stability of a simple baroclinic flow with horizontal shear.

by Leon S. Pocinki

Publisher: Geophysics Research Directorate, Air Force Cambridge Research Center in Cambridge, Mass

Written in English
Published: Pages: 78 Downloads: 566
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Subjects:

  • Stability.,
  • Laminar flow.

Edition Notes

SeriesGeophysical research papers ;, no. 38
Classifications
LC ClassificationsQC1 .U54 no. 55-212
The Physical Object
Pagination78 p. :
Number of Pages78
ID Numbers
Open LibraryOL6215959M
LC Control Number56060534
OCLC/WorldCa8214788

The linear baroclinic instability problem is developed in generality and then specialized to the case of constant vertical shear. It is found that non-quasigeostrophic effects appear only for perturbations with cross-front variation, and that perturbation energy can be generated through both baroclinic production and shear production. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The existence, scale, and growth rates of sub-synoptic scale warm core circulations are investigated with a simple parameterization for latent heat release in a non-convective basic state using a linear two-layer shallow water model. For a range of baroclinic flows from moderate to high Richardson number. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The existence, scale, and growth rates of subsynoptic-scale warm-core circulations are investigated with a simple parameterization for latent heat release in a nonconvective basic state using a linear two-layer shallow-water model. For a range of baroclinic flows from moderate to high Richardson number, condi-tionally. The model flow field consists of a pair of three-dimensional 'point potential vortices' with strengths Q1 and Q2 in a flow with constant horizontal and vertical shear. The two vortices are advected by the background flow as they interact with each other (see Fig. 1).

The obtained results are consistent with observations [50, 51, 54]: an increase in static stability and a decrease of the MTG have occurred over the past few decades in some areas of the SH, which has led to a decrease in the growth rate of baroclinic unstable waves, a shift of the spectrum of unstable waves in the long wavelength part of spectrum, and a weakened intensity of cyclogenesis. In this process, called baroclinic instability, potential energy is converted into kinetic energy—which occurs as wind—as warm, light air rises and cold, heavy air sinks. Since baroclinic instability is associated with horizontal temperature gradients, according to the thermal wind relation (3), there must be vertical wind shear. Static stability and the meridional temperature gradient (MTG) are among the most important fundamental parameters characterizing the state of the atmosphere and, in particular, midlatitude large-scale eddy dynamics [1, 2].Static stability and MTG play a significant role in the development of baroclinic instability which is the dominant mechanism for generating large-scale atmospheric eddies. Also, if there is a significant horizontal density (or temperature) gradient, or vertical shear in the background flow, then the controlling dynamics are much more likely to be baroclinic than.

It is argued that the adverse influence of submesoscale topography on baroclinic instability is ultimately caused by the homogenization tendency of potential vorticity in the bottom density layer. The multiscale model formally assumes a substantial separation between the scales of interacting flow components. shear in the lower stratosphere, since, as we will show, changes to the vertical shear at the top boundary have a simple effect on the linear growth of baroclinic eddies, which may determine the nonlinear development of baroclinic eddies and thus the tropospheric mean flow. To investigate the role of baroclinic instability in. Baroclinic Fluid An ocean or atmosphere in which density is a function of other parameters Isobaric and isopycnal surfaces do not coincide In a baroclinic fluid: ρ=ρ(S,T,P) or ρ=ρ(T,P) ∂Vg ∂z ≠0 ∇T ≠0 Baroclinic Fluid The geostrophic wind has vertical shear Thermal wind is not zero There is temperature advection by the geostrophic. Charney modes. This analysis allows relatively simple representation of the unstable Charney and Green modes. The rapidly growing Charney modes NH have a vertical scale of H/(l+y) and a horizontal scale of where B N2 H f(l+y) H = density scale height, y =, and ii = mean zonal flow. For y>>1l f2 - the waves are short and shallow.

stability of a simple baroclinic flow with horizontal shear. by Leon S. Pocinki Download PDF EPUB FB2

Additional Physical Format: Online version: Pocinki, Leon S. Stability of a simple baroclinic flow with horizontal shear (OCoLC) Material Type.

The stability of all baroclinic flows whose mean state consists of a uniform vertical shear (Eady's problem) plus a small but arbitrary deviation in the zonal velocity is obtained as a functional of the velocity by: 7.

horizontal gradient of temperature. The conversions of energy are proportional to perturbation heat fluxes in the horizontal and vertical. From thermal wind balance, a horizontal temperature gradient implies the presence of vertical shear.

So, baroclinic instability is also an instability of the vertical shear. The Boussinesq approximation is used, but the usual hydrostatic approximation in the vertical is relaxed. Dissipation effects are ignored. A baroclinic flow can always be destabilized by sufficiently large horizontal anticyclonic shear.

The results are relevant for the stability of differential rotation in radiative stars and accretion by: 6. The linear stability with respect to three-dimensional perturbations of unbounded barotropic and baroclinic shear flows depending linearly on both transverse coordinates is studied. The Boussinesq approximation is used, but the usual hydrostatic approximation in the vertical is relaxed.

Dissipation effects are ignored. A baroclinic flow can always be destabilized by sufficiently large Cited by: 6. with baroclinic instability. However, to study its properties in the purest and simplest form first consider a basic current which has horizontal but not vertical shear.

That is, let Uo = Uo(y) () We will also consider only a flat bottom. The normal mode equation () for such a basic flow. Stability with horizontal shear The retention of horizontal shears, A 0 in Eq.

(3), is not conducive to a simple analytical treatment. Barcilon and Blumen () have shown that the presence of constant v-shear can also be interpreted as an effective slope which alters the penetra- tion depth of the edge waves on the boundaries.

For baroclinic instability it is the vertical shear, rather than the horizontal shear, that is important. Baroclinic instability is often studied for the simple case of a two-layer fluid, for which waves are unstable if the following condition is true: () () () 2 4 2 2 2 4 2.

Formally, baroclinic instability results by generalizing the derivation for barotropic instability to the case where u ¯ = u ¯ z. Horizontal shear of the basic flow is unnecessary.

Physically the key difference between the two instabilities is the poleward advection of. Baroclinic instability is a fluid dynamical instability of fundamental importance in the atmosphere and in the the atmosphere it is the dominant mechanism shaping the cyclones and anticyclones that dominate weather in mid-latitudes.

In the ocean it generates a field of mesoscale ( km or smaller) eddies that play various roles in oceanic dynamics and the transport of tracers. Hollingsworth, Baroclinic instability of a simple flow on the sphere, Quarterly Journal of the Royal Meteorological Society, /qj, (), ().

Wiley Online Library. With the evolution of time, baroclinic instability occurs in a weakly stratified layer with large vertical shear of the basic zonal flow.

Horizontal wind associated with the baroclinic instability modes is of a few m s −1. The initial structure of the unstable modes is similar to those obtained in previous linear stability analyses. The two-layer model is used to study how horizontal shear in a baroclinic zonal flow affects the structure of growing baroclinic waves.

the baroclinic stability properties and the energy. The special role played by the kinematic and thermodynamic boundary conditions in the theory of baroclinic stability is clarified by re-examining earlier theories in the light of an analogy to two-dimensional shear flow.

Simple baroclinic flow with rigid horizontal boundaries is isomorphic to Couette flow with free boundaries. A baroclinic wave can develop in the atmosphere when the wind at a given pressure level is blowing parallel to the temperature (or potential temperature) isotherms and there is a nonzero temperature gradient across the flow.

If certain other conditions are met, a small initial wave perturbation superimposed on the flow will amplify, and the situation is referred to as a state of baroclinic.

where τ ax and τ ay are the shear stress components on the surface in the x and y directions, respectively, τ bx and τ by the shear stress components at the bottom in the x and y directions, respectively, δ x and δ y the extra stress terms resulted from the depth-averaging in the x and y directions, respectively, and u ¯ and v ¯ the depth-averaged horizontal velocity components in x.

Simple baroclinic flow with rigid horizontal boundaries is isomorphic to Couette flow with free boundaries. the jet is special role played by the kinematic and thermodynamic boundary conditions in the theory of baroclinic stability is clarified by re-examining earlier theories in the light of an analogy to two-dimensional shear.

Barotropic and baroclinic instability. One of the basic flow patterns encountered in meteorology is a jet stream that has shears in both the vertical and horizontal directions. Barotropic instability is associated with a jet embedded in a horizontal shear whereas baroclinic instability is associated with vertical shear.

Barotropic instabilities. A generalized stability theory (GST) analysis of baroclinic shear flow is performed using primitive equations (PEs), and typical synoptic-scale midlatitudinal values of vertical shear and stratification. GST is a comprehensive linear stability theory that subsumes modal stability theory and extends it to account for nonmodal interactions.

As in the previous model the dominant baroclinic instability is that of the gravest mode and a new barotropic instability is present due to the lateral shear in the mean flow at the shelf break.

For both models, a parameter study is presented in which we determine the effects of varying the shear, stratification and bottom slope. It is the induced strong horizontal shear in the zonal flow that is responsible for its stabilization in spite of the considerable residual baroclinicity.

In contrast, our analysis also reveals that the wave in a narrow domain equilibrates baroclinically in accordance with the notion of baroclinic adjustment. The linear stability of an inviscid, incompressible plane-parallel magnetohydrodynamic stratified shear flow with velocity)) and a constant magnetic field confined between two horizontal.

Abstract The baroclinic instability of a meridional current in a north–south channel is investigated in a two-layer model for the case when the current has no horizontal shear. The vertical shear o. The stability of rotating horizontal-shear flows is investigated within the framework of the linear approximation.

The shear flow perturbations are divided into three classes (symmetric and two. The stability is discussed of an infinitesimal quasi‐geostrophic perturbation to a baroclinic zonal wind which is independent of latitude, in terms of a two‐layer inviscid model with parallel but sloping upper and lower boundaries, so that the northwards gradient of potential vorticity in each layer is equal and opposite, but not a simple multiple of the difference between the basic.

The instability is a horizontal shear instability with a distinct phase velocity compared to that of the forced baroclinic critical layers, and thus will excite new baroclinic critical layers. A WKB solution for the exponential growth is derived, which indicates the secondary instability grows faster than a common normal mode due to the.

In order for such a simple model to support baroclinic instability it was necessary to have two horizontal boundaries sufficiently close together so that they could interact.

As () shows for a given mode it is necessary for the two boundary terms to cancel in traditional shear flow instability problem. Emphasis throughout the book is devoted to basing scaling techniques and the derivation of systematic approximations to the equations of motion.

Simple baroclinic flow with rigid horizontal. Phillips, N. Energy transformations and meridional circulations associated with simple baroclinic waves in a two-level, quasi-geostrophic model.

Tellus 6, – Plougonven, R., Muraki, D. & Snyder, C. A baroclinic instability that couples balanced motions and gravity waves. The stability of this flow is then analyzed: When the vertical stratification is stabilizing, there is a simple harmonic motion of the horizontal stratification N h 2 (t) and of the shear rate S(t), but this flow is unstable to certain disturbances, which are amplified by a Floquet mechanism.

Reflexion and stability of waves in stably stratified fluids with shear flow: a numerical study - Volume 34 Issue 3 - Walter L. Jones. N.R. and Staquet, C. Focusing of an inertia–gravity wave packet by a baroclinic shear flow.

Dynamics of Atmospheres and Oceans, Vol. 40, Issue.p. CrossRef.Example: Stability of free shear layer { Kelvin-Helmholtz instability consider a constant{density uid on the f-plane and a zonal basic ow with horizontal shear in the cross-stream direction, i.e.

U0 = U0(y) = ˆ U; y>0 U; y.Moreover, in all the simulations of aperiodic baroclinic shear flows, the barotropic component of the primary wave continues to grow after the adjustment by the nonlinearities. Furthermore, the authors find that the correction to the zonal mean flow can be much larger when the basic state is aperiodic compared to the periodic or steady limits.