Effects of General Flows on a Heat Island Convection

Abstract

Characteristics of two-dimensional heat island convection under general flows are investigated by numerical and laboratory experiments and the results are compared with those of the linear theory in Part 1 (Kimura, 1976). The aim in Part 2 is to examine the effects of 1) self-advection due to the convective motion, 2) vertical shear of the general flow, 3) Prandtl number and 4) ground temperature distribution upon the heat island convection. The main results obtained in the present study are as follows: 1) The self-advection has an effect to concentrate the updraft in a small area at the center of the heat island as stated in Kimura (1975), but the effect is reduced with the increase of the general flow. 2) The vertical shear of the general flow has an effect to increase the height of the inflow region of the perturbation flow field. 3) The small Prandtl number favours the development of the upstream perturbation in the middle layer as speculated in Part 1. 4) In Part 1 maximum values of the perturbation horizontal velocity (umax) decreased monotonously with the increase of the general flow, but in Part 2 it was found that umax is constant or slightly increases under the weak general flow for the more general ground temperature distributions than the form assumed in Part 1. 5) These effects shown in 1)~4), however, are not so significant as to alter the main features of the heat island convection obtained in Part 1.

Rayleigh Convection in a Fluid Heated Differentially at the Bottom

“…As shown by Kimura (1976) with a linear theory, when a stably stratified viscous Bcussinesq fluid layer is heated from below locally, the maximum height of convection Hmax is given by |R|1/6L, where R is Rayleigh number and L is the horizontal extent of the heating region. Applying this formula to the present case with |R| =194 and L = 2*, we obtain Hmax * *, which is the depth of the fluid layer.…”

“…Solutions (ii) and (iii) are not realistic since they fail to take into account the convective fluid motions which play an important role in the heat balance (for example Kimura, 1975) , nevertheless, it is not without interest to compare the results with that of the spectral model. In these cases, the Rayleigh-type convection is exited, but the amplitude of this mode cannot be determined by the linear theory.…”