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Ronald L. Drake, Patrick D. Coyle, and Daniel P. Anderson

Abstract

This paper is concerned with the effects of nonlinear eddy coefficients on rising, dry fine thermals. The base atmosphere in which these thermals are embedded is hydrostatic, horizontally homogeneous, nearly neutral, and without an ambient wind. By identifying the turbulent transfer terms with the subgrid–scale motions, a nonlinear formulation, based upon the worn. of Lilly and Smagorinsky, is obtained for the eddy coefficients. The mixing length in these terms is based upon a vorticity formulation rather than the size of the numerical grid used in the computations. Using numerical techniques based upon the work of Arakawa, and Adams and Bashforth, we tested these formulations by following the evolution of rising line thermals. We concluded that the eddy formulation used in this paper is more realistic than using constant coefficients throughout the field of computation. In addition, we found that the density stratification is important if the convective layer is deeper than 3 km.

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Ronald L. Drake, Patrick D. Coyle, and Daniel P. Anderson

Abstract

This paper is concerned with the time evolution of interactive dry line thermals in a convective layer. The temperature perturbations which produce these line thermals are randomly chosen. Since the domain of computation is the x-z plane, the evolving flow field is described by the streamfunction, vorticity, and the potential temperature. The nonlinear acceleration terms were differenced by an Arakawa scheme and the time differencing was the second-order, explicit, two-step Adams-Bashforth scheme. The turbulent transfer terms were given by a nonlinear formulation based on the work of Lilly and Smagorinsky. The convective layers in our numerical experiments were simulated by releasing a single set of thermals and by successive releases of thermals. Even though our work is a two-dimensional simulation, our results were consistent with the gross properties of real convective fields reported by several investigators. Hence, our system is a relatively inexpensive model that can be used to study convective layers over irregular surfaces and terrain.

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