| Present day models to determine the vertical temperature profile of the atmosphere are based on the thermodynamic energy equation with radiative transfer, including a convective adjustment scheme. These are called radiative-convective models. The convective process, however, is not included explicitly. Convection is considered in the form of a parameter called the adiabatic lapse rate, which is defined as the vertical temperature gradient in the troposphere. These models predict the height of the tropopause (the location where the temperature gradient inverts from a negative to a positive slope) through means of an overall energy balance of the system. The present work introduces techniques used in computational fluid dynamics to the study of the vertical atmospheric temperature profile. It uses fluid mechanics and energy equations to determine the location of the tropopause instead of an energy balance argument only. A new numerical scheme is developed to suit atmospheric-scale problems, which must include stratification. The new technique uses the finite volume method with an all speed flow type of algorithm. The method works well in laboratory-scale problems as well as in atmospheric-scale problems. It solves the full compressible fluid equations including gravity, which generates stratification of the fluid. The basic fluid problem related to the determination of the vertical temperature profile in the troposphere is the natural convection problem, which is typically handled using the Boussinesq approximation. The Boussinesq approximation is not used here because it is too restrictive for the present atmospheric study. Several natural convection problems, including problems that lie outside the range of validity of the Boussinesq approximation, are solved to validate and explore the validity and applicability of the present method. The thermal inversion at the tropopause is solved using fluid equations and a simple radiative model. The results show that the temperature decay with altitude in the troposphere stops at an altitude around where there is a positive energy source. The results also show that mass flow between troposphere and stratosphere is very small. This is very important in understanding and predicting how pollutant and other gases are transported to upper layers of the atmosphere. |
