On the stability of a cold-core eddy in the presence of convection: hydrostatic versus non-hydrostatic modeling

Geostrophic eddies in a stratified liquid are susceptable to baroclinic instabilities.In this paper,we consider these instabilities when such an eddy is simultaneously cooled homoge- neously from above.As a linear stability analysis shows,the developing convection modi ?es the background stratification,the stability boundaries and the patterns of the dominant modes.The coupling between the effects of convection and the large scale fiow devel- opment of the eddy is studied through high resolution numerical simulations,using both non-hydrostatic and hydrostatic models.In the latter models,several forms of convective adjustment are used to model convection.Both type of models conform the development of the dominant modes and indicate that their nonlinear interaction leads to localized in- tense convection.By comparing non-hydrostatic and hydrostatic simulations of the flow development carefully,it is shown that convective adjustment may lead to erroneous small scale variability.A simple alternative formulation of convective adjustment is able to give a substantial improvement

Imperfections of the North-Atlantic wind-driven ocean circulation: continental geometry and windstress shape

Multiple equilibria of the wind-driven gyres have been found in idealized quasi- geostrophic and shallow water models.In this paper we demonstrate that multiple equilibria persist within a reduced gravity shallow water model under quite realis- tic continental geometry and windstress orcing for the North-Atlantic.Multiple mean flow patterns of the Gulf Stream exist and differ with respect to their separation behavior along the North-American coast.The origin of these equilibria is investigated by determining the structure of steady solutions within a hierarchy of equivalent barotropic ocean models using continuation techniques.Within each model,the magnitude of lateral riction is used as a control parameter.It is shown that symmetry breaking, found in a quasi-geostrophic model for a rectan- gular ocean basin with idealized wind forcing is at the origin of two different mean states of the Gul Stream.The steady states ound become unstable only to a small number of oscillatory modes,which either have intermonthly or interannual periods.The modes of variability remain strongly related through the hierarchy of models indicating that their physics is not strongly dependent on the shape of the continents but is controlled by internal ocean dynamics

Nonaxisymmetric stability in the shearing sheet approximation

Aims: To quantify the transient growth of nonaxisymmetric perturbations in unstratified magnetized and stratified non-magnetized rotating linear shear flows in the shearing sheet approximation of accretion disc flows. Method: The Rayleigh quotient in modal approaches for the linearized equations (with time-dependent wavenumber) and the amplitudes from direct shearing sheet simulations using a finite difference code are compared. Results: Both approaches agree in their predicted growth behavior. The magneto-rotational instability for axisymmetric and non-axisymmetric perturbations is shown to have the same dependence of the (instantaneous) growth rate on the wavenumber along the magnetic field, but in the nonaxisymmetric case the growth is only transient. However, a meaningful dependence of the Rayleigh quotient on the radial wavenumber is obtained. While in the magnetized case the total amplification factor can be several orders of magnitude, it is only of order ten or less in the nonmagnetic case. Stratification is shown to have a stabilizing effect. In the present case of shearing-periodic boundaries the (local) strato-rotational instability seems to be absent.Comment: 8 pages, 7 figures, A&A (in press

A general theorem on angular-momentum changes due to potential vorticity mixing and on potential-energy changes due to buoyancy mixing

An initial zonally symmetric quasigeostrophic potential-vorticity (PV) distribution q_i(y) is subjected to complete or partial mixing within some finite zone |y| < L, where y is latitude. The change in M, the total absolute angular momentum, between the initial and any later time is considered. For standard quasigeostrophic shallow-water beta-channel dynamics it is proved that, for any q_i(y) such that dq_i/dy > 0 throughout |y| < L, the change in M is always negative. This theorem holds even when "mixing" is understood in the most general possible sense. Arbitrary stirring or advective rearrangement is included, combined to an arbitrary extent with spatially inhomogeneous diffusion. The theorem holds whether or not the PV distribution is zonally symmetric at the later time. The same theorem governs Boussinesq potential-energy changes due to buoyancy mixing in the vertical. For the standard quasigeostrophic beta-channel dynamics to be valid the Rossby deformation length L_D >> \epsilon L where \epsilon is the Rossby number; when L_D = \infty the theorem applies not only to the beta-channel, but also to a single barotropic layer on the full sphere, as considered in the recent work of Dunkerton and Scott on "PV staircases". It follows that the M-conserving PV reconfigurations studied by those authors must involve processes describable as PV unmixing, or anti-diffusion, in the sense of time-reversed diffusion. Ordinary jet self-sharpening and jet-core acceleration do not, by contrast, require unmixing, as is shown here by detailed analysis. Mixing in the jet flanks suffices. The theorem extends to multiple layers and continuous stratification. A corollary is a new nonlinear stability theorem for shear flows.Comment: 14 pages, 4 figures; Final version, accepted by J. Atmos. Sci, in pres

An hydrodynamic shear instability in stratified disks

We discuss the possibility that astrophysical accretion disks are dynamically unstable to non-axisymmetric disturbances with characteristic scales much smaller than the vertical scale height. The instability is studied using three methods: one based on the energy integral, which allows the determination of a sufficient condition of stability, one using a WKB approach, which allows the determination of the necessary and sufficient condition for instability and a last one by numerical solution. This linear instability occurs in any inviscid stably stratified differential rotating fluid for rigid, stress-free or periodic boundary conditions, provided the angular velocity $\Omega$ decreases outwards with radius $r$. At not too small stratification, its growth rate is a fraction of $\Omega$. The influence of viscous dissipation and thermal diffusivity on the instability is studied numerically, with emphasis on the case when $d \ln \Omega / d \ln r =-3/2$ (Keplerian case). Strong stratification and large diffusivity are found to have a stabilizing effect. The corresponding critical stratification and Reynolds number for the onset of the instability in a typical disk are derived. We propose that the spontaneous generation of these linear modes is the source of turbulence in disks, especially in weakly ionized disks.Comment: 19 pages, 13 figures, to appear in A&

A shallow-water theory for annular sections of Keplerian Disks

A scaling argument is presented that leads to a shallow water theory of non-axisymmetric disturbances in annular sections of thin Keplerian disks. To develop a theoretical construction that will aid in physically understanding the relationship of known two-dimensional vortex dynamics to their three-dimensional counterparts in Keplerian disks. Using asymptotic scaling arguments varicose disturbances of a Keplerian disk are considered on radial and vertical scales consistent with the height of the disk while the azimuthal scales are the full $2\pi$ angular extent of the disk. The scalings lead to dynamics which are radially geostrophic and vertically hydrostatic. It follows that a potential vorticity quantity emerges and is shown to be conserved in a Lagrangian sense. Uniform potential vorticity linear solutions are explored and the theory is shown to contain an incarnation of the strato-rotational instability under channel flow conditions. Linearized solutions of a single defect on an infinite domain is developed and is shown to support a propagating Rossby edgewave. Linear non-uniform potential vorticity solutions are also developed and are shown to be similar in some respects to the dynamics of strictly two-dimensional inviscid flows. Based on the framework of this theory, arguments based on geophysical notions are presented to support the assertion that the strato-rotational instability is in a generic class of barotropic/baroclinic potential vorticity instabilities. Extensions of this formalism are also proposed. The shallow water formulation achieved by the asymptotic theory developed here opens a new approach to studying disk dynamics.Comment: Accepted (July 21, 2008), now in final for

CUDA Implementation of a Navier-Stokes Solver on Multi-GPU Desktop Platforms for Incompressible Flows

Graphics processor units (GPU) that are traditionally designed for graphics rendering have emerged as massively-parallel co-processors to the central processing unit (CPU). Small-footprint desktop supercomputers with hundreds of cores that can deliver teraflops peak performance at the price of conventional workstations have been realized. A computational fluid dynamics (CFD) simulation capability with rapid computational turnaround time has the potential to transform engineering analysis and design optimization procedures. We describe the implementation of a Navier-Stokes solver for incompressible fluid flow using desktop platforms equipped with multi-GPUs. Specifically, NVIDIA’s Compute Unified Device Architecture (CUDA) programming model is used to implement the discretized form of the governing equations. The projection algorithm to solve the incompressible fluid flow equations is divided into distinct CUDA kernels, and a unique implementation that exploits the memory hierarchy of the CUDA programming model is suggested. Using a quad-GPU platform, we observe two orders of magnitude speedup relative to a serial CPU implementation. Our results demonstrate that multi-GPU desktops can serve as a cost-effective small-footprint parallel computing platform to accelerate CFD simulations substantially. I. Introductio

Bottom dissipation of subinertial currents at the Atlantic zonal boundaries

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90515/1/jgr_bbldiss_wrightetal_2012.pd

Imperfections of the North Atlantic wind-driven ocean circulation: Continental geometry and windstress shape

Multiple equilibria of the wind-driven gyres have been found in idealized quasi-geostrophic and shallow water models. In this paper we demonstrate that multiple equilibria persist within a reduced gravity shallow water model under quite realistic continental geometry and windstress forcing for the North Atlantic. Multiple mean flow patterns of the Gulf Stream exist and differ with respect to their separation behavior along the North American coast. The origin of these equilibria is investigated by determining the structure of steady solutions within a hierarchy of equivalent barotropic ocean models using continuation techniques. Within each model, the magnitude of lateral friction is used as a control parameter. It is shown that symmetry breaking, found in a quasi-geostrophic model for a rectangular ocean basin with idealized wind forcing is at the origin of two different mean states of the Gulf Stream. The steady states found become unstable only to a small number of oscillatory modes, which either have intermonthly or interannual periods. The modes of variability remain strongly related through the hierarchy of models indicating that their physics is not strongly dependent on the shape of the continents but is controlled by internal ocean dynamics

Influence of (sub)mesoscale eddies on the soft-tissue carbon pump.

In an idealized situation of a baroclinically unstable single eddy, we study the impact of eddy-induced mixing on the soft-tissue carbon pump. The new element here is the coupling of a three-dimensional nonhydrostatic ocean model with a physiological plankton model that is able to represent a variable plankton C:N ratio. During the development and breakup of the eddy, a complicated vertical velocity field appears. The processes of transport and plankton growth, as well as the effect of the flow on the C:N ratio, are studied in detail. The physical processes associated with eddy breakup have a strong impact on the local environment in which the plankton grows. The changes in the local environment lead to a decrease of the C:N ratio (about 30% throughout the upper 150 m of the domain) and hence a weakening of the soft-tissue carbon pump. According to a sensitivity analysis, the decrease of the C:N ratio as a consequence of the flow field appears robust; it does not depend on specific parameter values in the model. Copyright 2007 by the American Geophysical Union