Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session L34: Geophysical Fluid Dynamics: Rotating Flows |
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Chair: Philip Marcus, University of California, Berkeley Room: Georgia World Congress Center B406 |
Monday, November 19, 2018 4:05PM - 4:18PM |
L34.00001: Abstract Withdrawn Recent investigations have established the existence of a strong inverse energy cascade in rapidly rotating Rayleigh-Benard convection. This occurs as the result of an convective excitation of a barotropic manifold that possesses two volume-averaged quasi-invariant quantities, energy and enstrophy. A dual barotropic cascade is thus expected. The resulting condensate that appears at the domain scale is known to be sensitive to the domain aspect ratio. In this talk, I will discuss the impact of the domain anisotropy on the inverse cascade and effects of being on an f-plane where gravity and rotation are not aligned. |
Monday, November 19, 2018 4:18PM - 4:31PM |
L34.00002: Temperature Distribution in Coriolis-Centrifugal Convection Susanne Horn, Jonathan M Aurnou We present results of direct numerical simulations of Coriolis-centrifugal convection in a cylindrical container. In this system buoyancy effects not only drive convective motions in the vertical direction due to the gravitational acceleration, but also in the radial direction due to the centrifugal acceleration (Phys. Rev. Lett. 120, 2018). Here, we focus on the spatial distribution of the temperature field. Unlike in idealised Coriolis convection in which centrifugal buoyancy is neglected, the vertical temperature profiles become strongly radially dependent with increasing Froude number. In the quasi-cyclostrophic regime the temperature in the center of the fluid volume shows a strong enhancement, reaching values close to the bottom boundary temperature, whereas the temperatures at the midplane sidewall are well below the arithmetic mean. We find, further, that the axisymmetric, linear model by Hart & Ohlsen (Phys. Fluids 11.8, 1999) does not accurately predict the measured center temperatures, suggesting the need for a more sophisticated theory. |
Monday, November 19, 2018 4:31PM - 4:44PM |
L34.00003: Heat transfer characterization of extreme rotating convection regimes in TROCONVEX Jonathan S Cheng, Matteo Madonia, Andres Aguirre Guzman, Rudie Kunnen Many geophysical and astrophysical flows are driven by buoyant instabilities and heavily influenced by rotation. In lieu of the complexity of such systems, rotating Rayleigh-Bénard convection (RRBC) provides a simplified, canonical framework for understanding these flows. To date, however, laboratory experiments and numerical simulations cannot fully access the most geophysically-relevant regimes of rotating convection, which only emerge at extreme values of the governing parameters. Here we present a suite of heat transfer results from TROCONVEX, a new 4-meter-high rotating convection device capable of reaching Ekman numbers as low as 5x10^{-9} and Rayleigh numbers as high as 10^{14} – both nearly an order of magnitude more extreme than previously achievable. We show that vertical temperature profiles are consistent with asymptotically-reduced RRBC results, and clearly reflect flow regime transitions. In addition, thermal measurements hint at the existence of novel flow structures in regimes beyond the scope of asymptotic simulations. |
Monday, November 19, 2018 4:44PM - 4:57PM |
L34.00004: An Equatorial Thermal Wind Equation: Applications to Jupiter Philip S Marcus A fundamental tool of GFD is the Thermal Wind Equation (TWE), which relates the vertical shear of the horizontal wind to the horizontal temperature gradient. Unfortunately, the TWE is invalid at and near the equator because the Coriolis force goes to zero and the Rossby number becomes large. Moreover, at some latitudes, even if the Rossby number is small, the TWE is ill-conditioned because it requires division by a small number. We have derived a well-conditioned ``Equatorial Thermal Wind Equation'' (EQTWE) that relates the vertical derivative of the east-west velocity to the second-derivative of the temperature in the north-south direction that is valid at the equator and up to latitudes of 18^{o }and whose validity is independent of the traditional Rossby number. We apply the EQTWE to the Jovian wind measured by the Galileo probe Doppler wind experiment to reveal thermal anomalies at the Jovian equator at altitudes below 1~bar and show that they imply a Jovian global circulation model with two layers of Hadley cells, with an upper layer like the one on Earth, and the lower has cells with the opposite rotation. At altitudes above 1 bar we use IR temperatures and the EQTWE to determine velocities and show that there is a fast 205 m/s stratospheric jet at 3 mbar. |
Monday, November 19, 2018 4:57PM - 5:10PM |
L34.00005: Experiments on bubble plumes in a rotating environment Daria Frank, Julien Landel, Stuart B Dalziel, Paul F Linden We conducted small-scale experiments in the laboratory to investigate the effects of a rotating environment on the dynamics of multiphase plumes. Bubble plumes, produced using electrolysis, were released into the saline rotating environment. We studied how the rotation rate, the source buoyancy flux and the slip velocity of bubbles affect the plume characteristics such as its rise velocity and the temporal evolution of its width. Of particular interest is the question how the rotation rate modifies the area on the water surface which is affected by the plume after its rise through the water column. This can be, for example, important for modelling the spreading of the oil on the ocean surface after an accidental oil spillage such as the Deepwater Horizon disaster. In the near-source region, multiphase plumes also exhibit anticyclonic precession of the plume axis, similar to single-phase plumes. In this talk, we present our experimental results and develop simple theoretical models to explain the observed plume behaviour. |
Monday, November 19, 2018 5:10PM - 5:23PM |
L34.00006: Genesis of Taylor–Couette flow instabilities H. Oualli, M. Mekadem, M. Khirennas, Y. Rezga, S. Tebtab, T. Azzam, A. Bouabdallah, M. Gad-el-Hak Numerical simulations are conducted of a Taylor–Couette flow from early structuring stages to completion of the Taylor’s axial stationary waves. We seek to elucidate the underlying mechanisms responsible for the genesis of this flow type and to identify the intermediate embryonic stages up to the birth and completion of the Taylor’s axial stationary vortices. A 3D numerical simulations of liquid benzene are implemented on FLUENT. The calculations are based on the finite-volume method with a mesh size of 32X28X256 in, respectively, the radial, azimuthal, and axial directions. The simulations are validated using prior experimental results. The calculations span Taylor numbers from Ta=E-9 to Ta=43.8. The results show that the incipient pressure variations are of the order of E-12 Pa, detected at Ta=E-9, on four symmetrically separated cardinal points within the system. When Ta>E-9, a progressive propagation of alternating overpressure and depression zones operate in both azimuthal directions. This is the first step in the chain of mechanisms responsible for the Taylor’s wave building process. The study reports, for the first time, all the details to explain the instability mechanisms’ evolution. |
Monday, November 19, 2018 5:23PM - 5:36PM |
L34.00007: Increasing helicity to achieve a dynamo state in a spherical Couette sodium experiment Ruben E Rojas Garcia, Artur Perevalov, Daniel Perry Lathrop Dynamo theory describes the generation of magnetic fields in the highly turbulent flows of conducting fluids, for example, in stars and planetary cores. Spherical Couette flows, which are shear-driven flows between two concentric and independently rotating shells, are one of the experimental models used to achieve dynamo action in the laboratory. We aim to achieve a dynamo state in our three-meter spherical Couette model that currently reaches up to Re = 10^{8} with amplifications of the magnetic field between 10-30% but without a self-sustaining dynamo state. Numerical studies [K. Finke and A. Tilgner. Phys. Rev. E, 86:016310, Jul 2012] suggest adding roughness to the inner core, which we attempt by adding baffles on the inner sphere. Our proposed set up reduces the threshold for dynamo action by increasing the polodial flows with respect to the zonal flows and hence increasing helicity. In this work, we present measurements of the velocity profiles and torque measurements in a 40-cm spherical Couette water apparatus for different baffle designs of the inner sphere. These results are fundamental for future modifications in the three-meter model such as shape and height of the baffles, and power of the motors. |
Monday, November 19, 2018 5:36PM - 5:49PM |
L34.00008: Effect of thermal stratification on the symmetry-breaking in a differentially-rotating spherical fluid shell Taishi Inagaki, Kohei Iida, Tomoaki Itano, Masako Sugihara-Seki We consider the shear flow between double concentric spherical boundaries. Under the effect of rotation of the inner boundary (spherical Couette flow), the axisymmetric/non-axisymmetric transition from the trivial state is determined by the radius ratio β of the inner to outer spheres, which has been confirmed experimentally by Nakabayashi(2002) and Egbers(1995). With the comparison to previous studies, we have developed a direct numerical scheme to realize the spherical Couette flow under the weak effect of thermal stratification between the spherical boundaries, which has been unexplored. Here, restricting our attention to the case of non-axisymmetric transition (the radius ratio β>0.3), we numerically investigated the effect on the symmetry-breaking of the shear flow by the weak thermal stratification. In the non-rotating case, under the thermal effect a variety of states are bifurcated from the trivial conductive state at a critical Grashof number. We found that, at a relatively larger rotation number, the thermal effect reduces the transition Grashof number at which the (trivial) axisymmetric state bifurcates into a non-axisymmetric state. Our numerical results predict that axisymmetric states are realized only at less than a certain finite Grashof number. |
Monday, November 19, 2018 5:49PM - 6:02PM |
L34.00009: Variability of Stochastically Forced Beta-Plane Zonal Jets Laura Cope, Peter Haynes Turbulent flows on a beta-plane lead to the spontaneous formation and equilibration of persistent zonal jets. However, the equilibrated jets are not steady and the nature of the time variability in the equilibrated phase is of interest both because of its relevance to the behaviour of naturally occurring jet systems and for the insights it provides into the dynamical mechanisms operating in these systems. Variability is studied within a barotropic model, damped by linear friction, in which stochastic exogenous forcing generates a kind of turbulence that in more complicated systems would be generated by internal dynamical instabilities such as baroclinic instability. This nonlinear (NL) system is used to investigate the variability of zonal jets across a broad range of parameters. Comparisons are made with a reduced quasilinear (QL) system, where eddy-eddy interactions are neglected, permitting only nonlocal interactions between eddies and the zonal mean flow. Both systems reveal a rich variety of jet variability. In particular, the NL model is found to admit the formation of systematically migrating jets, a phenomenon that is observed to be robust in subsets of parameter space. Jets migrate north or south with equal probability, occasionally changing their direction of migration. |
Monday, November 19, 2018 6:02PM - 6:15PM |
L34.00010: Wake of inertial waves of a horizontal cylinder in horizontal translation Pierre-Philippe Cortet, Nathanaël Machicoane, Vincent Labarre, Bruno Voisin, Frédéric Moisy We analyze theoretically and experimentally the wake behind a horizontal cylinder of diameter $d$ horizontally translated at constant velocity $U$ in a fluid rotating about the vertical axis at a rate $\Omega$. Using PIV measurements in the rotating frame, we show that the wake is stabilized by rotation for Reynolds number ${\rm Re}=Ud/\nu$ much larger than in a non-rotating fluid. The limit of stability is ${\rm Re} \simeq (275 \pm 25) / {\rm Ro}$, with ${\rm Ro}=U/2\Omega d$ the Rossby number, indicating that the stabilizing process is governed by Ekman pumping in the boundary layer. At low Rossby number, the wake takes the form of a stationary pattern of inertial waves, similar to the wake of surface gravity waves behind a ship. We compare this steady wake pattern to a model assuming a free-slip boundary condition and a weak streamwise perturbation. Our measurements show a quantitative agreement with this model for ${\rm Ro}\lesssim 0.3$. At larger Rossby number, the phase pattern of the wake is close to the prediction for an infinitely small line object. However, the wake amplitude and phase origin are not correctly described by the weak-streamwise-perturbation model, calling for an alternative model for the boundary condition at moderate rotation rate. |
Monday, November 19, 2018 6:15PM - 6:28PM |
L34.00011: Dynamics of the flow in a precessing ellipsoid Patrice Meunier, Clement Nobili, Benjamin Favier, Michael Le Bars The flow induced by the precession inside the core of the Earth has often been considered as a potential source of energy for the Earth's magnetic field. We study the idealized flow inside a precessing ellipsoid using PIV measurements and numerical simulations. The viscous tilt-over solution splits into two different solutions in a specific range of precession frequencies, as predicted by Busse (1968). The hysteretic cycle between the two solutions is observed experimentally for the first time. For large tilt-over, each solution destabilises through triadic resonances related either to the eruption of boundary layers (critical shear instability, Lin, Marti & Noir 2015) or to the ellipiticity of the streamlines (elliptic instability, Kerswell 1993). Our study thus closes a long-lasting debate on the origin of the precession instability. |
Monday, November 19, 2018 6:28PM - 6:41PM |
L34.00012: Steady Flow in a Rapidly Rotating Spheroid with Weak Precession |
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