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Results for “baroclinic instabilities”

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

On the energetics and nonhydrostatic aspects of symmetric baroclinic instability

Dry symmetric baroclinic instability is studied using numerical analysis at the critical Richardson number (Ri) for varying thermal Rossby (Ro), Prandtl (Pr), and Ekman numbers. For small enough Ro, dissipation results in a lowering of the critical Ri as Ro decreases, and the critical wavelength is not proportional to Ro. For Pr = 1, the energy conversion is via both inertial and convective mechanisms.

Miller, T. L.↗
NASA NTRS1988

Upper-level baroclinic instability

Effects on baroclinic instability of 'partial equilibration' and an Ekman lower boundary condition were examined by considering the linear stability of various zonal wind profiles having, as in the Charney (1947) problem, constant vertical shear and positive meridional gradient of potential vorticity aloft, but with reduced shear and zero or negative potential vorticity gradient at low levels. It is shown that, compared to the Charney problem, the partially equilibrated basic state zonal wind profiles obtained here have instabilities whose growth rates are less sensitive to the presence of an Ekman lower boundary condition.

Snyder, Christopher M.↗
NASA NTRS1976

The effects of spherical geometry on baroclinic instability

A baroclinic stability analysis is performed for a simple family of zonal shear profiles over a sphere, using a two-layer, quasi-geostrophic model. The stability properties and the structure of the most unstable waves are qualitatively similar to those on a beta-plane. However, the spherical geometry plays a major role in locating some of the important features of the most unstable waves. In particular, the locations of the maximum wave amplitude, maximum eddy heat fluxes, and maximum convergence of the eddy angular momentum flux are all well correlated with the location of the maximum excess of the vertical shear over the minimum value necessary for local instability on a sphere. Consequently the eddy momentum flux tends to generate a mid-latitude jet even if there is no preexisting mid-latitude jet in the basic state zonal flow. These findings suggest some of the elements needed for parameterizing the meridional variations of baroclinic eddy fluxes accurately.

Moura, A. D.↗
NASA NTRS1980

The concept of wave overreflection and its application to baroclinic instability

The paper reviews the concept of wave overreflection and its application to baroclinic instability. The instabilities associated with overreflection are likely to be identical to critical layer instabilities; the baroclinic instability is examined in terms of overreflection of vertically propagating Rossby waves which leads to rapid estimates of growth rates and phase speeds of unstable modes for arbitrary distributions of zonal velocities in models with and without lids. It was found that Charney and Green modes are essentially critical-layer instabilities and that baroclinic instability can be eliminated by stretching the transition region from zero shear at the ground to the interior shear. Finally, it is shown that the potential vorticity flux of baroclinically unstable modes is confined to a layer between the ground and the neighborhood of the steering level.

Lindzen, R. S.↗
NASA NTRS1989

On the structure of potential vorticity in baroclinic instability

The structure of baroclinic modes is examined in terms of their potential vorticity. Baroclinic instabilities may be viewed as mutually reinforcing interactions between the disturbance potential vorticity at different levels in the atmosphere. A technique is introduced for diagnosing quantitatively which levels of potential vorticity are important in the growth of the instability. Both Charney and Green modes are found to depend on the interaction between the surface thermal anomalies and a thin layer of potential vorticity anomalies centered on the steering level. In the Green modes, the growth is retarded by the influence of the eddy potential vorticity at higher levels. The inclusion of a tropopause in the basic state does not modify the fundamental dynamics of the baroclinic modes in the presence of linear shear.

Robinson, Walter A.↗
NASA NTRS1979

Numerical modeling of baroclinic instability

The Eady model of baroclinic instability applied to a rotating channel with Ekman layers at the top and bottom is extended to a beta-plane channel. Changes in the shape and position of the boundary separating the regions of axially symmetric and wavelike motion are predicted.

Geisler, J. F.↗
NASA NTRS1980

A simple approximate result for the maximum growth rate of baroclinic instabilities

The Charney problem for baroclinic instability involves the quasi-geostrophic instability of a zonal flow on a beta plane where the zonal flow is characterized by a constant vertical shear. The atmosphere is non-Boussinesq and continuous. The solution of this problem involves confluent hypergeometric functions, and the mathematical difficulty of the problem has precluded extracting simple results of generality. It is shown that there exists very simple, powerful approximate result for the growth rate of the most rapidly growing instability, viz., that this growth rate is linearly proportional to the surface meridional temperature gradient. The coefficient of proportionality is also easily determined. The result extends to substantially more general profiles than those in the Charney problem.

Lindzen, R. S.↗
NASA NTRS1984

Numerical studies of baroclinic instability at small Richardson number

Baroclinic instability at small Richardson number consists of competition between symmetric (Solberg) modes, zonal (Eady) modes, and possibly other modes whose orientation is neither symmetric nor zonal. In FY-84, a study of the fully nonlinear development and energetics of the symmetric modes was completed. The nonlinear effects were quite strong and, in some senses, unexpected. Secondly, a study of the dependency of the energetics of the symmetric modes upon the physical parameters was completed.

Miller, T. L.↗
NASA NTRS1984

The nonaxisymmetric baroclinic instability in thin accretion disks

The instability of linear, nonaxisymmetric baroclinic waves in the radiative regions of a thin accretion disk is investigated with simplifying assumptions used in the representation of the structure of the basic state. As in stars with rotation laws deviating from rotation on cylinders, the departure from barotropy ('baroclinicity') resulting from such rotation feeds potential energy from the basic state into the kinetic energy of the baroclinic motions. The baroclinic instability is considered as a possible mechanism for driving turbulence in disks. Estimations of the Reynolds stress from baroclinic waves indicate that the degree of baroclinicity in stationary disk models is insufficient to account for the large viscosity inferred from observations of, e.g., cataclysmic variables.

Cabot, W.↗
NASA NTRS1982

Symmetric baroclinic instability of a Hadley cell

A symmetric baroclinic instability is examined in terms of a Boussinesq fluid contained between two horizontal plates to determine the effects of the Ekman and thermal layers. Governing equations are written for a rotating reference frame, taking into account the Rossby, Ekman, and Prandtl numbers. Equations are defined for the perturbation functions, treated as an eigenvalue problem, and a numerical integration of the full eighth order differential system is performed by a shooting technique. An instability is found to occur in the Hadley cell containing both Ekman and thermal boundary layers when the Richardson number is close to unity. If the Prandtl number is fixed the critical Richardson number decreases with an increasing Ekman number until the Ekman number reaches a certain value, at which time the fluid is stable.

Antar, B. N.↗
NASA NTRS1985

Baroclinic instability of easterly jets with applications to the summer mesosphere

A two-dimensional numerical analysis of baroclinic instability waves in zonally and seasonally averaged wind fields in the summer mesosphere is presented. The analysis is based on the linearized quasi-geostrophic potential vorticity equation of Simmons and Moskins (1973). Solutions are obtained for the wave structure, wave growth rates, and wave periods on the basis of idealized and realistic data, and the results are compared with one-dimensional analyses. It is shown that the wavenumbers of peak growth with periods of 1.4-3 days were consistently lower for the two-dimensional analysis than for previous one-dimensional analyses. The possibility of detecting baroclinic instability in summer winds at 80-100 km by means of nadir-sounding satellite observations is discussed.

Pfister, L.↗
NASA NTRS1982

Pulse asymptotics of the Charney baroclinic instability problem

The asymptotic response of the Charney baroclinic instability problem to a localized perturbation is determined using the formalism of Briggs (1964) and exploiting a recently obtained highly accurate WKB approximate dispersion relation (Lindzen and Rosenthal, 1981). Comparison is made with previous results for two-level and Eady models. Small scales and rapid growth characteristic of the initial stages of cyclogenesis are found and the linear dispersion relation, which can be obtained from observation of zonal wind and stability, emerges as a forecast tool for prediction of geographically local cyclogenesis.

Farrell, B. F.↗
NASA NTRS1980

Baroclinic instability with variable static stability - A design study for a spherical atmospheric model experiment

The effect of a radially-variable, dielectric body force, analogous to gravity on baroclinic instability for the design of a spherical, synoptic-scale, atmospheric model experiment in a Spacelab flight is investigated. Exact solutions are examined for quasi-geostrophic baroclinic instability in which the rotational Froude number is a linear function of the height. Flow in a rotating rectilinear channel with a vertically variable body force without horizontal shear of the basic state is also discussed.

Giere, A. C.↗
NASA NTRS1980

Baroclinic instability with variable gravity: A perturbation analysis

Solutions for a quasigeostrophic baroclinic stability problem in which gravity is a function of height were obtained. Curvature and horizontal shear of the basic state flow were omitted and the vertical and horizontal temperature gradients of the basic state were taken as constant. The effect of a variable dielectric body force, analogous to gravity, on baroclinic instability for the design of a spherical, baroclinic model for Spacelab was determined. Such modeling could not be performed in a laboratory on the Earth's surface because the body force could not be made strong enough to dominate terrestrial gravity. A consequence of the body force variation and the preceding assumptions was that the potential vorticity gradient of the basic state vanished. The problem was solved using a perturbation method. The solution gives results which are qualitatively similar to Eady's results for constant gravity; a short wavelength cutoff and a wavelength of maximum growth rate were observed. The averaged values of the basic state indicate that both the wavelength range of the instability and the growth rate at maximum instability are increased. Results indicate that the presence of the variable body force will not significantly alter the dynamics of the Spacelab experiment. The solutions are also relevant to other geophysical fluid flows where gravity is constant but the static stability or Brunt-Vaisala frequency is a function of height.

Giere, A. C.↗
NASA NTRS1980

Numerical study of baroclinic instability

The effect of a power law gravity field on baroclinic instability is examined with emphasis on the case of inverse fifth power gravity, since this is the power law produced when terrestrial gravity is simulated in spherical geometry by electrostatic means. Growth rates of unstable normal modes were obtained as a function of parameters of the problem by solving a second order differential equation numerically. Results are compared with those from an earlier study where gravity was a constant. The conclusion is that, over the range of parameter space explored here, there is no significant change in the character of theoretical regime diagrams if the vertically averaged gravity is used as a parameter.

Geisler, J. E.↗
NASA NTRS1988

Baroclinic instability in vertically discrete systems

The Charney-Phillips (1953) standard vertical grid for quasi-geostrophic models is compared with the Lorenz (1960) vertical grid (which departs from the standard grid by carrying horizontal velocity and potential temperature at same levels) in the framework of the quasi-geostrophic potential vorticity equation and baroclinic instability. It is demonstrated that the Charney-Phillips grid makes it possible to maintain important dynamical constraints on quasi-geostrophic flow, such as the conservation of quasi-geostrophic potential vorticity through horizontal advection and resulting integral constraints. The Lorenz grid, on the other hand, is not straightforward even to define quasi-geostrophic potential vorticity. Moreover, due to an extra degree of freedom in potential temperature, the Lorenz grid can falsely satisfy the necessary condition for baroclinic instability near the lower and the upper boundaries.

Arakawa, Akio↗
NASA NTRS1979

Baroclinic instabilities in Jupiter's zonal flow

The forms and behavior of baroclinic instabilities occurring in a particularly simple model Jovian atmosphere are studied. First, an extension of the quasi-geostrophic model developed for the earth's atmosphere is used. The second model assumes that the lower-layer perturbation is allowed to be nonhydrostatic, since on Jupiter the disturbance depth scale in the lower layer may be comparable to or greater than the horizontal scale. The results obtained show the importance for the upper-layer meteorology of the interface boundary condition with the lower fluid, which is radically different from the rigid lower boundary of the earth's troposphere.

Gierasch, P. J.↗