A Low-Order Thermal Model with a Flow Pattern Similar to Hill's Spherical Vortex

Abstract

A thermal model containing time-variable parameters is constructed from an assumed velocity field and density disturbance. The fluid field is similar to Hill's spherical vortex, and the density disturbance is represented by a low-order Hermitian function series. The time variation of the model parameters is estimated by an optimal approximation method for the inviscid and non-diffusive Boussinesq equations. Initially, there is no motion but there is a low-density disturbance in the environment of neutral stratification. The time variation of the model parameters is studied with the aid of numerical integration. The time evolution of this model within a short period seems to be qualitatively comparable with some computer simulation results.