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NASA NTRS1983

Charney's problem for baroclinic instability applied to barotropic instability

If barotropically unstable easterly jets may be approximated by broken line profiles, it becomes possible to use the solutions of the Charney (1947) problem for baroclinic instabilithy in order to solve the barotropic problem. Results are presented for easterly jets having an arbitrary degree of symmetry, and it is noted that the convenient calculation obtained for the growth of both localized and normal mode perturbations is important in the study of monsoon depressions over India.

Lindzen, R. S.↗
NASA NTRS1985

The observed life cycle of a baroclinic instability

Medium-scale waves (zonal wavenumbers 4-7) frequently dominate Southern Hemisphere summer circulation patterns. Randel and Stanford have studied the dynamics of these features, demonstrating that the medium-scale waves result from baroclinic excitation and exhibit well-defined life cycles. This study details the evolution of the medium-scale waves during a particular life cycle. The specific case chosen exhibits a high degree of zonal symmetry, prompting study based upon zonally averaged diagnostics. An analysis of the medium-scale wave energetics reveals a well-defined life cycle of baroclinic growth, maturity, and barotropic decay. Eliassen-Palm flux diagrams detail the daily wave structure and its interaction with the zonally-averaged flow.

Randel, W. J.↗
NASA NTRS1991

A study of baroclinic instability in a cylindrical annulus with the temperature gradient imposed on the lower surface

Results are presented from experimental and numerical-modeling studies carried out on a rotating thermally driven fluid system in a cylindrical annulus with the horizontal gradient imposed upon the lower horizontal surface. The rotation rate and the temperature difference were varied to construct a regime diagram in thermal Rossby-number/Taylor-number space. It is shown that the curve separating the axisymmetric flow from the wave flow is 'knee-shaped', similar to the conventional side-heated and side-cooled baroclinic annulus. The experimentally observed transition curve agrees well with numerical calculations and the agreement between the predicted and measured wavenumbers is good both near the transition and within the wave regime. Away from the transition curve and well within the wave regime, there is an evolution from larger to smaller wavenumbers as the flow equilibrates, which is well captured by the numerical model for these cases.

Miller, Timothy L.↗
NASA NTRS1981

Baroclinic instability of a rotating Hadley cell

The stability of a thin fluid layer between two rotating plates which are subjected to a horizontal temperature gradient is investigated. The solution for the stationary basic state is obtained in a closed form. It is pointed out that this solution identifies Ekman and thermal layers adjacent to the plates and interior temperature and velocity fields which are almost linear functions of height. The stability of that basic state with respect to infinitesimal zonal waves is then analyzed via the solution of the complete viscous linear equations for the perturbations. The character of the growth rates is found to be similar to those of the classical baroclinic waves. It is also found that the region of stability depends on the Prandtl number, the vertical stratification parameter, and both the meridional and zonal wavenumbers. The flow is generally unstable for small enough Ekman numbers and for Rossby numbers less than 10.

Antar, B. N.↗
NASA NTRS1979

The wave structures of the Eady model of baroclinic instability

By solving the linear quasi-geostrophic set of equations pertinent to the Eady model, the complex eigenvalues and the eigenfunctions are obtained. The propagation speed and the growth rate are computed. Quantitative information is provided about the wave structures for several unstable models, a marginally stable mode, and a stable mode. The peculiarities concerning the amplitude and the phase variations of the waves are noted as the wavenumber varies from the unstable region to the stable region. Physical interpretations of the interrelationships among the dynamical variables are given, with a view toward revealing important aspects of the energy transfer from the basic state to the growing waves.

Hyun, J. M.↗
NASA NTRS1980

Baroclinic instability of flows along sloping boundaries

In the two-layer quasi-geostrophic model with boundaries sloping perpendicular to the basic flow, the ratios of the slopes of the bottom and the top to that of the interface between the fluid layers in the basic state are important parameters in the expression of the growth rate of unstable waves. When Eady's (1949) model is extended to include sloping bottom and top boundaries, the growth rates of unstable waves depend on the ratios of the slopes of the bottom and the top to that of the isentropes of the basic state. For the Eady model with sloping bottom, an important parameter characterizing the instability is the ratio between the vertical and horizontal heat transports by the wave divided by the slope of the isentropes of the basic state. An interpretation of these ratios and their relations clarifies the stabilization of the system for large slopes, the variation of the wavelength of the most unstable wave with the bottom slope, and the destabilization of some short waves for negative bottom slopes. It is found that the most unstable wave of the system has zero vertical energy flux convergence at the sloping bottom.

Mechoso, C. R.↗
NASA NTRS1981

Separate and combined effects of static stability and shear variation on the baroclinic instability of a two-layer current

Quasi-geostrophic disturbance instability characteristics are studied in light of a linearized, two-layer Eady model in which both the static stability and the zonal current shear are uniform but different in each layer. It is shown that the qualitative character of the instability is determined by the sign of the basic-state potential vorticity gradient at the layer interface, and that there is a qualitative similarity between the effects of Richardson number variations due to changes in static stability and those due to changes in shear. The two-layer model is also used to construct an analog of the Williams (1974) continuous model of generalized Eady waves, the basic state in that case having zero potential vorticity gradient in the interior. The model results are in good agreement with the earlier Williams findings.

Hyun, J. M.↗
NASA NTRS1981

Long-wave baroclinic instability in the troposphere and stratosphere with spherical geometry

The most unstable normal modes are obtained for a global, quasi-geostrophic and spectral-form atmospheric model that includes wavenumbers one through six. In a first set of model calculations, the basic state represents Northern Hemisphere winter solstice conditions, whose long waves are deep modes having maximum kinetic energy in the stratosphere. These internal modes exist even in the presence of a stratospheric wind minimum, but propagate vertically into the stratosphere only north of this minimum, at the latitudes of the polar jet. The basic state for a second set of calculations is the axisymmetric solution corresponding to radiative equilibrium, with large vertical wind shear and all modes being essentially external, tropospheric Charney modes.

Straus, D. M.↗
NASA NTRS1983

Baroclinic instability in the stratosphere and mesosphere

The energy source of stratospheric planetary waves is largely due to vertical propagation from the troposphere, but the stratospheric zonal mean state which changes with time is not stable against small perturbations, whereby transient perturbation waves are generated at the expense of the stratospheric zonal mean available potential energy. This theoretical conclusion is obtained based on the quasi-geostrophic model in spherical coordinates which calculates the characteristic solutions for the basic zonal mean state changing with time.

Zhang, K. S.↗
NASA NTRS1990

A numerical study of the onset of baroclinic instabilities in spherical geometry

The onset of instabilities in a fluid contained in a rotating hemispherical shell, driven by thermal gradients imposed upon the hemispherical boundaries and by a spherically symmetric radial body force, is numerically studied. Computations are presented for a range of Taylor and thermal Rossby numbers. The analysis indicates the presence of an instability dependent upon the spherically radial gravity alone when the warmest temperatures are at the pole and an additional centrifugal buoyant instability for weak imposed gravity and fast rotation when the temperature decreases poleward.

Miller, Timothy L.↗
NASA NTRS1985

Theoretical and experimental design studies for the Atmospheric General Circulation Experiment

The major criterion for the Atmospheric General Circulation Experiment (AGCE) design is that it be possible to realize strong baroclinic instability in the spherical configuration chosen. A configuration was selected in which a hemispherical shell of fluid is subjected to latitudinal temperature gradients on its spherical boundaries and the latitudinal boundaries are insulators. Work in the laboratory with a cylindrical version of this configuration revealed more instabilities than baroclinic instability. Since researchers fully expect these additional instabilities to appear in the spherical configuration also, they decided to continue the laboratory cylindrical annulus studies. Four flow regimes were identified: an axisymmetric Hadley circulation, boundary layer convection, baroclinic waves and deep thermal convection. Regime diagrams were prepared.

Fowlis, W. W.↗
NASA NTRS1985

Theoretical and experimental studies of baroclinic processes

An experimental study in a baroclinic annulus with heating and cooling on the upper and lower horizontal surfaces was completed. Four basic regimes of flow were observed: (1) axisymmetric flow, (2) cellular (deep) convection, (3) convective rolls (boundary layer), and (4) baroclinic instability. There was no symmetric (or nearly symmetric) baroclinic instability observed, although it was determined by numerical calculations that we transversed regions in parameter space where the symmetric instability was present. The non-symmetric baroclinic instability (Eady type) was observed instead. Although the vertical depth was rather small and hence viscous damping was strong, large-amplitude baroclinic waves were made possible by imposing a very weak static stability.

Miller, T.↗
NASA NTRS2020

Sub-Mesoscales at Ocean Fronts: Dissipation of Eddy Kinetic Energy

D’Asaro et al. measured the dissipation of eddy kinetic energy at the Kuroshio ocean front, found it to be 1-2 orders of magnitude larger than the value predicted by the law of the wall and suggested that the enhancement is due to sub-mesoscales, SM. To assess their suggestion, we employ two SM models. In the first model the buoyancy flux is based on baroclinic instabilities only and there is no momentum flux (Reynolds stresses). The model is unable to reproduce the Kuroshio data. The second model includes baroclinic instabilities, wind stress and Reynolds stresses. It reproduces the data satisfactorily. The analytic formula for the dissipation that we present can be used in OGCMs to parameterize dissipation at ocean fronts other than Kuroshio, e.g., Gulf Stream and ACC, an extension that could improve the predictions of climate studies.

sub-mesoscale models↗
NASA NTRS1989

A normal-mode approach to Jovian atmospheric dynamic

A nonlinear, quasi-geostrophic, baroclinic model of Jovian atmospheric dynamics is proposed, in which vertical variations of velocity are represented by a truncated sum over a complete set of orthogonal functions obtained by a separation of variables of the linearized quasi-geostrophic potential vorticity equation. A set of equations for the time variation of the mode amplitudes in the nonlinear case is then derived. It is shown that, for a planet with a neutrally stable, fluid interior instead of a solid lower boundary, the barotropic mode represents motions in the interior, and is not affected by the baroclinic modes. One consequence of this is that a normal-mode model with one baroclinic mode is dynamically equivalent to a one-layer model with solid lower topography. It is also shown that, for motions in Jupiter's cloudy lower troposphere, the stratosphere behaves nearly as a rigid lid, so that the normal-mode is applicable to Jupiter. The accuracy of the normal-mode model for Jupiter is tested using the following simple problems: (1) forced, vertically propagating Rossby waves, using two and three baroclinic modes, and (2) baroclinic instability, using two baroclinic modes. It is found that the normal-mode model provides qualitatively correct results, even with only a very limited number of vertical degrees of freedom.

Achterberg, Richard K.↗
NASA NTRS1990

Laboratory and theoretical models of planetary-scale instabilities and waves

Meteorologists and planetary astronomers interested in large-scale planetary and solar circulations recognize the importance of rotation and stratification in determining the character of these flows. In the past it has been impossible to accurately model the effects of sphericity on these motions in the laboratory because of the invariant relationship between the uni-directional terrestrial gravity and the rotation axis of an experiment. Researchers studied motions of rotating convecting liquids in spherical shells using electrohydrodynamic polarization forces to generate radial gravity, and hence centrally directed buoyancy forces, in the laboratory. The Geophysical Fluid Flow Cell (GFFC) experiments performed on Spacelab 3 in 1985 were analyzed. Recent efforts at interpretation led to numerical models of rotating convection with an aim to understand the possible generation of zonal banding on Jupiter and the fate of banana cells in rapidly rotating convection as the heating is made strongly supercritical. In addition, efforts to pose baroclinic wave experiments for future space missions using a modified version of the 1985 instrument led to theoretical and numerical models of baroclinic instability. Rather surprising properties were discovered, which may be useful in generating rational (rather than artificially truncated) models for nonlinear baroclinic instability and baroclinic chaos.

Hart, John E.↗
NASA NTRS1991

Research highlights: June 1990 - May 1991

Linear instability calculations at MSFC have suggested that the Geophysical Fluid Flow Cell (GFFC) should exhibit classic baroclinic instability at accessible parameter settings. Interest was in the mechanisms of transition to temporal chaos and the evolution of spatio-temporal chaos. In order to understand more about such transitions, high resolution numerical experiments for the physically simplest model of two layer baroclinic instability were conducted. This model has the advantage that the numerical code is exponentially convergent and can be efficiently run for very long times, enabling the study of chaotic attractors without the often devastating effects of low-order trunction found in many previous studies. Numerical algorithms for implementing an empirical orthogonal function (EOF) analysis of the high resolution numerical results were completed. Under conditions of rapid rotation and relatively low differential heating, convection in a spherical shell takes place as columnar banana cells wrapped around the annular gap, but with axes oriented along the axis of rotation; these were clearly evident in the GFFC experiments. The results of recent numerical simulations of columnar convection and future research plans are presented.

Source record↗
NASA NTRS1984

Theoretical flow regime diagrams for the AGCE

The major criterion for the design of the Atmospheric General Circulation Experiment is that it be possible to realize strong baroclinic instability in the apparatus. A spherical annulus configuration which allows only steady basic state flows was chosen for the first set of stability analyses. Baroclinic instability was found for this configuration and few results suggest a regime diagram very different from the cylindrical annulus regime diagram.

Fowlis, W. W.↗