On the Parameter Dependence of Two-Dimensional Sea-Breeze Models

Abstract

Parameter dependence of the sea breeze is discussed by using four types of simplified two-dimensional numerical models; (A) linear and hydrostatic, (B) linear and non-hydrostatic, (C) non-linear and hydrostatic, (D) non-linear and non-hydrostatic models. Various combinations of parameters with regard to the basic situation in the sea breeze are considered. The parameters are the amplitude ΔT, the frequency ω, of the diurnal change of land-surface temperature, the eddy diffusion coefficient t, and the lapse rate of basic potential temperature Γ (or Brunt Vaisala frequency N). Two non-dimensional parameters are a non-linear parameter ε(=ΔT/[Γ(κ/ω)^1/2]) and a hydrostatic parameter δ(=ω/N), which appear in the governing equations through a scaling (Niino, 1987).
The main conclusions are as follows, (1) The behavior of flows is quite different, depending on whether the set of equations is linear or non-linear. However, there is no serious difference between the cases with and without the hydrostatic assumption under the common sea-breeze parameters. (2) The size of the computation domain plays an important role in determining the scale of the sea breeze. (3) In the non-linear model, the maximum wind velocity of the sea breeze varies in proportion to ε². When ε is greater than about 3, the maximum wind velocity in the non-linear model becomes much greater than that in the linear model. (4) The maximum wind velocity varies in proportion to δ-1 in both linear and non-linear cases. The dependency on δ slightly differs with ε in the non-linear cases. (5) The maximum Rayleigh number over land during the daytime is estimated to be Ra=0.1ε⁴δ^-2 The computational results suggest that the maximum wind velocity is proportional to Ra^1/2 in the non-linear case.
Further, the dependence of the maximum wind velocity on the mesh size in the numerical computation is discussed.