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 RG: Stratified Flows II |
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Chair: Stefan Llewellyn Smith, University of California, San Diego Room: Long Beach Convention Center 103B |
Tuesday, November 23, 2010 3:05PM - 3:18PM |
RG.00001: Steady solutions for plumes in non-uniform stratifications Nigel Kaye, Matthew Scase The plume conservation equations of Morton et al. (1956) are recast in terms of the plume radius, flux balance parameter $\Gamma$, and a dimensionless parameter that characterizes the stratification. This set of equations lead to simple analytic solutions for steady straight sided plumes in non-uniformly stratified environments. Steady plumes in non-uniform stratification can occur for both stable (Caulfield \& Woods 1998) and unstable (Batchelor 1954) stratifications whose strength has a power law variation with height. We present analytic solutions for the range of stratification power-law decay rates $\kappa$ for which straight sided plumes are possible. The approach used provides significant physical insight into the limits on $\kappa$ that permit straight sided solutions. We also present analytic solutions for the power law behaviour with height of the fluxes of volume, momentum and buoyancy. This result demonstrates that the models of Batchelor and Caulfield \& Woods are two halves of the same continuum of solutions. The flux power law behavior explains the transition between the Batchelor solutions and the Caulfield \& Woods solutions that occurs when $\kappa=-8/3$. For $\kappa<-8/3$ the buoyancy flux decays with height and, therefore, the stratification must be stable. Whereas for $\kappa>-8/3$ the buoyancy flux must increase with height, requiring an unstable stratification. [Preview Abstract] |
Tuesday, November 23, 2010 3:18PM - 3:31PM |
RG.00002: 3D Vortices in Protoplanetary Disks Samy Kamal, Joseph Barranco, Philip Marcus Like the atmosphere of Jupiter, protoplanetary disks (thin disks
of gas \& dust in orbit around newly-formed stars) are
characterized by rapid rotation and intense shear, inspiring
proposals that disks may also be populated with long-lived,
robust storms analogous to the Great Red Spot. Such vortices may
play key roles in the formation of stars and planets by
transporting angular momentum, as well as
trapping and concentrating dust grains, seeding the formation of
planetesimals, the ``building blocks'' of planets.
In our previous work (Barranco \& Marcus 2005), we showed via
numerical simulation (with an anelastic spectral code) that
vortices near the midplane of the disk suffer an antisymmetric
instability and are destroyed. However, internal gravity waves
propagate away from the midplane, amplify and break, creating
bands of vorticity that roll-up into new long-lived, stable
vortices above and below the midplane. We will present new
results on 3D vortex dynamics in protoplanetary disks, exploring
the role of factors unique to this context: the Coriolis
parameter $f$, the shear rate $\sigma$, and the
Brunt-V\"{a}is\"{a}l\"{a} frequency $N$ are all of the same order
of magnitude. In the region around the midplane $N |
Tuesday, November 23, 2010 3:31PM - 3:44PM |
RG.00003: Stratified Flows with Vertical Layering of Density: Theoretical and Experimental Study of the Time Evolution of Flow Configurations and their Stability Matthew Moore, Roberto Camassa, David Hendel, Richard M. McLaughlin, Marshall Newman, Kuai Yu A vertically moving boundary in a stratified fluid can create and maintain a horizontal density gradient or vertical layering of density. Such a flow is created experimentally by towing a narrow fiber upwards through an initially stable stratification, as a layer of heavier fluid entrained by the fiber forms a vertical column. We develop a lubrication model to predict the time evolution which shows close agreement with the experiment. We perform stability analysis on a class of vertically layered shear flows and find a critical length-scale for the size of the entrained layer, below which the flow is stable and above which the flow is unstable. The bifurcation behavior is independent of the Reynolds number. Flows with unstable layer sizes have been created experimentally, however the small amplification rates prevent the instabilities from being observed. [Preview Abstract] |
Tuesday, November 23, 2010 3:44PM - 3:57PM |
RG.00004: The Collapse of an Axisymmetric Mixed Patch and Internal Wave Generation in Uniformly Stratified Fluid Amber Holdsworth, Bruce Sutherland Hurricanes are responsible for mixing localized patches of the upper ocean leaving cooler waters in their wakes. The region collapses into a stratified ambient forming an gravity current and generating internal waves beneath the mixed patch. In an effort to understand the axisymmetric collapse of a mixed patch into uniformly stratified fluid laboratory experiments are performed and wave properties are determined using a non-intrusive technique called Synthetic Schlieren. We find internal wave frequencies are set by the buoyancy frequency, $(\omega \approx 0.8 N_0)$ and that the horizontal wavelength is set by the radius of the cylinder so that $k_r \approx 2 R_c$. Vertical displacement amplitudes scale with the depth of the mixed patch according to $\left| \xi \right| / H_m = .016 \pm .001$ and we find that about $2 \%$ of the available potential energy of the mixed region is extracted by vertically propagating internal waves. The work presented here is a precursor to the more complicated rotating case which will more realistically simulate the oceanic example. Extrapolation of these results is certainly premature, but a conservative estimate of the energy extracted by internal waves through the process of mixed region collapse is on the order of $1$\,GW. That is an estimated $2$\,TW of power over the generation time and is comparable to the power exerted by tides and winds over the ocean. [Preview Abstract] |
Tuesday, November 23, 2010 3:57PM - 4:10PM |
RG.00005: Joint downscale fluxes of energy and potential enstrophy in rotating stratified Boussinesq flows Susan Kurien, Hussein Aluie We use high-resolution simulations of Boussinesq flows, forced in the large-scales, with fixed rotation and stable stratification along the vertical axis, to study the cascades of energy and potential enstrophy to small-scales in three different regimes of stratification and rotation. For strongly stratified flow with moderate rotation, we observe constant fluxes of both energy and potential enstrophy into fourier modes with large vertical component $k_z$, while being entirely suppressed in modes with large horizontal component $k_h$. The fluxes in this regime are predominantly due to a highly non-local transfer from the large-scales directly to the smallest scales. On the other hand, for strongly rotating flow with moderate stratification, there are constant fluxes of energy and potential enstrophy to modes with large $k_h$ while being completely suppressed to modes with large $k_z$. We find that the fluxes in this regime are due to a ``diffusely'' local transfer much like in isotropic Navier-Stokes turbulence. In the third case of equally strong rotation and stratification, there are only slightly anisotropic constant fluxes of energy and potential enstrophy, mostly to modes with large $k_h$. The fluxes in this regime are due to an ultra-local transfer in which the energy gained by an inertial scale comes almost exclusively from the adjacent larger scales. [Preview Abstract] |
Tuesday, November 23, 2010 4:10PM - 4:23PM |
RG.00006: Stability of a pancake vortex in a stratified fluid M. Eletta Negretti, Paul Billant Vortices in stably stratified fluids have generally a pancake shape with a small vertical thickness compared to their horizontal size. Such vortices exhibit a high vertical shear which may induce Kelvin-Helmholtz instabilities. The pressure and density anomaly in their core might trigger also gravitational instabilities. In order to understand which mechanism determines the minimum thickness of the vortex, we investigate the three-dimensional linear stability of an axisymmetric pancake vortex in a stably stratified fluid. The angular velocity of the base flow has a Lamb-Oseen radial profile with a Gaussian distribution in the vertical direction. We find that the vortex becomes unstable when the aspect ratio is below a critical value, which scales with the Froude number. We show that the instability is gravitational by looking at the classical criteria for each instability, which predict larger critical aspect ratios for the gravitational instability as compared to the shear instability. The numerical results agree well with the gravitational instability theory. We have generalized this result to any vertical distribution of the angular velocity and almost any profile of the vortex. We show that the properties of the gravitational instability can be explained by considering an unstably stratified fluid in solid body rotation. The influence of the Reynolds number will be also discussed. [Preview Abstract] |
Tuesday, November 23, 2010 4:23PM - 4:36PM |
RG.00007: Vortex dynamics in a wave field Gaele Perret, Adrien Poupardin, Jerome Brossard The interaction of waves and current with submerged structures in coastal zones generates some complex hydrodynamics features which may considerably impact the local environment. The geometrical singularities of the structures produce concentrated vortex filaments which may impact the sea bed and/or the free surface. The objective of the present study is to characterize the vortex dynamics generated by a horizontal plate considered as a vortex generator, in a regular wave field. Vortices are generated at the edges of the plate. They undergo three-dimensional instabilities leading to their destruction. Their dynamics is investigated thanks to laboratory experiments conducted in two different wave flumes to study the impact of the scale on the dynamics. The two-dimensional vortex dynamics is characterized using PIV measurements. Vortex intensity, trajectory and life time are determined. The three-dimensional dynamics is studied thanks to stereo photography. The vortices are visualised with hydrogen bubbles generated at the edges of the plate by electrolyse. The evolution of the vortices is visualized by two CCD cameras located in different planes. Two most unstable wavelengths are observed which do not seem to depend on the width of the wave flume. [Preview Abstract] |
Tuesday, November 23, 2010 4:36PM - 4:49PM |
RG.00008: Numerical simulation of flow around a sphere moving through a stratified fluid Trevor Orr, Julian Domaradzki, George Constantinescu Flows generated by submersed bodies in stratified fluids have been investigated in numerous experiments and numerical simulations. Numerical simulations are focused in the far-wake region, where computational costs prohibit including the explicit computation of the flow around the sphere. Initial conditions for such far-wake simulations are constructed using information gathered from experimental results of the near-wake properties, but these initializations lack full information about the density field. We present results of numerical simulations that explicitly include the sphere in the computational domain over a range of Reynolds numbers and Froude numbers. The simulations are compared with existing experimental and numerical data. In particular, turbulent simulations using the Spalart-Allmaras DES method are included along with comparison of experimental data collected at USC for Re=5000 and Fr=4. [Preview Abstract] |
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