Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session M1: Geophysical: General II - Stratified Flows |
Hide Abstracts |
Chair: Pedram Hassanzadeh, University of California, Berkeley Room: 323 |
Tuesday, November 26, 2013 8:00AM - 8:13AM |
M1.00001: The Oceanic Charney Problem Shane Keating, K. Shafer Smith We examine the effect of a surface buoyancy gradient on the formation, vertical structure, and transport properties of mesoscale eddies in an `oceanic' version of the classical Charney problem. The analysis is carried out in the context of a general mean state that permits a systematic study of the competing effects of surface buoyancy, planetary vorticity, and baroclinic shear. We show that the presence of a surface buoyancy gradient subtly modifies the Charney-Stern-Pedlosky necessary criteria for instability and has important implications for the resulting nonlinear equilibrated flow. In particular, a surface buoyancy gradient rapidly generates buoyancy variance close to the surface, strongly modifying the nature of the turbulent cascades, the kinetic energy spectrum, and the vertical structure of the eddies. Idealized numerical simulations of the resulting flow show a transition from surface quasigeostrophic turbulence near the surface to classical geostrophic turbulence in the interior. [Preview Abstract] |
Tuesday, November 26, 2013 8:13AM - 8:26AM |
M1.00002: Global instabilities of internal gravity waves Ga\'etan Lerisson, Sabine Ortiz, Jean-Marc Chomaz Internal gravity waves are particularly important in the ocean where they are generated by different mechanisms, interaction of currents or tides with topography, or coupling with waves at the thermocline. By their breaking they are thought to influence the deep ocean mixing and so contribute to the thermohaline circulation. We reconsider the experiment and theory of Bourget et al who considered stationary quasi-monochromatic beam to include the influence of a uniform background horizontal flow. Specifically we consider two limit cases: the non translating wave maker in which the waves are stationary and the wave maker translation at the horizontal phase velocity which to the classical lee wave problem of a sinusoidal mountain. We show that the global stability properties of these different flows differ strongly whereas locally they involve the same unstable gravity wave solution. This change in global stability is then linked to the absolute or convective nature of the local instability which are for the first time determined for a periodic base flow and for 2D wave packets. [Preview Abstract] |
Tuesday, November 26, 2013 8:26AM - 8:39AM |
M1.00003: A Unified Model of Geostrophic Adjustment and Frontogenesis John Taylor, Callum Shakespeare Fronts, or regions with strong horizontal density gradients, are ubiquitous and dynamically important features of the ocean and atmosphere. In the ocean, fronts are associated with enhanced air-sea fluxes, turbulence, and biological productivity, while atmospheric fronts are associated with some of the most extreme weather events. Here, we describe a new mathematical framework for describing the formation of fronts, or frontogenesis. This framework unifies two classical problems in geophysical fluid dynamics, geostrophic adjustment and strain-driven frontogenesis, and provides a number of important extensions beyond previous efforts. The model solutions closely match numerical simulations during the early stages of frontogenesis, and provide a means to describe the development of turbulence at mature fronts. [Preview Abstract] |
Tuesday, November 26, 2013 8:39AM - 8:52AM |
M1.00004: Turbulent mixing in stratified wall-bounded turbulent flows Subhas Venayagamoorthy, Farid Karimpour The focus of this study is to investigate the effect of density stratification in wall-bounded turbulent flows. For a steady fully developed stably stratified channel flow, we invoke the equilibrium assumption between the turbulent kinetic energy production rate ($P$), dissipation rate ($\epsilon$) of the turbulent kinetic energy ($k$) and the turbulent potential energy dissipation rate ($\epsilon_{PE}$) to highlight a number of pertinent issues that have direct implications for predicting turbulent mixing. Simple formulations for the momemtum and scalar diffusivites are proposed based on the irreversible flux Richardson number and the turbulent Prandtl number. Comparisons with data of direct numerical simulation of stably stratified channel flow show remarkable agreement. These findings could be useful for modeling stratified channel flows. [Preview Abstract] |
Tuesday, November 26, 2013 8:52AM - 9:05AM |
M1.00005: Lilly mechanism versus Zigzag instability in the destabilisation of a stratified turbulent flow initially uniform on the vertical Jean-Marc Chomaz, Cristobal Arratia It is now well established that strongly stratified turbulence involves a direct inhomogeneous cascade where the vertical scale is given by the buoyancy length scale as predicted by the Billant \& Chomaz (2001) scaling (BCS). But the role of the so-called zigzag instability (ZZI) in imposing this scaling remains an open question, in particular because Lilly's arguments (similar to the toroidal cascade) do not involve vertical transport as ZZI does. The argument also predicts the occurrence of vertical scales much smaller than the horizontal scale. By performing transient energy growth of perturbations around an evolving, or even turbulent, flow that is vertically uniform we demonstrate that, except for flows made of well separated vortices, the layering of the flow results from the 2D perturbation mode associated to the leading Lyapunov exponent (measuring the sensitivity to initial condition of the 2D base flow) and not from the zigzag modes coming from neutral 2D mode associated with rotation and translation. The generic route to stratified turbulence seems then to be following a Lyapunov-Lilly avenue and not the zigzag winding road. Still, no matter which mechanism involved, the BCS scaling applies to the optimal gain explaining the anisotropy of stratified turbulence. [Preview Abstract] |
Tuesday, November 26, 2013 9:05AM - 9:18AM |
M1.00006: Buoyant Jets in Stratification; Mixing Efficiencies, Entropy Conditions and Wall Effects Chung-Nan Tzou, Roberto Camassa, Marlow Durbin, Richard McLaughlin, Jeremy Ward, Cole Whetstone, Brian White An exact integral solution to the steady buoyant jet closure model in linearly stratified ambient environment is derived so that in the limit of a sharply stratified environment an entropy (nonlinear jump) condition can be established. Comparing the density evolution for the buoyant jet in the extremes of linear and sharp stratification using experiments and exact formulas, mixing efficiencies can be assessed. In turn, wall effects are explored experimentally in sharp stratification and compared to the closure theory. Lastly, the modeling of entrainment in these systems will be revisited. [Preview Abstract] |
Tuesday, November 26, 2013 9:18AM - 9:31AM |
M1.00007: Jets generated by a sphere moving vertically in stratified fluids Hideshi Hanazaki, Shinya Okino, Shota Nakamura, Shinsaku Akiyama Unsteady development of buoyant jets generated by a sphere moving vertically at constant speeds in stratified fluids is investigated. Initially, the sphere simply drags light upper fluids or isopycnal surfaces as it goes down, as long as the molecular diffusion of density is negligible. In the succeeding period, molecular diffusion of density in the boundary layer on the sphere surface becomes increasingly significant, especially in the lower hemisphere. Then, the density is no longer conserved and a vertical jet starts from the rear/upper stagnation point of the sphere, since the fluid particle of altered but small density tends to go back to its original height. Strength and radius of those jets depend significantly on stratification (Froude number), as well as the Reynolds number and the Schmidt number. These mechanisms are investigated by numerical simulations and measurements by laser induced fluorescence (LIF). [Preview Abstract] |
Tuesday, November 26, 2013 9:31AM - 9:44AM |
M1.00008: 3D Zombie Vortices in Rotating Stratified Shear Philip Marcus, Suyang Pei, Chung-Hsiang Jiang, Pedram Hassanzadeh, Joseph Barranco, Daniel Lecoanet We have shown that there is a finite-amplitude instability in linearly-stable, rotating, vertically-stratified, horizontally-shearing flows. The instability is due to excitations of baroclinic critical layers in which the vertical velocity of a neutrally-stable eigenmode is singular in the inviscid limit. This singularity coupled with the Coriolis and stretching terms in the vertical vorticity equation create intense vortex layers. Those layers roll-up into 3D vortices, which then de-stabilize other critical layers. These vortices, which we call {\it zombie} vortices, can fill the {\it dead zone} of a protoplanetary disk around a forming star. The vortices, either by themselves or by exciting inertio-gravity waves or acoustic waves, can transport angular momentum in a protoplanetary disk and thereby allow a protostar to form into a star. We find that the zombie vortices are similar in flows with Boussinesq, anelastic, and fully compressible equations of state. However, the rates of angular momentum transport and the mechanisms by which it is transported vary significantly in flows with different equations of state. [Preview Abstract] |
Tuesday, November 26, 2013 9:44AM - 9:57AM |
M1.00009: Noise and Turbulence Generate 3D Zombie Vortices in Stably Stratified Rotating Shear Flows Suyang Pei, Philip S. Marcus, Chung-Hsiang Jiang, Pedram Hassanzadeh, Daniel Lecoanet, Joseph A. Barranco We showed previously that a linearly stable shearing, rotating, stably stratified flow has a finite-amplitude instability creating ``zombie vortices'' that self-replicate and fill the domain. Our flows were initialized with perturbations of one or two vortices. Our motivation was to determine whether ``dead zones'' in protoplanetary disks were stable, or whether they could be de-stabilized to produce vortices necessary for the final part of star formation and for planet formation. To be more relevant to astrophysics, we choose the initial conditions to be noise or turbulence with a Kolmogorov spectrum with small kinetic energy and Mach number. In a Kolmogorov spectrum, the largest eddies determine the kinetic energy and Mach number, while the smallest determine the vorticity and Rossby number $Ro \equiv \omega/f$, where $\omega$ is the vertical vorticity and $f$ is the Coriolis parameter. The protoplanetary disks (which have large inertial ranges due to their large Reynolds numbers), can have large Rossby numbers, but weak Mach numbers and kinetic energies. It is important to know whether the triggering of the finite-amplitude instability that creates zombie vortices depends on threshold values of Mach number, kinetic energy, or the Rossby number. Here, we show it is the latter. [Preview Abstract] |
Tuesday, November 26, 2013 9:57AM - 10:10AM |
M1.00010: Statistical Equilibrium and Inverse Cascades of vortical modes for rotating and stratified flows Corentin Herbert, Raffaele Marino, Annick Pouquet Most turbulent flows appearing in nature are subjected to strong rotation and stratification. These effects break the symmetries of homogenous isotropic turbulence. In doing so, they introduce a natural decomposition of phase space in terms of wave modes and potential vorticity modes. The appearance of a new time scale associated to the propagation of waves increases the complexity of the energy transfers between the various scales; nonlinearly interacting waves may dominate at some scales while balanced motion may prevail at others. In the end, it is difficult to predict if the energy cascades downscale as in homogeneous isotropic turbulence, upscale as expected from balanced dynamics, or follows yet another phenomenology. In this contribution, we suggest a theoretical approach based on equilibrium statistical mechanics for the ideal system. We show that when the dynamics is restricted to the vortical modes, the equilibrium spectrum features an infrared divergence characteristic of an inverse cascade regime. This can be interpreted as a metastable state for the full system. We discuss how the waves are expected to deflect the energy cascade, for purely rotating, purely stratified and rotating-stratified flows, finally leading to inverse or direct cascade scenarios. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700