The Linear Theory of Land and Sea Breeze Circulation

Abstract

The linear theory of land and sea breeze circulation (LSBC) shows that, in the absence of the Coriolis force and under the hydrostatic approximation, there exists a similarity solution. In this solution, the horizontal coordinate is scaled by Nκ1/ω_*-^3/2, the vertical coordinate by κ1/2ω_*-^l/2 the horizontal velocity by gαΔT/N, the vertical velocity by gαΔT•ω_*/N2 and the pressure by gαΔTκ1/2ω_*-^1/2, respectively, where ω_* and ΔT are the frequency and amplitude of the temperature variation at the ground, respectively, N the Brunt-Vaisali frequency corresponding to the basic density stratification, κ the eddy thermal diffusivity, g the gravity acceleration and α the thermal expansion coefficient. The eddy Prandtl number is assumed to be unity.
In the immediate neighborhood of the coastline, a small region in which non-hydrostatic effects are significant and the similarity solution is invalid is present. The horizontal and vertical dimensions of the non-hydrostatic region are of the order of (κ/N)1/2 and the vertical velocity becomes of the same order of the horizontal one in this region. Outside of the region, however, the similarity solution remains always valid.
When the Coriolis force is present, the solution outside of the non-hydrostatic region depends only on the non-dimensional Coriolis parameter f defined by f_*/ω_*. If the horizontal dimension λ_* of LSBC is defined by the distance from the coastline at which the non-dimensional velocity of the onshore wind becomes equal to 0.03, λ_* is given by λ_*=Nκ^1/2ω_*-^3/2F(f), where F(f) is a universal function off. F remains almost constant (about 2.1) for f<1(latitude less than 30°). When f becomes larger than 1, however, F starts to decrease rapidly and becomes equal to 0.9 for f=2.0 (at the Arctic or the Antarctic).
Effects of the eddy Prandtl number and the non-linear process on the flow characteristics are also discussed.