Abstract
Effects of uniform flows on a two-dimensional heat island convection were investigated by obtaining the steady solutions of the linearized vorticity and thermodynamic equations. The calculations were performed for fluids whose values of Prandtl number (Pr) are unity and zero.
By introducing the suitable scalings, it was found that the effects of the general flow can be expressed by a non-dimensional parameter F' defined by U/(E'1/3l√agΓ), where U is the velocity of the general flow, l is the horizontal scale of the heat island, √agΓ' is the buoyancy frequency and E' is a non-dimensional parameter defined by k/√agΓ l2, where κ is the thermal diffusivity of the fluid. F' corresponds to γ-1/3, where γ is the non-dimensional parameter used in the linear theory of Olfe and Lee (1971).
The convective patterns in a fluid with Pr=1 are classified into three types according to the intensity of the general flow. When F' is less than 1, the dynamics of the convection is essentially the same as that without the general flow. The circulation consists of a pair of symmetric convection cells with an updraft over the heat island. When F' is greater than 3, the effects of the stable stratification is reduced compared with those of the horizontal advection due to the general flow and the dynamics becomes essentially the same as that in the neutral fluid layer. The temperature perturbation takes a form of the bent-over plume in this regime. When F' is between 1 and 3, a convective pattern extending to the upstream direction of the heat island appears in the middle layer.
The convective patterns in a fluid with Pr=0 are classified in two types; the bent-over plume for the small values of γ and the upstream boundary layer for the large values of γ. The latter structure corresponds well to the patterns observed in the viscous fluid layer for F' between 1 and 3.
