Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session R14: Rotating Flows III |
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Chair: Susan Kurien, Los Alamos National Laboratory Room: 27B |
Tuesday, November 20, 2012 1:00PM - 1:13PM |
R14.00001: Flow Characterization in a Spinning Film Apparatus Alonso Alvarado-Savarain, Ellen Longmire Flow generated in a mixing apparatus with similarities to but distinct deviations from a standard Taylor-Couette geometry is examined. Here an inner cylinder rotates about a vertical axis as an impeller within a stationary outer cylinder. The radius ratio is 0.95 and the aspect ratio of outer cylinder length to gap width is 27.5. The inner cylinder is hollow and shorter than the outer cylinder, leaving a bottom gap of 2.5 times the inter-cylinder gap width. The apparatus volume is partially full of liquid such that an inner free surface forms during operation. Velocity statistics in the side and bottom gaps are determined by laser Doppler velocimetry for characteristic Taylor (or Reynolds) numbers based on gap width in the range 1100-4700 which represent wavy vortex and turbulent regimes in Taylor-Couette flow. Experimental results for the aforementioned Reynolds numbers in conditions where the liquid present in the system is 30{\%}, 43{\%} and 52{\%} of the total volume are shown. Additional results having the system modified to allow axial throughflow maintaining dimensions and liquid holdup equal to the batch conditions are also shown. [Preview Abstract] |
Tuesday, November 20, 2012 1:13PM - 1:26PM |
R14.00002: Layer formation in rotating and stratified flows Susan Kurien, Leslie Smith We present a numerical study of layer formation in forced, rotating, stably stratified Boussinesq flows. We focus on parameter regimes with buoyancy frequency $N$ and rotation frequency $f$ chosen such that the timescales $1/N$ and $1/f$ are at least as fast as the nonlinear timescales. The aspect-ratio of the domain is $\delta = H_d/L_d$ where $H_d$ and $L_d$ are the domain height and width respectively. Two sets of calculations are studied at small, nearly fixed Froude number $Fr = U/(H N) \approx 0.002$ where $H$ is fixed at one-quarter of $H_d$ and $U$ is the characteristic forcing based velocity scale. The first set fixes $\delta = 1$ with $N/f$ values ranging from 1 to 32. The second set fixes the Burger number $Bu = \delta N/f = 1$ with aspect ratio $\delta = H_d/L_d$ ranging from 1 to 1/16. We show that both rotation rate and domain aspect-ratio conspire to set the scale and structure of the layers formed in the flows. [Preview Abstract] |
Tuesday, November 20, 2012 1:26PM - 1:39PM |
R14.00003: Density Stratification of Rotating Flow in Coaxial Cylinder Sungsu Lee, Hyun Ah Son, Albert S. Kim Flows containing particulates often pose problems in many engineering practices among which the separation of clean water from polluted solution is essential in environmental engineering. In this study, the stratification of density in a coaxial cylinder are investigated using computational fluid dynamics with Boussinesq approximation. Particulate flow is injected into the domain between the vertical coaxial cylinders and allowed to leave the domain through the exit located upper part of the inner cylinder. During the rotation initiated by the tangential momentum, the hydrodynamic forces stratifies the particulate flow and interact with gravitational force as well as friction, which make the flow instable and complex. This study includes parametric investigation by varying the density of the particulates in the flow and the size of the inner cylinder. The results will present the effectiveness of the stratification which corresponds to the vortex separation in many engineering practice. This work was financially supported by projects of the ``Development of Energy utilization technology with Deep Ocean Water,'' KIOST of Korea. [Preview Abstract] |
Tuesday, November 20, 2012 1:39PM - 1:52PM |
R14.00004: Transitions in turbulent plane Couette flow with rotation Matthew Salewski, Bruno Eckhardt The interplay of shearing and rotational forces in fluids significantly affects the transport properties of turbulent fluids such as the heat flux in rotating convection and the angular momentum flux in a fluid annulus between differentially rotating cylinders. A numerical investigation was undertaken to study the role of these forces using plane Couette flow subject to rotation about an axis perpendicular to both wall-normal and streamwise directions. Using a set of progressively increasing Reynolds numbers ($650 \leq Re \leq 5200$), our primary findings show the momentum transport for a given $Re$ is a smooth but non-monotonic function of inverse Rossby number ($1/Ro$). For lower turbulent Reynolds numbers, $Re \leq 1300$, a peak in momentum transport occurs at $1/Ro=0.2$; this peak is 50\% higher than the non-rotating ($1/Ro=0$) flux and is attributed to the turbulent Taylor vortices. However, as the shear is increased to $Re=5200$, a second stronger peak emerges at $1/Ro=0.03$. The flux at the second peak is nearly 20\% larger than the non-rotating flux compared to the Taylor vortex peak which is now only 16\% larger. This finding contributes to the understanding of the torque maximum found in the high-turbulence Taylor-Couette experiments in Maryland, USA and Twente, NL. [Preview Abstract] |
Tuesday, November 20, 2012 1:52PM - 2:05PM |
R14.00005: Stability and transition in rotating plane Couette flow Conor Daly, Nigel Peake It is well known that the addition of spanwise Coriolis rotation to plane Couette shear flow causes the laminar solution to destabilise. Linear stability theory predicts a secondary solution of steady, streamwise oriented vortices, with numerical and experimental evidence in support of the predicition. We compute the linear stability of the secondary solutions, and find that the characteristics of the least stable mode depend on the non-dimensionalised rotation parameter. We discuss the transition phenomena arising from the different secondary instabilities, which lead to a range of steady and unsteady tertiary states. [Preview Abstract] |
Tuesday, November 20, 2012 2:05PM - 2:18PM |
R14.00006: Rotating plane Couette flow at high rotation number A. Suryadi, N. Tillmark, P.H. Alfredsson Flow structures in the rotating plane Couette flow facility at KTH (described in Tsukahara, et al. {\it J. Fluid Mech.} vol.~{\bf 648}) have been studied at high rotation numbers. The test section is 20~mm wide with a length of 1500~mm in the streamwise ($x$) and 360~mm in the spanwise ($z$) directions and can be rotated in the spanwise direction up to angular velocities of $\Omega_z \approx 0.6$~rad/s. The flow is characterised by: (1) the Reynolds number $Re$ based on the test section's half-width $(h)$ and half of the velocity difference between the moving walls, (2) the rotation number $\Omega = 2\Omega_z h^2/\nu$. For low rotation numbers the primary instability consists of streamwise-oriented roll cells, but Tsukahara, et al. showed the secondary instability in the form of wavy streamwise oriented roll-cells at $Re=100$ and $\Omega = 3 - 12$, whereas for higher $\Omega$, the flow structures again stabilize to streamwise-oriented roll cells. Here we find that at even higher $\Omega$ in the range $40 - 70$, a new type of secondary instability develops in the form of counter-rotating helical roll-cells. The structure of this instability, as well as other instabilities, are investigated by flow visualization as well as two-dimensional PIV-measurements in several $xz$-planes. [Preview Abstract] |
Tuesday, November 20, 2012 2:18PM - 2:31PM |
R14.00007: Nonlinear evolution of the elliptical instability Adrian Barker, Yoram Lithwick Tidal interactions between short-period gaseous planets and their host stars can have important effects on the orbits of the planets. In particular, the observational preponderance of circular orbits amongst short-period planets, relative to those in wider orbits, is thought to be explained by tidal dissipation in the planets. However, the mechanisms responsible for this are poorly understood. To a first approximation, the linear response of a rotating gaseous planet to the tidal gravitational perturbation of its host star is an elliptical flow, with its major axis aligned with the star. This flow is subject to the elliptical instability, which is a generic linear instability of elliptical streamlines. We will discuss results from a set of high-resolution numerical simulations of the nonlinear evolution of the elliptical instability in a local model of a rotating tidally deformed fluid body. This model allows a detailed study of the dissipative properties of the turbulence driven by the elliptical instability. We will also present results of simulations including the effects of a weak magnetic field, and how this modifies the resulting evolution. The importance of this mechanism for explaining the observations will be discussed. [Preview Abstract] |
Tuesday, November 20, 2012 2:31PM - 2:44PM |
R14.00008: Experimental evidence of a triadic resonance of plane inertial waves in a rotating fluid Thierry Dauxois, Guilhem Bordes, Fr\'{e}d\'{e}ric Moisy, Pierre-Philippe Cortet Plane inertial waves are generated using a wavemaker, made of oscillating stacked plates, in a rotating water tank. Using particle image velocimetry, we observe that, after a transient, the primary plane wave is subject to a subharmonic instability and excites two secondary plane waves. The measured frequencies and wavevectors of these secondary waves are in quantitative agreement with the predictions of the triadic resonance mechanism. The secondary wavevectors are found systematically more normal to the rotation axis than the primary wavevector: this feature illustrates the basic mechanism at the origin of the energy transfers towards slow, quasi two-dimensional, motions in rotating turbulence.\\[4pt] Reference: G. Bordes, F. Moisy, T. Dauxois, P.-P. Cortet, Phys. Fluids \textbf{24}, 014105 (2012), doi: 10.1063/1.3675627 [Preview Abstract] |
Tuesday, November 20, 2012 2:44PM - 2:57PM |
R14.00009: Earth rotation prevents exact solid body rotation of fluids in the laboratory Pierre-Philippe Cortet, Jean Boisson, David C\'ebron, Fr\'{e}d\'{e}ric Moisy We report direct evidence of a secondary flow excited by the Earth rotation in a water-filled spherical container spinning at constant rotation rate. This so-called {\it tilt-over flow} essentially consists in a rotation around an axis which is slightly tilted with respect to the rotation axis of the sphere. In the astrophysical context, it corresponds to the flow in the liquid cores of planets forced by precession of the planet rotation axis, and it has been proposed to contribute to the generation of planetary magnetic fields. We detect this weak secondary flow using a particle image velocimetry system mounted in the rotating frame. This secondary flow consists in a weak rotation, thousand times smaller than the sphere rotation, around a horizontal axis which is stationary in the laboratory frame. Its amplitude and orientation are in quantitative agreement with the theory of the tilt-over flow excited by precession. These results show that setting a fluid in a perfect solid body rotation in a laboratory experiment is impossible --- unless tilting the rotation axis of the experiment parallel to the Earth rotation axis.\\ Reference: J. Boisson, D. C\'{e}bron, F. Moisy and P.-P. Cortet, EPL \textbf{98}, 59002 (2012), doi: 10.1209/0295-5075/98/59002 [Preview Abstract] |
Tuesday, November 20, 2012 2:57PM - 3:10PM |
R14.00010: A fluid Foucault pendulum: the impossibility of achieving solid-body rotation on Earth Robert Blum, Daniel Zimmerman, Santiago Triana, Daniel Lathrop Rotating fluid dynamics is key to our understanding of the Earth's atmosphere, oceans, and core, along with a plethora of astrophysical objects. Laboratory study of these natural systems often involves spinning experimental devices, which are assumed to tend to rigid rotation when unstirred. We present results showing that even at the tabletop scale, there is a measurable oscillatory flow driven by the precession of the experiment's axis as the earth rotates. We measure this flow in a rotating cylinder with an adjustable aspect ratio. The horizontal flow in the rotating frame is measured using particle tracking. The steady state is well-described by an inertial mode whose amplitude is maximum when the height to diameter ratio is 0.995, which matches theoretical predictions. We also quantify the resonant amplitude of the inertial mode in the cylinder and estimate the amplitude in other devices. We compare our results to similar studies done in spherical devices. [Triana et al, JGR, 117 (2012), B04103][Boisson et al, EPL, 98 (2012), 59002] [Preview Abstract] |
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