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Using Mathematica to Enhance Learning of Atmospheric Processes: Entrainment into Cumulus Clouds

J. Preyer
David R. Smith
Reza Malek-Madani
Organization: U.S. Naval Academy
Department: Department of Mathematics
Journal / Anthology

United States Naval Academy, Annapolis, MD
Year: 1994

Topics in the atmospheric sciences offer excellent real-world examples of physical phenomena that demonstrate the application of advanced mathematical concepts. Since the differential equations governing the behavior of many atmospheric phenomena are quite complex, utilization of mathematical software packages, such as Mathematica, can be valuable tools to enhance the understanding of such mathematical concepts. Application of the software package provides a technique to solve the differential equations and graphically display the solutions for the mathematical representation of the physical phenomenon under investigation. This paper reconsiders a classical model of entrainment of cumulus clouds described in the works of Stommel (1947) and Austin & Fleischer (1948). The entire derivation of the governing equations of this model is based on the first principles of thermodynamics. The solutions to these equations for various physically significant parameter ranges are carried out and results presented on the symbolic manipulator Mathematica. In addition, pedagogical aspects of the mathematical and physical treatment of the entrainment process are discussed.

*Science > Atmospheric Science