A numerical simulation of a cold orographic cloud system
Date
1973-02
Authors
Derickson, Russell Glynn, author
Nickerson, Everett C., author
Peterka, J. A. (Jon A.), author
Fluid Dynamics and Diffusion Laboratory, College of Engineering, Colorado State University, publisher
Journal Title
Journal ISSN
Volume Title
Abstract
A computer simulation of a two-dimensional, meso-scale, cold orographic cloud system, which represents the first stage of development of a comprehensive model, is presented. Simulation is achieved by numerically solving, in finite difference form, a set of time dependent hydrodynamic and thermodynamic equations. The domain of solution is an 11 kilometer long and 3.5 kilometer deep rectangular box containing a triangular orographic barrier with an altitude of 1 kilometer and base of 3 kilometers. Grid spacing is constant at 100 meters. The equations of the model are based upon Ogura and Phillips (1962), Ogura (1963), and Orville (1965), with appropriate modifications in the energy and vorticity equations relevant to a cold cloud system. Ice microphysics is not included. The condensation-evaporation process is included by parameterization, but the precipitation mechanism is omitted. Condensation is continually driven by the forced lifting of upstream moisture over the orographic barrier and is influenced by the formation of a lee wave structure that evolves in time as the solution progresses from the initial state. The bulk thermal stratification of the model is stable, as governed by the upstream temperature sounding. An expedient method of initialization, which minimizes the adjustment or "settling down" period associated with the degree of refinement of the initial state of a numerical solution, was developed. Special emphasis was given to the development of physically realistic boundary conditions that minimize artificialities inherent in numerical solutions as caused by wrongly posed numerical boundary conditions. A significant "state of the art" achievement was realized in developing the appropriate boundary conditions. Two basic cases were performed, corresponding to one elapsed hour of atmospheric time: one in which the top boundary was a rigid lid, and the other in which the boundary was flexible, allowing wave energy to pass through the boundary. These two cases utilized a "locally" constant eddy exchange coefficient i.e. the coefficient appears as a constant in the transport equations. In both cases a cap cloud formed over the orographic obstacle and a lenticular cloud formed downstream in the first lee wave crest. The clouds contain water only, no ice. A comparison of kinetic energy and cloud evolutions indicated that the flexible boundary is more appropriate than the rigid boundary. A third case was performed, simulating a shorter span of time than the other cases, using a non-linear, finite-differenced eddy exchange coefficient. The flexible boundary was employed in this case. Results favored using the non-linear coefficient over the "locally" constant coefficient of the other cases pending an improvement on the boundary condition for the eddy coefficient at the lower boundary.
Description
CER72-73RGD-ECN-JAP19.
February 1973.
Includes bibliographical references (pages 59-62).
Circulating copy deaccessioned 2020.
February 1973.
Includes bibliographical references (pages 59-62).
Circulating copy deaccessioned 2020.
Rights Access
Subject
Clouds -- Mathematical models