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NASA NTRS1979

Theoretical regime diagrams for thermally driven flows in a beta-plane channel

It is noted that thermally driven flows in rotating laboratory containers with cylindrical geometry can be axially symmetric or wavelike depending on the experimental parameters. In anticipation that rotating fluid experiments might soon be done in spherical shell geometry, Barcilon's model has been extended to a beta-plane channel in order to gain a rough understanding of the effects of rotating spherical geometry. An incompressible fluid version of the Charney (1947) model of baroclinic instability, modified to include Ekman pumping at rigid horizontal boundaries is used. With this model, stability boundaries are mapped out for individual zonal wavenumbers in the parameter space used by Barcilon.

Geisler, J. E.↗

NASA NTRS1980

Theoretical regime diagrams for thermally driven flows in a beta-plane channel in the presence of variable gravity

The effect of a power law gravity field on baroclinic instability is examined, with a focus on the case of inverse fifth power gravity, since this is the power law produced when terrestrial gravity is simulated in spherical geometry by a dielectric force. Growth rates are obtained of unstable normal modes as a function of parameters of the problem by solving a second order differential equation numerically. It is concluded that over the range of parameter space explored, there is no significant change in the character of theoretical regime diagrams if the vertically averaged gravity is used as parameter.

Geisler, J. E.↗

NASA NTRS1981

Stability of zonal flows on Jupiter

Gierasch et al. (1979) have shown that the question of the stability of zonal flows on Jupiter is influenced strongly by the lower boundary condition. In the case of Jupiter, the troposphere rests above a deep layer of fluid which is probably extremely close to adiabatic. The present study extends the earlier investigations to a wider range of conditions, taking into account the nongeostrophic limit and the presence of horizontal shear. The major difference between the behavior of the model derived in the study and the behavior of a model with a rigid lower boundary, corresponding to the terrestrial conditions, is that baroclinic instability by the Eady mechanism is suppressed. The influence of beta (Charney-type instability) operates only at the top of the troposphere, not at its base. The suppression of the Eady modes seems to apply all the way down to the nongeostrophic limit where the Rossby number is order unity.

Conrath, B. J.↗

NASA NTRS1982

Vacillations due to wave interference - Applications to the atmosphere and to annulus experiments

It is noted that vacillations in zonally averaged flows can arise from wave interference between coexisting waves with the same zonal wavenumber but different phase speeds. It is shown that the appropriate baroclinic instability problem for the annulus does yield multiple instabilities which can produce vacillations via interference. It is also shown that the interference of traveling Rossby waves with stationary forced waves can lead to vacillations whose amplitudes and periods are consistent with the observed index cycle.

Lindzen, R. S.↗

NASA NTRS1982

Short-term fluctuations in the eddy heat flux and baroclinic stability of the atmosphere

National Meteorological Center data from midlatitudes for three Januaries is used in calculating time series of the zonal mean meridional eddy heat flux and the zonal mean baroclinic stability, as measured by the difference between the zonal wind shear and the critical value of the shear in two-level models. Time-lagged correlations between the two series reveal a highly significant negative correlation for short time lags, peaking at approximately -0.4 when the stability parameter lags one half day behind the eddy flux. They also reveal that strongly unstable conditions are not followed by significant increases in the eddy flux. These results are seen as indicating that the synoptic variations of the zonal mean eddy flux are not closely related to the degree of baroclinic instability of the zonal mean flow. The autocorrelation of the eddy flux is then compared with those expected for autoregressive processes. A Bayesian information criterion suggests that the behavior is represented best by a damped oscillation, with a damping time of 0.8 day and a period of five days.

Stone, P. H.↗

NASA NTRS1982

Calculations of the quasi-geostrophic potential vorticity gradient from climatological data

Climatological data (5-year sets) are used in calculating the quasi-geostrophic potential vorticity meridional gradient between 10 and 1000 mb for latitudes from 25 to 65 deg N in the months of January, April, July, and October. The data comprise zonal and one-month averaged values of the zonal velocity and temperature and represent seasonal transitions and extremes. It is noted that previous papers have shown that zeros of the meridional gradient are important in determining the stability properties of the atmosphere. It is shown that the profiles of the meridional gradient generated from the climatological data possess zero in all seasons and at many latitudes and levels. In all seasons, therefore, the atmosphere is shown to have a wide variety of potential sources of baroclinic instability.

Fullmer, J. W. A.↗

NASA NTRS1984

The Influence of Synoptic Scales on Low-frequency Modes of Variability

Model analysis and predictablity studies using an equivalent barotropic empirical orthogonal function (EOF) model described in Schubert (1984b) are dicussed. An extensive set of 10-day forecasts was produced for the 12 component version of the model. Comparisons with observed data show apparently useful forecasts for individual winters. However, when averaged over 10 winters, the improvement over persistence was marginal and only one of the EOF's (resembling North Atlantic blocking) showed a statistically significant improvement. These results suggest the need for a more realistic model which includes shorter time scale baroclinic processes and spatial modes capable of efficiently representing the characteristic structures associated with baroclinic instability.

Schubert, S. D.↗

NASA NTRS1985

Transient Eddies in the UCLA GCM

The simulation of transient eddies in the nine level UCLA general circulation model (GCM) was examined and compared to observations, with emphasis on the Northern Hemisphere winter. Qualitatively, the UCLA GCM reproduces many features of the observed circulation and the relationship between the time mean flow and transient eddies; however, the magnitudes of transient eddies in the UCLA GCM, particularly at frequencies lower than those associated with baroclinic instability, appear to be much less than those observed. The pattern of low level transient eddy heat fluxes were similar to observations and acted to dissipate the low level seasonal mean temperature field. The simulated transient eddy kinetic energy at 300 mb is given for eddies of all time scales shorter than a season.

White, G. H.↗

NASA NTRS1984

Some interhemispheric comparisons of medium-scale waves in the lower stratosphere

Remarkable domination of the summer Southern Hemisphere (SH) circulation by medium-scale features (zonal waves 4-7) has been reported. More recently, it has been shown that these features derive their energy from baroclinic instabilities of the mean state. As one aspect of attempting to further explain the unusual spectral peak and phase-time continuity of the SH waves, the same microwave satellite instrument is used to compare characteristics of medium-scale lower stratospheric temperature waves in the Northern Hemisphere (NH) and SH summertimes. Data from the Tiros-N Microwave Sounding Unit from August 1979 are analyzed here and compared with previous analyses for January 1979 reported by Yu et al. (1983) and others. The interhemispheric comparison reveals that summertime medium-scale waves in the NH do not exhibit the striking phase-time continuity of their SH summer counterparts. In addition, winter NH medium-scale waves are also found to have less phase-time continuity than those in the SH winter. The reason for the interhemispheric difference in maintenance of the medium-scale waves, especially in summertime, remains to be explained.

Yu, W.-B.↗

NASA NTRS1984

The response of a nonlinear, time-dependent, baroclinic model of the atmosphere to tropical thermal forcing

A multi-level, sigma coordinate, primitive equation atmospheric model has been utilized to study both the tropical and extratropical response to an isolated region of steady thermal forcing in the tropics. The nonlinear response during the first 28 days of the simulation is described. The response can be generally characterized by two distinct components. The first component is a quasi-stationary disturbance which extends eastward and poleward away from the source region along a 'great circle' path. The structure of this disturbance is essentially barotropic away from the source region. The second component is a growing baroclinic wave propagating zonally at mid-latitudes. Significantly, this disturbance is apparently the result of baroclinic instability induced by the quasi-stationary wavetrain. The discussion is predominantly heuristic in form and relies heavily on graphical presentation and quasi-geostrophic theory to interpret the response and individual components of the thermodynamic energy and momentum equations.

Grose, W. L.↗

NASA NTRS1985

A simple model for the interaction between vertical eddy heat fluxes and static stability

A numerical model for studying the interaction of vertical eddy heat fluxes and vertical temperature structure in midlatitude regions is described. The temperature profile for the model was derived from calculations of the equilibrium among heating rates in simplified representations of large-scale vertical eddy heat flux, moist convection and radiation. An eddy flux profile is calculated based on the quasi-geostrophic, liner baroclinic instability of a single wave. Model equilibrium states for summer and winter conditions are compared with observations, and the results are discussed in detail.

Gutowski, W. J., Jr.↗

NASA NTRS1985

The effect of topography on the evolution of unstable disturbances in a baroclinic atmosphere

A two layer spectral quasi-geostrophic model is used to simulate the effects of topography on the equilibria, their stability, and the long term evolution of incipient unstable waves. The flow is forced by latitudinally dependent radiative heating. Dissipation is in the form of Rayleigh friction. An analytical solution is found for the propagating finite amplitude waves which result from baroclinic instability of the zonal winds when topography is absent. The appearance of this solution for wavelengths just longer than the Rossby radius of deformation and disappearance of ultra-long wavelengths is interpreted in terms of the Hopf bifurcation theory. Simple dynamic and thermodynamic criteria for the existence of periodic Rossby solutions are presented. A Floquet stability analysis shows that the waves are neutral. The nature of the form drag instability of high index equilibria is investigated. The proximity of the equilibrium shear to a resonant value is essential for the instability, provided the equilibrium occurs at a slightly stronger shear than resonance.

Clark, J. H. E.↗

NASA NTRS1986

The structure, energetics and evolution of the dominant frequency-dependent three-dimensional atmospheric modes

The three-dimensional structure of the dominant modes of wintertime variability are examined, and the mode structures are determined by an EOF analysis of the coupled vertical mean and shear streamfunction fields for a wide range of time-scale classes. The time mean energy conversions are determined from a two-layer quasigeostrophic model. Lag-cross correlations between the dominant low-frequency modes tend to be small and/or symmetric about zero, the high frequency modes are found to show highly asymmetric sinusoidal cross correlation functions similar to traveling waves, and some intermediate and short-time scale modes exhibit correlations indicating an association with the decaying phases of blocking in the Pacific. It is suggested that the mean flow barotropic (baroclinic) instabilities are an important source of variance for some of the lowest (highest) fluctuations considered.

Schubert, S. D.↗

NASA NTRS1986

The Saturnian ribbon feature: A baroclinically unstable model

Using measurements made by the Voyager spacecraft, an oscillatory feature in the northern midlatitudes of Saturn is examined. Measurements made by the imaging and infrared instruments are used to estimate its horizontal wavelength and vertical extent. Some of these characteristics suggest that the feature could be due to baroclinic instability. A numerical model is described of such an instability with parameters based upon the Voyager observations, and using the lower boundary condition developed by Gierasch et al for the Jovian planets.

Godfrey, D.↗

NASA NTRS1986

A diagnostic study of baroclinic disturbances in polar air streams

Quasi-Lagrangian budgets of mass, vorticity and heat are calculated following disturbances that form within polar air streams. Observed cases are extracted from the European Centre for Medium-range Weather Forecasts analyses during the First GARP Global Experiment. Model-generated cases are extracted from the simulations of extratropical cyclogenesis by Sandgathe. These polar lows grow primarily through basic baroclinic instability processes and exhibit many features of larger maritime extratropical cyclones. Polar lows that originate on the poleward (or Cyclonic - Type C) side of the jet and have considerable midtropospheric positive vorticity advection at formation time are contrasted with lows that form on the equatorward (or Anticyclonic - Type A) side of a nearly straight upper-level jet. The midtropospheric positive vorticity advection must be present to enhance the vertical circulation when the large surface fluxes that are associated with strong outbreaks act to damp the thermal wave amplification. Although latent heat release is an important factor in both types, it is an essential energy source for the Type A low developments on the equatorward side. Although the vorticity balance is initially different for the two types of polar lows, the vorticity budgets during later stages are similar. The heat budget and the thickness tendency equation demonstrated that the self-development process that is present in larger maritime cyclones is also important for polar low intensification. The absence of favorable coupling to a jet stream is the missing factor in a model-generated Type A polar low that failed to develop. Consequently, the mid- and upper-tropospheric wind fields determine which polar lows will intensify to significant amplitudes.

Sinclair, Mark R.↗

NASA NTRS1986

The life cycles of persistent anomalies and blocking over the North Pacific

The evolution of persistent anomaly patterns over the central North Pacific is investigated. Composite time evolution fields of the 500-mbar anomaly patterns are constructed from low-pass and unfiltered height anomaly data; the time scales for the development and decay of these persistent anomalies are analyzed. The relationship between zonal flow in the Pacific jet region and the development of the anomaly patterns is examined. The effect of baroclinic instabilities on the development of the anomalies is studied. The vertical structure and synoptic characteristics of the evolution of the anomalies are described. It is noted that the initial rapid growth of the main center may be associated with a propagating, intensifying, synoptic-scale disturbance which originates in the midlatitudes over eastern Asia.

Dole, Randall M.↗

NASA NTRS1987

Development of a two-dimensional zonally averaged statistical-dynamical model. II - The role of eddy momentum fluxes in the general circulation and their parameterization

The role of eddy momentum fluxes in the general circulation was investigated using a two-dimensional zonally averaged statistical-dynamical model described by Yao and Stone (1987), which is almost two orders of magnitude faster than the three-dimensional climate model of Hansen et al. (1983). Results show that the vertical structure of the meridional eddy flux has relatively little impact on the general circulation, presumably because the vertical structure is strongly constrained by the thermal wind relation and surface friction. On the other hand, it was found that, in order to simulate accurately the general circulation and its response to climate changes, parameterization of the vertically integrated meridional eddy flux of angular momentum is necessary. A new parameterization of this eddy momentum transport was carried out, which is intended to represent the transport due to large-scale transient eddies arising from baroclinic instability.

Stone, Peter H.↗

NASA NTRS1987

An analytic study of the Charney problem on the sphere

An analytic study of the Charney (1947) problem is presented, in which a shortwave approximation and a two-scale assumption are adopted to derive approximate solutions for the problem. The solutions contain a second-order turning point whose location is important in determining the properties of baroclinic unstable waves. This turning point is located at the maximum of the meridional temperature gradient. The solutions indicate a close relation between baroclinic instability on the sphere and on a Beta-plane. The solutions have some limitations and are not valid for long waves. It is suggested that the solutions have implications for parameterizations of eddy fluxes in climate modeling.

Lee, Yung-An↗