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NASA NTRS1987

Developing disturbances in shear

The origin and growth to moderate amplitude of disturbances in shear flow has been traditionally ascribed to the linear modal instability of the flow. Recent work on initial value problems has suggested that nonmodal growth of perturbations may be of equal and perhaps greater importance, at least in cases of rapid development. Examples of robust growth in model problems which support no instabilities and in baroclinic flows with realistic Ekman damping for which the exponential modes have zero or negative growth rates have been shown. Such examples have focused attention on the perturbations which are configured to tap the energy of mean flows. Here a critical examination of these favorably configured perturbations is given, making use of the simple constant free shear barotropic model which allows construction of exact two-dimensional isolated wave packet solutions.

Farrell, Brian↗

NASA NTRS1998

Seasonal Cycles of Meridional Overturning and Heat Transport of the Indian Ocean

A general circulation model of the Indian Ocean is fitted to monthly averaged climatological temperatures, salinities, and surface fluxes using the adjoint method. Interannual variability is minimized by penalizing the temporal drift from one seasonal cycle to another during a two-year integration. The resultant meridional overturning and heat transport display large seasonal variations, with maximum amplitudes of 18 and 22 (x 10(exp 6) cubic m/s) for the overturning and 1.8 and 1.4 (x 10(exp 15) W) for heat transport near 10 S and 10 N, respectively. A dynamical decomposition of the overturning and heat transport shows that the time-varying Ekman How plus its barotropic compensation can explain a large part of the seasonal variations in overturning and heat transport. The maximum variations at 10 deg N and 10 deg S are associated with monsoon reversal over the northern Indian Ocean and changes of the easterlies over the southern Indian Ocean. An external mode with variable topography has a moderate contribution where the Somali Current and the corresponding gyre reverse direction seasonally. Contribution front vertical shear (thermal wind and ageostrophic shear) is dominant near the southern boundary and large near the Somali Current latitudes. The dominant balance in the zonally integrated heat budget is between heat storage change and heat transport convergence except south of 15 S. Optimization with seasonal forcings improves estimates of sea surface temperatures, but the annual average overturning and heat transport are very similar to previous results with annual mean forcings. The annual average heat transport consists of roughly equal contributions from time-mean and time-varying fields of meridional velocities and temperatures in the northern Indian Ocean. indicating a significant rectification to the heat transport due to the time-varying fields. The time-mean and time-varying contributions are primarily due to the overturning and horizontal gyre, respectively. Inclusion of TOPEX data enhances the seasonal cycles of the estimated overturning and heat transport in the central Indian Ocean significantly and improves the estimated equatorial zonal flows but leads 10 unrealistic estimates of the velocity structure near the Indonesian Throughflow region, most likely owing to the deficiencies in the lateral boundary conditions.

Lee, Tong↗

NASA NTRS1985

Persistent anomalies, blocking and variations in atmospheric predictability

The fully nonlinear, equivalent-barotropic vorticity equation on the sphere, with simplified forcing, dissipation and topography, is the model used in the present consideration of low frequency variability regimes in large scale atmospheric dynamics. The solutions obtained are studied as a function of the nondimensional intensity of the forcing and dissipation. The number of modes retained in the analysis allows the multiple equilibria thus obtained, which exhibit blocked and zonal flow patterns very similar to synoptically defined zonal and blocked Northern Hemisphere midlatitude flows, to appear for realistic values of the forcing. The number of episodes of blocked or zonal flow decreases monotonically as their duration increases, in agreement with observations.

Legras, B.↗

NASA NTRS1985

A Comparison of the Bounded Derivative and the Normal Mode Initialization Methods Using Real Data

Browning et al. (1980) proposed an initialization method called the bounded derivative method (BDI). They used analytical data to test the new method. Kasahara (1982) theoretically demonstrated the equivalence between BDI and the well known nonlinear normal mode initialization method (NMI). The purposes of this study are the extension of the application of BDI to real data and comparison with NMI. The unbalanced initial state (UBD) is data of January, 1979 OOZ which were interpolated from the adjacent sigma levels of the GLAS GCM to the 300 mb surface. The global barotropic model described by Takacs and Balgovind (1983) is used. Orographic forcing is explicitly included in the model. Many comparisons are performed between various quantities. However, we only present a comparison of the time evolution at two grid points A(50 S, 90 E) and B(10 S, 20 E) which represent low and middle latitude locations. To facilitate a more complete comparison an initialization experiment based on the classical balance equation (CBE) was also included.

Semazzi, F. H. M.↗

NASA NTRS1993

GCM simulations of intraseasonal variability in the Pacific/North American region

General circulation model (GCM) simulations of low-frequency variability with time scales of 20 to 70 days are analyzed for the Pacific sector during boreal winter. The GCM's leading mode in the upper-tropospheric zonal wind is associated with fluctuations of the East Asian jet; this mode resembles, in both structure and amplitude, the Pacific/North American (PNA) pattern found in the observations on these time scales. In both the model and observations, the PNA anomaly is characterized by: (1) a linear balance in the upper-tropospheric vorticity budget with no significant Rossby wave source in the tropics, (2) a barotropic conversion of kinetic energy from the time mean Pacific jet, and (3) a north/south displacement of the Pacific storm track. In the GCM, the latter is associated with synoptic eddy heat flux and latent heat anomalies that appear to contribute to a strong lower-tropospheric source of wave activity over the North Pacific. This is in contrast to the observations, which show only a weak source of wave activity in this region.

Schubert, Siegfried↗

NASA NTRS1985

A model of the wave 1 - wave 2 vacillation in the winter stratosphere

A three-dimensional, severely truncated, quasi-geostrophic model in a beta channel is used to explore the dynamics of the observed anticorrelation between the amplitudes of planetary waves 1 and 2 in the Northern Hemisphere winter stratosphere. The model, which includes interactions among eight horizontal modes, generates realistic wave 1-wave 2 vacillations when westward traveling wave 1 interacts with stationary waves 1 and 2. It is found that while wave 1 oscillates in response to wave-mean flow interactions, the oscillations in the amplitude of wave 2 are driven primarily by wave-wave interactions. Experiments with a barotropic model reveal that the timing of the strongest wave-wave interactions is determined by the wave 1 interaction with the mean flow.

Robinson, W. A.↗

NASA NTRS1987

Resonant excitation of hemispheric barotropic instability in the winter mesosphere

In the present consideration of the subtropical mesospheric jet observed by the Nimbus 7 Limb IR Monitor of the Stratosphere in late 1978, where enhanced planetary wave activity propagating upward into the mesosphere in mid-December led to visible overreflection from the low-latitude reversed gradient region and rapid deceleration of the jet, the possible Rossby wave and mean meridional circulation causes for these observations are considered and rejected as unsuitable. The wave 1 mode is for practical purposes a radiating mode, excitable by sources in the far field. Since the phase speed of the eigenmodes can be made exactly zero when the mean flow vanishes within this region, as observed in mid-December 1978, resonant excitation is possible.

Dunkerton, Timothy J.↗

NASA NTRS1981

Comparison of a barotropic blocking theory with observation

Hart (1979) showed that the truncated spectral equations obtained by Charney and Devore (1979) could be derived merely by assuming that the cross-stream scale of the topography was large compared to the downstream scale. Since actual topography does not have the large y scales postulated by Hart, his model was modified in the current investigation to obtain equations with arbitrary zonal variations of topography by projecting all variable functions onto the first topographic cross-stream mode. The topographic heights and streamfunctions are expanded as Fourier series in the cross-stream coordinate and the series are truncated after the first term. This accomplishes Hart's results but permits more realistic y variations in the topography. The present investigation is the first in a two-part series. The second part will deal with a two-layer baroclinic channel flow, again with arbitrary zonal variations of topography.

Charney, J. G.↗

NASA NTRS1985

Vacillations induced by interference of stationary and traveling waves

It was shown that there exists a correspondence between interference of the 16-day wave with the stationary planetary wave and vacillations in eddy heat and momentum fluxes. There has been speculation on the role such interference may play in stratospheric warmings. The appearance of higher-order normal modes, e.g., the 16-day wave, prior to disturbances in the stratospheric vortex has also been noted. Since amplitudes of the 16-day wave are compared to those of the stationary component, it can significantly alter the instantaneous total wave field. The behavior of the wave number 1 height field at 60 deg N during January 1979 is shown when a large amplitude disturbance retrogressed barotropically around the globe over much of the troposphere and stratosphere. This transient disturbance has been identified with the 16-day wave. More generally, the presence of fluctuating planetary wave activity can, through combined interference, alter the instantaneous planetary wave field as well as the transports it produces. The implications of such interference in a quasi-geostrophic framework has been explored, using the Eliassen-Palm (EP) flux as a diagnostic.

Salby, M. L.↗

NASA NTRS1987

An analysis of the vertical structure equation for arbitrary thermal profiles

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.

Cohn, Stephen E.↗

NASA NTRS1989

An analysis of the vertical structure equation for arbitrary thermal profiles

Cohn, Stephen E.↗

NASA NTRS1989

Three-dimensional linear instability modeling of the cloud level Venus atmosphere

Based on the success of several two-dimensional (latitude, longitude) linear barotropic instability models at matching some of the observed characteristics of the cloud level, polar region of the Venus atmosphere, a more realistic, linear, three-dimensional (height, latitude and longitude) model has been developed to further test the hypothesis that the observed features can be described by linear instability theory. The approach taken is to vary the model input parameters to see whether it is possible to produce modes that resemble the observations of wave activity and to compare those input parameters with other observations of the mean state. Sensitivity studies show that in addition to a well-documented dependence on the mean zonal wind, the growth and propagation of unstable modes depends on the latitude variation of the mean temperature (and hence static stability). These studies have led to the specification of a model basic state wind and temperature field that produces modes which are matched to observations of spatial structure, preferred wavenumber and phase speed of the polar disturbances. Wavenumber 2 is found to have the shortest growth time and unlike the two-dimensional results, wavenumbers 1-3 share a nearly common period of about 3 days. The derived basic state has a temperature field that is quite similar to Pioneer Venus observations; however, in some regions the model basic state wind field departs from cyclostrophic values based on temperature observations.

Elson, Lee S.↗

NASA NTRS1993

Intraseasonal variability in a barotropic model with seasonal forcing

It has recently been suggested that oscillatory topographic instability could contribute to low-frequency variability over the Northern Hemisphere midlatitudes. A barotropic potential vorticity model, with a hierarchy of forcing and topography configurations on the sphere, is used to investigate the nature of low-frequency oscillations induced by such instabilities. Steady-state solutions of the model include multiple unstable equilibria that sustain oscillatory instabilities with periods of 10 - 15 days, and 150 - 180 days, for a realistic forcing pattern, Time-dependent solutions exhibit chaotic behavior with episodic oscillations, featuring both the intraseasonal (35 - 50 day) and biweekly (10 - 15 day) modes. The former is dominated by standing spatial patterns, the latter by traveling wave patterns. The phases of the intraseasonal oscillation are robust for all cases, exhibiting a clear oscillatory exchange of atmospheric angular momentum with the solid earth via mountain troque. It is demonstrated, through linear stability analysis on the sphere, that the intraseasonal oscillations are induced by topographic instabilities. The role of the seasonal cycle is studied by prescribing an annual cycle in the forcing. In this case, the winter forcing is more favorable than the summer for the occurrence of episodic intraseasonal oscillations. Recent observations are consistent with this model result.

Strong, Christopher M.↗

NASA NTRS1980

Eddy heat fluxes and stability of planetary waves. I, II

The stability of baroclinic Rossby waves in a zonal shear flow was analyzed by a linear, quasigeostrophic, two-level, adiabatic, and frictionless midlatitude beta-plane model. The ratio of the basic wave scale and the radius of deformation together with two nondimensional parameters which describe the amplitudes of the barotropic and baroclinic components of the basic wave constitute the three parameters of the stability problem. The parameter space is partitioned according to the dominant energy source for instability; the Lorenz and Kim conditions are characterized by significant horizontal and vertical shears of the basic wave, while the Phillips regime has a strong zonal flow. The stability analysis is then applied to the atmosphere, with the primary motivation being to examine the midlatitude planetary scale (zonal wavenumbers 1, 2, 3) transient waves that transport heat. It is found that the most unstable mode consists of a spectrum of waves, with a maximum amplitude at wavenumber 3; the response is thus maximum at a zonal scale intermediate between the basic wave scale and the radius of deformation.

Lin, C. A.↗

NASA NTRS2019

Extratropical Large-Scale Traveling Weather Systems in the Southern Hemisphere on Mars

From late-autumn through early-spring, the middle- and high-latitudes of both hemispheres of Mars and its predominantly carbon-dioxide atmosphere support mean equator-to-pole thermal contrasts, and then, support a strong mean westerly polar vortex. Observations from orbiting spacecraft indicate that this intense mean baroclinicity-barotropicity supports large-scale eastward traveling weather systems (i.e., transient, traveling synoptic-period waves, on the order of the Rossby deformation scale). On Earth, extratropical weather disturbances arise from wind-shear instabilities, and these are critical components of the terrestrial global circulation. So it is the case for Mars. Large-scale traveling weather systems on Mars serve as agents in the transport of heat, momentum and scalar and tracer quantities (e.g., atmospheric dust, watervapor, ice clouds, chemical species, etc). Such weather systems interact with other large-scale atmospheric circulation components, namely, quasi-stationary (i.e., forced Rossby) modes; global thermal tidal modes; and then, upon large-/continental- geographical scales, upslope/ down-slope flows amongst high relief, low relief, impact basins, and volcanic rises, and more. The character of Mars' traveling extratropical weather disturbances in its southern hemisphere during late winter through early spring is investigated using a high-resolution Mars global climate model (i.e., Mars GCM), and one from the Agency's Mars Climate Modeling Center (MCMC) based at the NASA Ames Research Center. The climate model includes several complex atmospheric physical packages. With such physics modules, our global climate simulations present comparatively well with observations of the planet's current water cycle (Haberle et al.,2019). The climate model is "forced" with an annual dust cycle (i.e., nudged based on MGS/TES observations). Compared to the northern-hemisphere counterparts, the southern synoptic-period weather disturbances and accompanying frontal waves have smaller meridional and zonal scales, and are less intense. Influences of the zonally asymmetric (i.e., east-west varying) topography on southern large-scale weather are investigated, in addition to large-scale up-slope/down-slope flows and the diurnal cycle. A southern storm zone in late winter and early spring presents in the western hemisphere via orographic influences from the Tharsis highlands, and the Argyre and Hellas impact basins. Geographically localized transient-wave activity diagnostics are constructed that illuminate dynamical differences amongst the simulations and these are presented.

Hollingsworth, Jeffery L.↗

NASA NTRS2012

African Easterly Jet: Barotropic Instability, Waves, and Cyclogenesis

This study investigates the structure of the African easterly jet, focusing on instability processes on a seasonal and subseasonal scale, with the goal of identifying features that could provide increased predictability of Atlantic tropical cyclogenesis. The Modern-Era Retrospective Analysis for Research and Applications (MERRA) is used as the main investigating tool. MERRA is compared with other reanalyses datasets from major operational centers around the world and was found to describe very effectively the circulation over the African monsoon region. In particular, a comparison with precipitation datasets from the Global Precipitation Climatology Project shows that MERRA realistically reproduces seasonal precipitation over that region. The verification of the generalized Kuo barotropic instability condition computed from seasonal means is found to have the interesting property of defining well the location where observed tropical storms are detected. This property does not appear to be an artifact of MERRA and is present also in the other adopted reanalysis datasets. Therefore, the fact that the areas where the mean flow is unstable seems to provide a more favorable environment for wave intensification, could be another factor to include-in addition to sea surface temperature, vertical shear, precipitation, the role of Saharan air, and others-among large-scale forcings affecting development and tropical cyclone frequency. In addition, two prominent modes of variability are found based on a spectral analysis that uses the Hilbert-Huang transform: a 2.5-6-day mode that corresponds well to the African easterly waves and also a 6-9-day mode that seems to be associated with tropical- extratropical interaction.

Wu, Man-Li C↗

NASA NTRS1984

A numerical simulation of barotropic instability. II Wave-wave interaction

A fully nonlinear numerical model of the point jet barotropic instability is used to test and confirm the hypothesis that the magnitude of the wave vorticity does not exceed the magnitude of the initial shear. This result arises directly from the local conservation of vorticity following a parcel and the fact that unstable waves are principally confined to the region where the zonal mean vorticity can be smoothed by the wave so as to eliminate the instability. Comparisons are made between fully nonlinear and quasi-linear models of the point jet instability and their tracer transport properties. Differences become particularly evident after wave saturation. The most important effect neglected by the wave-mean flow model appears to be the advection of wave vorticity by the most unstable mode. However, as equilibration of the instability proceeds, the globally averaged properties of both models are found to be similar.

Nielsen, J. E.↗

NASA NTRS1992

Dynamics of atmospheric teleconnections during the northern summer

The mechanisms of northern summertime teleconnections are investigated using a barotropic model. In a series of numerical experiments the atmospheric response over the eastern Pacific-North America to an idealized local divergence source corresponding to the northward displacement of the ITCZ in the eastern Pacific is studied. It is found that the response is much stronger in June than in May and is strongest when the forcing is located north of about 10 deg N. This can be explained in terms of the refractive properties of the climatological summertime subtropical jet stream over North America. In another series of experiments the global response as a function of the longitudinal location of the tropical forcing is examined. A wave train emanating from the subtropics of the western Pacific near the Philippines, arching across the Aleutians and the Gulf of Alaska, and terminating with a high anomaly over the continental United States appears over a wide longitudinal range of local forcing, suggesting the existence of a normal mode for the northern summertime climatological flow. The normal-mode concept is supported by further experiments using extratropical forcings as well as free-mode integrations.

Lau, K.-M.↗