylinder and 10 Hz rotation rate of the outer cylinder. The corresponding maximum Reynolds numbers for the inner and outer cylinder are Re$_{i}$ = 2.0 x 10$^{6}$, and Re$_{o}$ = 1.4 x 10$^{6}$, respectively. The system has a radius ratio of 0.716 and an aspect ratio of 11.68, and the end plates are attached to the outer cylinder. We measured the global torque (G) as a function of the inner and outer cylinder Reynolds numbers in the unexplored parameter space of co- and counter-rotation. [Preview Abstract] |
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