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Robert L. Gall

Abstract

A simple vertically-integrated axisymmetric model is used to Calculate axisymmetric flows for different swirl ratios(s) in tornado simulators. Thew axisymmetric states are then tested for stability using a primitive-equation linear model where the waves have both an azimuthal and a vertical wavenumber.

For S high enough for there to be a central downdraft in the axisymmetric vortex, the vortex is unstable; otherwise it is stable. For relatively lows only azimuthal waves 1 and 2 are unstable, with wave 1 most unstable at lows followed by 2 at somewhat highers As S is further increased, the most unstable wave shifts to 4, then 5, and so forth. With some tuning, the model predicts the transitions from 0–1 and 1–2 secondary vortices to occur at about the observed value ofs Vertical wavelength are about 3 m, but they increase with increases

There are two modes of instability: one in which only waves 1 or 2 are unstable and which appears at lows and a second mode where waves 4, 5 or 6 are most unstable and which appears at highs These two modes am distinguished mostly by their energetics. Mode 1 receives most of its energy from the radial shear of the vertical wind, while mode 2 receives most of its energy from the radial shear of the tangential wind. In mode 1, all the amplitude of the horizontal streamfunction is contained inside the tangential wind maximum, while in mode 2 much of the amplitude is outside the tangential wind maximum.

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Robert L. Gall

Abstract

The reason for existence of two separate unstable modes, previously described by Gall for flows in vortex simulators, is explored. When the energy equation for an unstable disturbance is considered, it is clear that the most unstable wave must be centered inside the maximum in the vertical vorticity of the basic state if this vorticity has a radial distribution that is triangular-shaped and this triangle is near the center of the vortex. When this vorticity is at large radius, the most unstable wave can be centered near or even outside the basic-state vorticity maximum. This suggests different modes when the triangular profile of vorticity is near or far from the center and that the transition from one to another mode should be gradual. These notions are verified by a careful analysis of the stability properties of the triangular-shaped vorticity profile.

It is shown that the triangular-shaped vorticity profile closely resembles the vorticity distribution in the vortex simulator after a downdraft has been established along the centerline of the vortex. In fact, the stability properties of these triangular profiles closely resemble the stability properties of the simulated vortex when the scale of the triangular profile is comparable to the vorticity distribution in the simulators.

Square-shaped vorticity profiles, which have been considered in the past, have significantly different stability properties, as compared to the triangular profiles. In particular, there is only one unstable mode, and the instability is extinguished as the vorticity region approaches the center of the basic vortex. The reason for this is easily explained by considering the perturbation energy equation.

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Robert L. Gall

Abstract

A simple model of flow through a tornado vortex simulator is described. This model assumes a very simple distribution in the vertical of the radial and tangential components of the wind, consistent with the flow found in the simulator. With these assumptions, and with careful attention to the distribution of pressure in the lower and upper portions of the chamber, the axisymmetric equations can be reduced to one-dimensional equations.

The model illustrates that all interesting dynamics of the vortex, such as the development of the downdraft and the expansion of the core, are a result of the pressure distribution in the upper part of the chamber. In this model, this pressure distribution is caused by a slow radial spreading with height of the vorticity of the vortex, due to diffusion processes.

The model is shown to provide a realistic distribution of observed velocity fields in the simulator, including the downdraft at the center.

The dependence of the vertical velocity distribution on swirl ratio is shown and the details explained. An equation that predicts the core radius as a function of swirl ratio is given; it appears superior to previous similar equations.

Finally, predictions of the minimum pressure as a function of swirl ratio given by the model are presented. It is suggested that the observed minimum pressure curve shows two regimes, turbulent at high swirl ratio and nonturbulent at low swirl ratio. It is shown why the pressure in a turbulent vortex is much higher than in a nonturbulent vortex at the same swirl ratio and volume flow rate, and why this explains the observed curve.

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Terry L. Clark and Robert Gall

Abstract

Numerical simulations of airflow over two different choices of mountainous terrain and the comparisons of results with aircraft observations are presented. Two wintertime casts for flow over Elk Mountain, Wyoming where surface heating is assumed to be zero and one case for airflow over Mt. Withington, New Mexico where surface heating is strong are considered.

In the Elk Mountain simulations the flow becomes approximately steady state since the upstream conditions are assumed to be constant and the surface heating is assumed to be zero. The response is significantly different in the two cases. In one case (dynamic Elk) strong lee waves formed with a horizontal separation of ∼10 km whereas in the second case (microphysical Elk) mainly weak untrapped waves formed with a vertical wavelength of ∼2.5 km. Because of the presence of the lee waves in the first case it is shown that the ridges south of Elk Mountain affect the flow near Elk Mountain. In the second case where there were no strong lee waves, the ridges to the south had very little effect on the flow near Elk Mountain so Elk acted as an isolated peak. The comparison between the simulation and the observations of the Elk Mountain experiments was good. In particular, the model's prediction of the location and intensity of trapped lee waves in the dynamic Elk case was good.

In the Mt. Withington simulations, the presunrise response was very weak though there were some weak lee waves. After sunrise, strong longitudinal rolls developed in the lower 1 km. These rolls were parallel to the mean wind direction in the lowest first kilometer and had an initial cross roll separation of 4–5 km for a mixed layer depth of 1.5 km. Later in the morning, after additional surface heating, the longitudinal rolls tended to increase their cross roll separation distance and to break up into a more cellular pattern although still retaining a well-defined roll structure. The ratio of cross roll separation to mixed layer depth was within the typically observed ratio of ∼2–3.

The overall comparison between the observations and the simulated flow fields in the Mt. Withington case was reasonable although detailed comparisons between individual features met with mixed success. The low-level observations appeared to represent cellular patterns as opposed to the simulated roll patterns although the horizontal scales perpendicular to the simulated rolls compared favorably. This difference in convective regime between the model and observations may be due in part to the very crude surface layer treatment of the model used to treat the unstable boundary layer as well as due to difficulties in choosing representative low-level winds. In the upper levels the comparison was successful in that the observations corroborate the presence of the trapped lee waves simulated by the model.

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Timothy L. Miller and Robert L. Gall

Abstract

Numerical models are utilized to study a spherical analogue of the rotating annulus experiments modeling atmospheric motion. Motivation for this work is partially provided by NASA's proposal to conduct such an experiment on Spacelab (the Atmospheric General Circulation Experiment). A liquid is contained between two rigid, co-rotating, concentric hemispheres, with thermal gradients imposed upon both spheres. Temperature are lower on the inner sphere than on the outer sphere, and decrease towards the pole. A constant radial body force (inward) is assumed. Utilizing the Navier-Stokes equations assuming symmetry about the polar axis, finite-difference numerical models obtain steady-state solutions to the equations. The differences in solutions for case of varying rotation rates and latitudinal thermal gradients are discussed and explained. Hydrostatic and nonhydrostatic solutions are compared for cylindrical and spherical cases. For the spherical shell, it is found that the differences between hydrostatic and nonhydrostatic solutions are small, and the differences are confined mostly to regions near the pole and equator. It is suggested that nonhydrostatic effects upon the axisymmetric state will not affect the baroclinic stability of the flow.

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Timothy L. Miller and Robert L. Gall

Abstract

A rotating cylindrical annulus of an incompressible fluid with horizontal density gradients is studied by the use of numerical models. Steady axisymmetric states are calculated using the full Navier-Stokes equations for a broad range of thermal Rossby number (Ror) and Taylor number (Ta). These states are tested for stability to nonaxisymmetric perturbations by the use of a model based upon the linearized hydrostatic primitive equations. The results include a prediction of the transition curve, the curve separating axisymmetric flow and nonaxisymmetric flow. This predicted curve is very close to that observed in the laboratory.

The structure and energetics of the fastest growing eigenmodes are examined. It is found that the structure of the linear wave, for one point in the nonaxisymmetric regime, has only small differences from the nonlinear wave calculated by Williams. The structures of the waves at this and other points are similar to the classic Eady wave, except near the extreme lower part of the transition curve. There, the waves have little structure with height, and the present models fail to predict the cutoff of nonaxisymmetric flow, probably due to the assumption that the upper surface is flat.

In all regions in parameter space, the eddy kinetic energy generation was found to be baroclinic in nature. Large static stability of the basic state is important in suppressing the generation of eddy potential energy near the upper part of the transition curve but not near the lower part, in agreement with previous theoretical results. Dissipation of the eddies is important near all boundaries.

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Thomas C. Adang and Robert L. Gall

Abstract

The Arizona Monsoon Boundary is defined as the boundary separating two distinctly different air masses over Mexico and the adjacent Pacific during the summer. The structure and dynamics of this boundary are examined by cross-sectional analysis using three different data sources: 1) a composite cross section through the boundary, constructed from the Fleet Numerical Oceanography Center (FNOC) analysis; 2) a time-height cross section, constructed using radiosonde observations at the time the boundary passed through Tucson in 1984; and 3) a cross section through the boundary on 22 July 1985, using high-resolution fields of temperature, moisture, and geopotential height obtained from the VISSR Atmospheric Sounder (VAS). All draw cross sections showed similar structure.

In some respects, the Arizona monsoon boundary resembles a midlatitude front (i.e., there is a distinct and relatively sharp air mass change) forced almost entirely by confluence. A direct ageostrophic circulation is produced by this forcing, giving weak ascent on the warm, moist side of the boundary. The gradients and flow associated with the composite boundary are weaker, by a factor of four, than those associated with strong midlatitude fronts. However, the VAS cross section suggests that, at times, the strength of the boundary approaches that of midlatitude fronts. The wind shear suggested by the composite boundary ought to be unstable to baroclinic or barotropic processes and, hence, disturbances developing along the boundary are a distinct possibility. These disturbances are indeed observed and are the subject of a companion paper by Moore et al.

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Kenneth C. Young and Robert L. Gall

Abstract

A spring-runoff forecast model for central Arizona was developed based on multiple discriminant analysis. More than 6500 potential predictor variables were analyzed, including local precipitation and temperature variables, as well as global sea level pressure variables. The forecast model was evaluated on nine years exclusive of the years on which the model was based. Forecasts are provided in the form of a cumulative distribution function (cdf) of the expected runoff, based on analogs. A ranked probability score to evaluate forecast skill for the cdf forecasts was developed. Ranked probability skill scores ranged from 25% to 45%.

Local and global forecast models were developed and compared to the combined data source model. The global forecast model was equivalent in skill to the local forecast model. The combined model exhibited a marked improvement in skill over either the local or global models.

Three recurrent patterns in the predictor variables used by the forecast model are analyzed in some depth. Above-normal pressure at Raoul Island northeast of New Zealand 14 to 18 months prior to the event forecast was found to be associated with above-normal runoff. A westward shift of the Bermuda high, as evidenced by the pressure change at Charleston, South Carolina, from December to August of the preceding year, was found to be associated with above-normal runoff. Above-normal pressure at Port Moresby, New Guinea coupled with below-normal pressure at San Diego, California, the month prior to the forecast, was found to be associated with above-normal runoff.

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Walter P. Smith and Robert L. Gall

Abstract

Squall lines possessing nearly all the characteristics of tropical squall lines occasionally develop during the summer monsoon over southern Arizona and northwestern Mexico. Initial thunderstorm formation is over the Continental Divide in the late afternoon and the systems become organized within a few hours. Satellite imagery, cloud-to-ground lightning strike data, and surface observations indicate the squall lines move from east to west or northeast to southwest by discrete propagation faster than the environmental flow at all levels below 20 kPa so that most of the anvil clouds lag behind.

The synoptic-scale circulation is anomalous with a strong ridge located over the western United States and a deep trough located over the eastern United States. West to northwest winds are found in the boundary layer over southern Arizona and northwest Mexico while a deep layer of east winds are observed above. As a result most of the environmental wind shear is confined to the lowest 2.5 km above the ground with very little shear at higher altitudes. The low-level wind shear seems to be required for the westward propagation of thunderstorms and the formation of the squall lines. Extremely dry midtropospheric air develops in the easterly flow through some combination of advection and subsidence and also appears to be an important factor in the development of the squall lines and in the creation of severe thunderstorms.

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TRANSITION OF WEATHER RESEARCH TO OPERATIONS

Opportunities and Challenges

Robert J. Serafin, Alexander E. MacDonald, and Robert L. Gall

The National Weather Service (NWS) of the United States has recently completed its modernization phase. This comprehensive modernization has put into place new observing systems, both ground-based and in space. The modernization has also involved the consolidation of field forecast offices, the relocation of field offices, and changes in the staffing profiles of field offices. Finally, next generation supercomputing facilities, communications, and interactive systems have been installed. Taken together, these substantial investments have resulted in a new and flexible infrastructure that is producing significant improvements in NWS weather forecasts and warnings. Benefits can also be found in the value-added services provided by the private sector. Anticipated advances scientifically and technologically will provide abundant opportunities for further major improvements to weather services of the future. Accuracy and specificity will improve on all relevant time and space scales, and the world of information technology will ensure that weather forecasts are provided to all who need them expeditiously and reliably. The challenge to the NWS, and to all who provide weather services, is to ensure that the results of research are effectively, regularly, and cost-effectively transferred into the operational system. For this to happen, the research agenda must be properly structured and the community of researchers, forecasters, and users must work interactively and cooperatively.

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