Applicability of Mean Field Approximation to Numerical Experiments of Thermal Convection during the Cooling Period of Lake Biwa

Abstract

This paper describes the applicability of a stochastic model to the numerical experiments of thermal convection carried out under the condition of the northern part of Lake Biwa, Shiga Prefecture, Japan. It was shown in the previous study that the temporal changes of vertical water temperature distributions during the cooling period between September and February can be reproduced by a simple 3D-CFD model. It was also pointed out that the spatial distributions of cooled water body sinking to the bottom due to water surface cooling represent similar features of forest gap distribution, which can be clarified by a stochastic model. The basic features of numerical experiments on thermal convection such as the spatial distribution of cooled water body are firstly shown with several cooling rates at water surface. Then, a stochastic model, which was originally introduced to explain forest gap dynamics, is shown with its MFA (mean field approximation) as first approximation of stochastic model. It is pointed out through the comparison of theoretical results by MFA with tuned model constants to numerical experiments that MFA with some refinement can be applicable to reproduce the basic features of simulated results to some extent, although further investigations are required to clarify the applicability of the model to more detailed mechanism of thermal convection such as size distribution of cooled water body, phase change of flow pattern, etc..