Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session D13: Geophysical Fluid Dynamics: Rotating Stratified Flows |
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Sponsoring Units: DFD GPC Chair: Monica Martinez, University of California - Riverside Room: C124 |
Sunday, November 20, 2016 2:57PM - 3:10PM |
D13.00001: Vorticity Transport in a Two Layer, Double Gyre Ocean Basin Bryan Kaiser, Carol Anne Clayson, Steve Jayne The double gyre ocean circulations predicted by strongly frictional, barotropic, linearized ocean models qualitatively agree with the patterns of large scale gyres in the world ocean. However, nonlinear ocean models featuring less intense eddy diffusion parameterization can converge to an infinite number of statistically stationary circulations, depending on the parameterization of dissipation of energy and vorticity. Patterns of vorticity flux and dissipation in a barotropic ocean have been examined previous studies; in this work the inclusion of the first baroclinic mode is examined. The first vertical mode permits the model to be split into two layers, the top approximating the thermocline and the bottom approximating the abyssal circulation. The separation into two layers not only adds realism and but also removes the nonphysical direct restraint of the upper ocean by bottom friction. Steady state circulations for various boundary conditions, sources and sinks of vorticity, and Reynolds numbers are simulated using a parallel pseudo-spectral quasi-geostrophic flow solver and mechanisms of vorticity flux and dissipation are discussed. [Preview Abstract] |
Sunday, November 20, 2016 3:10PM - 3:23PM |
D13.00002: The sensitivity of rotating Rayleigh-B\'enard convection to the Ekman number Meredith Plumley, Keith Julien, Philippe Marti, Stephan Stellmach, Jonathan Aurnou, Emily Hawkins Many geophysical and astrophysical applications of rotating Rayleigh-B\'enard convection require no-slip boundaries. These boundaries lead to Ekman pumping, which has a dominant impact on the heat transport and affects the transfer of energy within the system. Here I present the 2D surface of the Nusselt number as a function of the Rayleigh number ($Ra$) and the Ekman number ($E$) for no-slip boundaries, generated through a combination of results from experiments, DNS, rescaled DNS, and asymptotic simulations. The $Ra$--$E$ space is mapped from the transition of the weakly-rotating into the rotation-dominated regime ($E \approx 10^{-7}$) to lower $E$ in the rapidly-rotating regime ($E \approx 10^{-11}$). This exploration provides insight into the sensitivity of the flow to the Ekman number, specifically the effect of the boundaries on the types and ranges of flow structures and the difference between stress-free and no-slip boundaries at low $E$, a regime of interest for modeling planetary interiors. [Preview Abstract] |
Sunday, November 20, 2016 3:23PM - 3:36PM |
D13.00003: On the lifetime of a pancake anticyclone in a rotating stratified flow Giulio Facchini, Michael Le Bars We present an experimental study of the time evolution of an isolated anticyclonic pancake vortex in a laboratory rotating stratified flow. Motivations come from the variety of compact anticyclones observed to form and persist for a strikingly long lifetime in geophysical and astrophysical settings combining rotation and stratification. We generate anticyclones by injecting a small amount of isodense fluid at the center of a rotating tank filled with salty water linearly stratified in density. Our two control parameters are the Coriolis parameter $f$ and the Brunt-V\"ais\"al\"a frequency $N$. We observe that anticyclones always slowly decay by viscous diffusion, spreading mainly in the horizontal direction irrespective of the initial aspect ratio. This behavior is correctly explained by a linear analytical model in the limit of small Rossby and Ekman numbers, where density and velocity equations reduce to a single equation for the pressure. Direct numerical simulations further confirm the theoretical predictions. Notably, they show that the azimuthal shear stress generates secondary circulations, which advect the density anomaly: this mechanism is responsible for the slow time evolution, rather than the classical viscous dissipation of the azimuthal kinetic energy. [Preview Abstract] |
Sunday, November 20, 2016 3:36PM - 3:49PM |
D13.00004: Cylindrical gravity currents in a rotating system Ching-Sen Wu, Albert Dai This study aims at investigating the dynamical processes in the formation of stable cylindrical gravity currents, by a full-depth lock release, in a rotating system conducted by direct numerical simulations. The simulations reproduce the major features observed in the laboratory and provide more detailed flow information. Both the qualitative and quantitative measures are provided through the flow patterns and the predicted energy budgets. At the initial stage, during tenth of a revolution of the system, the Kelvin-Helmholtz vortices form and the flow structure maintain nearly axisymmetric. Afterwards, three-dimensionality of flow quickly develops and the outer rim of current breaks away from the body, which gives rise to the maximum dissipation rate in the system. The detached outer rim continues to propagate outward until a maximum radius of propagation is attained. Then the body of current exhibits a regularly contraction-relaxation motion in a period, the energy is transformed back and forth between potential energy and kinetic energy. With the use of high-resolution of numerical computations, the formation of lobe-and-cleft structure and swirling strength for the rotating gravity currents are clearly observed. [Preview Abstract] |
Sunday, November 20, 2016 3:49PM - 4:02PM |
D13.00005: Convection in rotating flows with simultaneous imposition of radial and vertical temperature gradients Ayan Kumar Banerjee, Amitabh Bhattacharya, Sridhar Balasubramanian Laboratory experiments, with a rotating cylindrical annulus and thermal gradient in both radial and vertical directions (so that radial temperature difference decreases with the elevation), were conducted to study the convection dynamics and heat transport. Temperature data captured using thermocouples, combined with ANSYS Fluent simulation hinted at the co-existence of thermal plume and baroclinicity (inclined isotherms). Presence of columnar plume structure parallel to the rotation axis was found, which had a phase velocity and aided in vertical heat transport. Nusselt number (Nu) plotted as a function of Taylor number (Ta) showed the effect of rotation on heat transport in such systems, where the interplay of plumes and baroclinic waves control the scalar transport.~ Laser based PIV imaging at a single vertical plane also showed evidence of such flow structures. [Preview Abstract] |
Sunday, November 20, 2016 4:02PM - 4:15PM |
D13.00006: Experiments on point plumes in a rotating environment Daria Frank, Julien Landel, Stuart Dalziel, Paul Linden Motivated by the Deepwater Horizon oil spill in the Gulf of Mexico we study the dynamics of point plumes in a stratified and homogeneous rotating environment. To this end, we conduct small-scale experiments in the laboratory on salt water and bubble plumes over a wide range of Rossby numbers. The rotation modifies the entrainment into the plume and also inhibits the lateral spreading of the plume fluid which leads to various instabilities in the flow. In particular, we focus on the plume behaviour in the near-source region (where the plume is dominated by the source conditions) and at intermediate water depths, e.g., lateral intrusions at the neutral buoyancy level in the stratified environment. One of the striking features in the rotating environment is the anticyclonic precession of the plume axis which leads to an enhanced dispersion of the plume fluid in the ambient and which is absent in the non-rotating system. In this talk, we present our experimental results and develop simple models to explain the observed plume dynamics. [Preview Abstract] |
Sunday, November 20, 2016 4:15PM - 4:28PM |
D13.00007: Quasigeostrophic investigations of non-hydrostatic, stably- stratified and rapidly rotating flows Keith Julien, David Nieves, Ian Grooms, Jeffrey Weiss We present an investigation of rapidly rotating stratified turbulence where the stratification strength is varied from weak to strong. The investigation is set in the context of a reduced model derived from the Boussinesq equations that retains anisotropic inertia-gravity waves with order-one frequencies and highlights a regime of wave–eddy interactions. Numerical simulations are performed where energy is injected by a stochastic forcing of vertical velocity, which forces wave modes only. The simulations reveal two regimes characterized by the presence of well-formed, persistent and thin turbulent layers of locally weakened stratification at small Froude numbers, and by the absence of layers at large Froude numbers. Both regimes are characterized by a large-scale barotropic dipole enclosed by small-scale turbulence. When the Reynolds number is not too large, a direct cascade of barotropic kinetic energy is observed, leading to total energy equilibration. We examine net energy exchanges that occur through vortex stretching and vertical buoyancy flux. We find that the baroclinic motions inject energy directly to the largest scales of the barotropic mode, implying that the large-scale barotropic dipole is not the end result of an inverse cascade within the barotropic mode. [Preview Abstract] |
Sunday, November 20, 2016 4:28PM - 4:41PM |
D13.00008: Observations of Instabilities in Stratified Taylor-Couette Flow Bruce Rodenborn, Ruy Ibanez, Harry L. Swinney Inviscid analyses by Molemaker et al. (Phys. Rev. Lett. 86, 5270, 2001) and by Dubrulle et al. (Astron. Astrophys. 29, 1, 2005) predicted that a fluid with a vertically varying density will be less stable than a uniform fluid when the fluid is contained inside a concentric rotating cylinder system and subject to anticyclonic shear. Dubrulle et al. named this instability the stratorotational instability and a subsequent viscous theory by Shalybkov and Rudiger (Astron. Astrophys. 438, 411, 2005) hypothesized that such stratified flow is stable when the ratio of outer and inner cylinder rotation rates $\mu$ is less than the ratio of the inner and outer cylinder radii $\eta$. Le Bars and Le Gal (Phys. Rev. Lett. 99, 064502, 2007) confirmed this hypothesis in experiments for $Re<1200$ with $Re\equiv (r_o-r_i)\Omega_i r_i/\nu$. However, we find the SRI exists for $\mu>\eta$ when the density gradient is large. We also find that the axial wavelength scales linearly with the internal Froude number and that the onset of the SRI is suppressed for $Re>4000$, a region previously unexplored in experiments. For $Re>8000$, we find that the fluid does not exhibit the SRI but transitions to a spatially nonperiodic state that mixes the fluid. [Preview Abstract] |
Sunday, November 20, 2016 4:41PM - 4:54PM |
D13.00009: Characterisation of a quasi-periodic mixing mechanism in stratified turbulent Taylor-Couette flow Kanwar Nain Singh, Jamie Partridge, Stuart Dalziel, C.P. Caulfield We conduct experiments to examine a quasi-periodic mixing event that occurs in stratified Taylor-Couette flow, i.e. axially-stratified flow in the annular region between two concentric cylinders which can rotate at different angular velocities. It has been previously observed that, in two-layer density stratified Taylor-Couette flow, there is an intermittent periodic mixing event which is continuously advected around the annulus. We track this mixing event within the annular gap of the Taylor-Couette apparatus by continuously measuring density perturbations at the sharp interface separating the two layers as a function of radial location. It has been seen that when $Ri = \frac{g'R_o}{(R_i\Omega_i)^2}\sim 7$, where $R_i$, $R_o$ are the inner and outer cylinder radius, respectively, $g'$ the reduced gravity characterising the density jump between the layers and $\Omega_i$ is the rotation rate of the inner cylinder, the power of the mixing event in the frequency spectrum of the density data drops significantly. This process seems to be consistent at all radial locations throughout the annulus. This phenomenon is further investigated using velocity information obtained from particle image velocimetry (PIV). [Preview Abstract] |
Sunday, November 20, 2016 4:54PM - 5:07PM |
D13.00010: Quantifying mixing in stratified plane Couette flows in a tracer-based coordinate Qi Zhou, John Taylor, Colm-cille Caulfield, Paul Linden The mixing properties of statically stable density interfaces subject to imposed vertical shear are investigated using direct numerical simulations. At the start of each simulation, a sharp density interface is introduced at the mid-plane between two flat, counter-moving horizontal walls. Particular attention is paid to the effects of varying Prandtl number over two orders of magnitude from 0.7, 7 to 70. The dynamics of the interface varies from shear-induced overturning at small Richardson numbers to internal waves at large Richardson numbers. At sufficiently large Peclet number, the dynamics allows the density interface to remain sharp. This is due to the combined effects of the `scouring' induced by the turbulence external to the interface and comparatively weak molecular diffusion across the core region of the interface. The effective diapycnal diffusivity and irreversible density flux are quantified in the tracer-based coordinate proposed by Winters and D'Asaro (\textit{J. Fluid Mech.}, 317, 1996) and Nakamura (\textit{J. Atmos. Sci.}, 53, 1996). We further discuss the dependence of the effective diffusivity on the characteristic parameters of the flow, and the implications for mixing efficiency and layer formation. [Preview Abstract] |
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