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T. L. Clark
and
W. R. Peltier

Abstract

We examine the evolution of a field of internal waves launched by stratified flow over symmetric topography in mean flows which reverse direction at some height above the surface. With the gradient Richardson number at this “critical level” in the undisturbed flow restricted to values greater than 0.25, the nonlinear interaction in the region is such that the surface strongly reflects large amplitude internal waves incident upon it. When the critical level is located near certain discrete heights above the ground the incident and reflected waves interfere constructively and the wave amplitude in the low levels is resonantly enhanced by a large factor. These results are related to our previous analyses of the process by which breaking internal waves are able to induce intense downslope windstorms.

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W. R. Peltier
and
T. L. Clark

Abstract

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W. R. Peltier
and
T. L. Clark

Abstract

The transient evolution of internal waves which are forced by the flow of stably stratified fluid over two-dimensional topography exhibits several pronounced nonlinear effects for geophysically relevant values of the governing parameters. For homogeneous flows in which the internal Froude number is constant, the importance of nonlinearity is determined by the aspect ratio of the topography and the flow in the steady-state regime is as predicted by Long's model. When the background flow is inhomogeneous, Long's model no longer applies and new nonlinear effects may occur. One example of such an effect is the marked increase in the efficiency with which resonant lee waves are excited beyond the linear efficiency. A second example concerns the possibility of the trapping and subsequent amplification of the internal wave beneath its own level of supercritical steepening. The latter process appears to be important in understanding the strong downslope windstorm which occurred at Boulder, Colorado, on 11 January 1972.

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T. L. Clark
and
W. R. Peltier

Abstract

We describe a series of fixed Froude number numerical simulations of the generation of internal gravity waves by the flow of stably stratified fluid over an isolated obstacle. Upstream of the obstacle the parallel flow is shear free and the Brunt-Väisälä frequency is independent of height. Under these conditions the nonhydrostatic model which we employ does not support resonance modes. In this model the nonlinear lower boundary condition is treated via a general tensor transformation which maps the domain with an irregular lower boundary into a rectangle. We explore the characteristics of the wave field as a function of the aspect ratio of the topography and show that there exists a critical aspect ratio which, if exceeded, results in the generation of internal waves which are subject to a local convective instability. In the long time limit we compare the numerically determined wave drag, the vertical profile of Reynolds stress and the downslope wind amplification to the corresponding predictions of linear steady-state theory. In the limit of small aspect ratio the analytic and numerical results coincide; in particular the Eliassen-Palm theorem is recovered. In the unstable regime the drag on the obstacle increases drastically, the strength of the downslope flow is enhanced and the vertical profile of Reynolds stress is strongly divergent. We discuss the implications of these results to the understanding of certain characteristics of mountain waves in the atmosphere.

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R. L. Gall
,
R. T. Williams
, and
T. L. Clark

Abstract

Gravity waves forced by nonhydrostatic and nongeostrophic processes within a frontal zone are discussed. In particular, stationary waves immediately above and below the surface front are considered.

The waves that appear above the front are horizontally stationary with respect to the front, but are vertically propagating. The vertical wavelength here is given by 2πυ/N, since the waves are nearly hydrostatic.

The horizontal wavelength of the waves above the front is determined by standing waves that set up below the Front. These waves corrugate the frontal surface, and these corrugations, in turn, determine the horizontal scale of the waves above the front.

The waves under the front are standing and are trapped between the earth's surface and the frontal zone which, due to its conditions of flow reversal and small Ri, is assumed to be a reflector of gravity waves. The horizontal scale of the standing waves is determined by their vertical wavelength and the slope of the frontal surface. These waves are shown to break, and additional stationary waves appear above each of the breaking zones.

We suggest that the waves described here might account for some of the banding seen in satellite images of frontal zones.

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R. L. Gall
,
R. T. Williams
, and
T. L. Clark

Abstract

A series of numerical experiments of a surface front forced by stretching deformation using Clark's nonhydrostatic model at very high resolution is presented. These simulations are compared to those reported by Williams who used hydrostatic models at lower resolution. The main purpose was to determine whether this front would collapse (in the absence of friction) to a scale similar to that reported by Shapiro et al. (most of the temperature gradient contained in 200 m). The question is whether there is a natural physical process in the frontal dynamics which limits the frontal collapse in the absence of diffusion processes.

For this front we could not find a natural limiting process, although the mechanism discussed by Orlanski et al. appears to be operating. The minimum scale is determined by the vertical resolution. At the vertical and horizontal resolutions we tried, the vertical resolution determined the scale because the slope of the front is so shallow.

Some of the structure found by Cullen and Purser by extending the semigeostrophic models beyond the initial development of a discontinuity is apparent in our solutions.

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Roelof T. Bruintjes
,
Terry L. Clark
, and
William D. Hall

Abstract

A three-dimensional, time-dependent, nested-grid model is used to calculate the targeting of tracer or Seeding material over complex terrain in northern Arizona. Good agreement with measurements of SF6 tracer is reported in three case studies. Released in upwind valleys, the tracer movement and dispersion are strongly influenced by both valley flow and gravity waves excited by the mountains, as well as by changes in the synoptic flow, which can change substantially even during a single storm. The interaction between the airflow and the topography seem to be the dominant factor determining the dispersion and transport of tracer material.

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T. L. Clark
,
F. I. Harris
, and
C. G. Mohr

Abstract

Simulations from a time-dependent model of moist convection have been used to assess magnitudes of errors in the estimates of derived wind fields from the synthesis of data from a network of Doppler radars. The two types of errors considered are, first, those due to temporal changes in the scales of deep convection resolved by the model, and second, those due to the random contributions of radial velocity estimates by scales smaller than model resolution (noise). Due to the coarse spatial resolution of the model, much of the assumed noise error is due to spatial scales between the model's resolution (∼1 km) and the Doppler radar sampling scale (∼100 m) and should not be considered in reality as “white” noise with respect to the radar sampling problem. The results presented in this paper must be interpreted only in terms of wind estimates derived by using radar sample volumes comparable to the models resolution. Much higher spatial resolution experiments with the model are necessary to clearly delineate the differences between temporal and noise errors for scales larger than the typical radar sampling volumes.

The temporal errors for the resolved scales of the model using a 3 min scan time were found to be less than those due to noise and in general quite tolerable in magnitude for three or more radars. A dual-Doppler analysis in x, y, z Cartesian space (as opposed to x, y, elevation angle coplane analysis) was considered. In this case the derived errors (in the steady state) were found to be significantly large.

The effects of scan time and number of radars were assessed and two methods of reducing temporal errors were investigated.

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Daren Lu
,
T. E. VanZandt
, and
W. L. Clark

Abstract

The Platteville VHF Doppler radar, located on the Colorado piedmont near Platteville, Colorado, continuously measured the vertical wind velocity during a 12-day period in late July and early August 1981. Measurements were made every 2.5 min on the average with range gates centered at 3.3, 5.7, 8.1, 10.5, 12.9, 15.3, 17.7, and 20.1 km above sea level.

Periods of active thunderstorms were identified from the PPI maps from the National Weather Service 10 cm weather radar at Limon, Colorado. When no thunderstorm activity was present, the vertical velocity fluctuations were small and erratic. But a few hours after strong thunderstorm activity began, large quasi-sinusoidal wave trains with periods of about 40 min were observed. Power spectra of the vertical velocity time series showed enhancements at all frequencies during thunderstorm activity, but for periods longer than 30 min the enhancements were larger, particularly for the mid-tropospheric range gates from 5.7 to 12.9 km.

Some of the implications of these observations on the relations between thunderstorms and buoyancy waves in the free atmosphere are discussed.

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Roelof T. Bruintjes
,
Terry L. Clark
, and
William D. Hall

Abstract

A case study showing comparisons between observations and numerical simulations of the passage of a winter storm over complex terrain is presented. The interactions between the mesoscale and cloud environments and the microphysical and dynamical processes are addressed using both observations and numerical simulations.

A three-dimensional, time-dependent nested grid model was used to conduct numerical simulations of the three-dimensional airflow and cloud evolution over the Mogollon Rim and adjacent terrain in Arizona. The modeling results indicated that the flow patterns and cloud liquid water (CLW) were closely linked to the topography. To a large extent, gravity waves excited by the flow over the mountains determine the distribution of clouds and precipitation. The waves extend through deep layers of the atmosphere with substantial updrafts and downdrafts, at times exceeding 5 m s−1. The simulated vertical velocities and horizontal wavelengths of about 20 km were in good agreement with the aircraft observations. The CLW regions associated with the waves extended through much deeper layers of the atmosphere and in quantities a factor of 2 larger than those associated with the forced ascent over the ridges. The CLW associated with waves may provide an additional source for precipitation development not previously considered in cloud seeding experiments. In addition, synoptic-scale flow patterns over the area change from one storm system to the next and even during one storm system. Consequently, both the winds and the evolution of clouds over the area are highly space and time dependent

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