Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session A30: Geophysical Fluid Dynamics: Rotating and Stratified Convection |
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Sponsoring Units: DFD Chair: Keith Julien, University of Colorado Room: 311 |
Sunday, November 22, 2015 8:00AM - 8:13AM |
A30.00001: Asymptotically reduced equations for rapidly rotating and stably stratified flow David Nieves, Keith Julien Observations by van Haren & Millot (2005) of the deep Western Mediterranean Sea and by Timmermans et al. (2006) of the deep Canadian Basin find vertical fluid motions to be as significant as horizontal motions for ocean dynamics. Since the classical quasi-geostrophic equations do not allow for such vertical motions reduced equations for geostrophically balanced flow with O(1) vertical motions are presented alongside their numerical solutions and results. The reduced equations describe flow constrained by rapid rotation and stable stratification and, in fact, are the stably stratified counterpart to the reduced equations used by Julien et al. in successful studies of rapidly rotating Rayleigh-BĀ“enard convection. Specifically, the equations are valid in the small Rossby number (Ro 1) and O(1) Froude number limit. The focus here is a comparison to similar studies of rotating and stratified flow by Smith & Waleffe (2002), Wingate et al. (2011), and Marino et al. (2013) among others. [Preview Abstract] |
Sunday, November 22, 2015 8:13AM - 8:26AM |
A30.00002: Rotating Rayleigh-B\'enard convection with Ekman pumping Meredith Plumley, Keith Julien, Philippe Marti, Jonathan Aurnou, Stephan Stellmach Rotating Rayleigh-B\'{e}rnard convection is of interest in many geoscience applications, with examples like deep ocean convection or the magnetic field generation of planets occurring in the regime where convectively driven motions are dominated by the effects of rotation. To better understand the dynamics of these large physical systems, several techniques are used including asymptotic methods, DNS and experiments. While these three methods have seen good agreement in results for stress free boundary conditions, the case of rigid no-slip boundaries presents an interesting difference. Along the no-slip boundaries, Ekman layers form and Ekman pumping occurs. It has been thought that the effect of these boundary layers is negligible for small Ekman number because of how thin they become. However, new DNS of the 3D Boussinesq equations have provided evidence that this is not the case. A new asymptotic model has been developed to include these boundary layers and verify the impact of the Ekman boundaries on the flow. Results from simulations of this new model will be compared with DNS and experimental results. The results support the findings of increased global heat transfer due to the presence of Ekman pumping. [Preview Abstract] |
Sunday, November 22, 2015 8:26AM - 8:39AM |
A30.00003: Mixing efficiency of buoyancy forced circulation in a rotating basin Catherine Vreugdenhil, Bishakhdatta Gayen, Ross Griffiths We ask whether rotation influences the mixing efficiency in horizontal convection in a rectangular basin. Direct numerical simulations are reported for a rotating $f$-plane ocean with an applied basal temperature differential over a wide range of Ekman number $E_L=6\times10^{-8}-1\times10^{-5}$, with Prandtl number $Pr=5$. Two values of the Rayleigh number are considered which, in the absence of rotation, relate to the viscous ($Ra=7.4\times10^8$) and inertial ($Ra=7.4\times10^{11}$) regimes. The heat flux decreases and boundary layer thickness increases with rotation rate, consistent with geostrophic scaling. At very high rotation rates and the smaller $Ra$ a regime dominated by Ekman pumping is revealed, with strong interior stratification. For the larger $Ra$ turbulent convective plumes in the boundary layer region form cyclonic vortices that extend through the depth, weakening the stratification. The global mixing efficiency $\eta$ is consistent with the theoretical prediction $\eta=1-(HNu/L)^{-1}$ (where $Nu$ is the Nusselt number, $H$ is height and $L$ is length of the domain) for $Nu\gg10$. Independent of rotation, $\eta$ approaches unity at large $Nu$, and therefore at large $Ra$. Laboratory experiments in the inertial regime with an applied heat flux are also considered. [Preview Abstract] |
Sunday, November 22, 2015 8:39AM - 8:52AM |
A30.00004: Spinup of a stratified fluid in a sliced, circular cylinder M.R. Foster, R.J. Munro Experiments were performed in a linearly salt-stratified fluid in a circular cylindrical tank, with a planar bottom boundary sloped at a small angle $\alpha$ to the horizontal. The container rotated initially at an angular velocity $\Omega$, so that the Ekman number, $E$, was typically $10^{-5}$. We examined the adjustment when the container's angular speed is abruptly increased by $\epsilon \Omega$, with $\epsilon\sim .01$. Further, $\alpha \gg E^{1/2}$, and the Burger number $S$ is large. There are similarities and differences between this spinup and that in a sliced square cylinder (Munro \& Foster, {\it Phys.~Fluids} {\bf 26}, 2014, denoted by MF14). Unlike MF14, the axisymmetry of the initial core motion means there are no core eddies generated by boundary-layer eruption. In fact, since the core motion is nearly axisymmetric for all time at large $S$, eddy formation is confined to the region of height ${\cal{O}}(S^{-1/2})$ near the lower slope, within which the Rossby waves are confined. Just as in MF14, after several ``spinup times,'' the cross-container velocity profiles agree very well with a linear asymptotic theory for small $\epsilon, E$ and large $S$, provided one properly accounts for the Rayleigh layers on the cylinder's sidewall. [Preview Abstract] |
Sunday, November 22, 2015 8:52AM - 9:05AM |
A30.00005: Regimes of axisymmetric flow in a rotating annulus with local convective forcing Helene Scolan, Sylvie Su, Roland M.B. Young, Peter L. Read We present a numerical study of axisymmetric flows in a rotating annulus convectively forced by local thermal forcing via a heated annular ring at the bottom near the external wall and a cooled circular disk near the centre at the top surface. This new configuration is a variant of the classical thermally-driven annulus analogue of the atmosphere circulation, where thermal forcing was previously applied on the sidewalls. Two vertically and horizontally displaced heat sources/sinks are arranged so that, in the absence of rotation, statically unstable convection would be induced above the source and beneath the sink, thereby relaxing strong constraints placed on background temperature gradients in previous setup. By using the Met Office/ Oxford Rotating Annulus Laboratory code, we investigated a series of equilibrated, 2D axisymmetric flows for a large range of dimensionless parameters and characterized them in terms of velocity and temperature fields. Several distinct flow regimes were identified, depending upon the rotation rate and strength of differential heating. These regimes will be presented with reference to variations of horizontal Ekman layer thickness versus the thermal boundary layer thickness and corresponding scalings for various quantities such as the heat transport. [Preview Abstract] |
Sunday, November 22, 2015 9:05AM - 9:18AM |
A30.00006: A Laboratory Study of Vortical Structures in Rotating Convection Plumes Hao Fu, Shiwei Sun, Yuan Wang, Bowen Zhou A laboratory study of the columnar vortex structure in rotating Rayleigh-B\'{e}nard convection is conducted. A rectangular water tank is uniformly heated from below and cooled from above, with $Ra=(6.35\pm 0.77)\times 10^{7}$, $Ta=9.84\times 10^{7}$, $\Pr =7.34$. The columnar vortices are vertically aligned and quasi steady. Two 2D PIV systems were used to measure velocity field. One system performs horizontal scans at 9 different heights every 13.6s, covering 62{\%} of the total depth. The other system scans vertically to obtain the vertical velocity profile. The measured vertical vorticity profiles of most vortices are quasi-linear with height while the vertical velocities are nearly uniform with only a small curvature. A simple model to deduce vertical velocity profile from vertical vorticity profile is proposed. Under quasi-steady and axisymmetric conditions, a ``vortex core'' assumption is introduced to simplify vertical vorticity equation. A linear ODE about vertical velocity is obtained whenever a vertical vorticity profile is given and solved with experimental data as input. The result is approximately in agreement with the measurement. [Preview Abstract] |
Sunday, November 22, 2015 9:18AM - 9:31AM |
A30.00007: Local Available Potential Energy in Simulations of Stratified Turbulence with Uniform and Non-uniform Ambient Density Gradients Gavin Portwood, Stephen de Bruyn Kops In stratified flows, the maximum amount of potential energy that can be converted to kinetic energy is the difference between the potential energy in the instantaneous flow and that in the flow if the fluid parcels were adiabatically sorted to produce the lowest energy configuration. Lorentz (1955) defines this global quantity as available potential energy (APE). Holliday and McIntyre (1981) introduces the concept of local available potential energy ($E_a$) associated with a fluid parcel, and Molemaker and McWilliams (2010) develop the transport for this quantity for a viscous, Boussinesq fluid. Here, we characterize $E_a$ in simulations of a vortex street with uniform and non-uniform stabilizing ambient density gradients. In pseudo-spectral direct numerical simulations resolved on up to $4096 \times 2048 \times 2048$ grid points, we find that the majority of APE is due to fluid parcels displaced a small distance, relative to the buoyancy length scale, from their locations in the sorted density field. By computing each term in the transport equation for $E_a$, we observe by how much $E_a$ of a fluid parcel changes in time due to local dipycnal mixing, and by how much global mixing alters the position of the local parcel in the sorted density field. [Preview Abstract] |
Sunday, November 22, 2015 9:31AM - 9:44AM |
A30.00008: Heat flux in a penetrative convection experiment in water Yoann Corre, Thierry Alboussi\`{e}re, St\'{e}phane Labrosse, Philippe Odier, Sylvain Joubaud In geophysical systems, stably stratified fluids adjacent to convective regions often experience thermal plume penetration from the latter. This penetrative convection occurs in stellar interiors between radiative and convective regions and possibly in liquid envelopes of planets, such as the Earth's core. We are interested in quantifying this process experimentally as it could play a crucial role in their dynamics. A volume of water initially at ambiant temperature is cooled from below at 0 degrees Celsius. Due to the maximum density of water near 4 degrees, a convective region develops and grows below a purely conductive region. A laser sheet crosses the experimental cell, lightening both neutrally buoyant particles and a thermosensitive fluorescent dye, which allows to monitor the velocity and temperature fields respectively (PIV-LIF technique), giving access to the local convective and conductive heat flux. The apparatus is placed on a rotating table to inspect the effect of the Coriolis force on the interfacial region. We find that increasing the rotation rate deepens the penetration of vortices into the conductive region, thus changing the structure of the interfacial layer and possibly eroding the stable region. [Preview Abstract] |
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