Terry L. Clark

A small-scale dynamic model using a terrain-following coordinate transformation

Abstract This paper describes a three-dimensional finite-difference model of air flow over an irregular lower surface. The model is nonhydrostatic and the anelastic approximation has been used to filter sound waves. Second-order difference equations are employed which provide excellent momentum and energy budgets. An outflow radiation boundary condition using a generalized Kreiss extrapolation scheme has been designed and implemented. Some two-dimensional applications of the model to air flow over a “Witch of Agnesi” mountain barrier are described. Comparison with the linear theory of Queney indicates, for the cases treated, that the nonlinearity of the boundary condition has a first-order effect on the resulting flow.

Severe Downslope Windstorm Calculations in Two and Three Spatial Dimensions Using Anelastic Interactive Grid Nesting: A Possible Mechanism for Gustiness

Abstract The Clark nonhydrostatic anelastic code is extended to allow for interactive grid nesting in both two and three spatial dimensions. Tests are presented which investigate the accuracy of three different quadratic interpolation formulae which are used to derive boundary conditions for the fine mesh model. Application of the conservation condition of Kurihara and others is shown to result in significant improvements in the treatment of interactive nesting. A significant improvement in the solutions for interactive versus parasitic nesting is also shown in the context of forced gravity wave flow. This result, for the anelastic system, is in agreement with the earlier results of Phillips and Shukla, who considered the hydrostatic shallow water system of equations. The interactive nesting model is applied to the simulation of the severe downslope windstorm of 11 January 1972 in Boulder using both two and three spatial dimensions. The three-dimensional simulation results in a gustiness signature in the ...

The Evolution and Stability of Finite-Amplitude Mountain Waves. Part II: Surface Wave Drag and Severe Downslope Windstorms

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 Longs model. When the background flow is inhomogeneous, Longs 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 1...

Numerical Modeling of Gravity Wave Generation by Deep Tropical Convection

Although convective clouds are known to generate internal gravity waves, the mechanisms responsible are not well understood. The present study seeks to clarify the dynamics of wave generation using a high-resolution numerical model of deep convection over the Tiwi Islands, Australia. The numerical calculations presented explicitly resolve both the mesoscale convective cloud cluster and the gravity waves generated. As the convective clouds evolve, they excite gravity waves, which are prominent features of the model solutions in both the troposphere and stratosphere. The source location is variable in time and space but is related to the development of individual convective cells. The largest amplitude gravity waves are generated when the cloud tops reach the upper troposphere. A new analysis technique is introduced in which the nonlinear terms in the governing equations are taken as the forcing for linear gravity waves. The analysis shows that in the present calculation, neither the shear nor the diabatic heating are the dominant forcing terms. Instead, the wave source is most easily understood when viewed in a frame of reference moving with the wind at the level of neutral buoyancy, whereupon the source may be described as a vertically oriented, oscillating convective updraft. This description is consistent with the properties of the modeled stratospheric waves.

The multidimensional positive definite advection transport algorithm: further development and applications

Abstract This paper presents further generalizations of the advection algorithm described in J. Comput. Phys. (54 (1984), 325). Time-dependent velocity fields and a generalized form of the continuity equation are considered. Applicability of the algorithm to the diffusion equation and to the transport of nonpositive scalars is also discussed. Theoretical considerations are illustrated through numerical tests and applications to some particular geophysical fluid dynamics problems.

Numerical Simulations with a Three-Dimensional Cloud Model: Lateral Boundary Condition Experiments and Multicellular Severe Storm Simulations

Abstract Simulations with a three-dimensional numerical cloud model are presented for airflow over a bell-shaped mountain and for a multicellular severe storm. A comparison of results using the Orlanski (1976) and Klemp and Wilhelmson (1978) treatments for the normal velocities shows that physical modes can be computationally excited using the latters treatment with the result of very large horizontally averaged vertical velocities. Cell splitting occurs for the model calculations and the analysis indicates the splitting is caused by an entrainment effect which may be an artifact of the experimental design. An analysis of subgrid/resolved scale kinetic energy shows that this ratio is much smaller for the current severe storm simulations than that found by Lipps (1977) for his trade wind cumuli simulations. A comparison of some general features of the multicellular severe storm with observational data is presented.

A Coupled AtmosphereFire Model: Convective Feedback on Fire-Line Dynamics

Abstract The object of this paper is to describe and demonstrate the necessity and utility of a coupled atmosphere-fire model: a three-dimensional, time-dependent wildfire simulation model, based on the primitive equations of motion and thermodynamics, that can represent the finescale dynamics of convective processes and capture ambient meteorological conditions. In constructing this coupled model, model resolution for both the atmosphere and the fuel was found to be important in avoiding solutions that are physically unrealistic, and this aspect is discussed. The anelastic approximation is made in the equations of motion, and whether this dynamical framework is appropriate in its usual form for simulating wildfire behavior is also considered. Two simple experiments-the first two in a series of numerical simulations using the coupled atmosphere- fire model-are presented here, showing the effect of wind speed on fire-line evolution in idealized and controlled conditions. The first experiment considers a 42...

On the Dynamics of Hawaiian Cloud Bands: Island Forcing

Abstract This study focuses on basic island scale forcing mechanisms for the formation and evolution of a band cloud typically present upwind of the island of Hawaii. By means of numerical experiments and verification of our results against observations and laboratory experiments reported in the literature, we show that the band cloud is a complex three-dimensional phenomenon which is inseparable from the airflow around the island. In particular, we demonstrate that the event needs to be analyzed in terms of the basic fluid dynamics of strongly stratified flow past a three-dimensional obstacle. The band cloud is found to arise primarily from the dynamic interaction of the trade winds with the island. The upwind surface flow forms a separation line with an associated stagnation point. A low-level convergence zone forms along this line, resulting in an updraft line. If the updrafts are strong enough, a band cloud forms. Formation and characteristics of such a system are mostly controlled by the environmenta...

On the Evolution and Stability of Finite-Amplitude Mountain Waves

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-Vaisala 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 prediction...

An Investigation of Turbulence Generation Mechanisms above Deep Convection

Abstract An investigation of the generation of turbulence above deep convection is presented. This investigation is motivated by an encounter between a commercial passenger aircraft and severe turbulence above a developing thunderstorm near Dickinson, North Dakota, on 10 July 1997. Very high-resolution two- and three-dimensional numerical simulations are used to investigate the possible causes of the turbulence encounter. These simulations explicitly resolve the convection and the turbulence-causing instabilities. The configurations of the models are consistent with the meteorological conditions surrounding the event. The turbulence generated in the numerical simulations can be placed into two general categories. The first category includes turbulence that remains local to the cloud top, and the second category includes turbulence that propagates away from the convection and owes its existence to the breakdown of convectively generated gravity waves. In both the two- and three-dimensional calculations, th...