Linear theory calculations for the sea breeze in a background wind: The equatorial case

The equatorial coastal circulation is modeled in terms of the linear wave response to a diurnally oscillating heat source gradient in a background wind. A diurnal scaling shows that the solution depends on two parameters: a nondimensional coastal width L and a nondimensional wind speed U. The solutions are interpreted by comparing to the U = 0 theory of Rotunno.

For non-zero U, the Fourier integral solution consists of three distinct wave branches. Two of these branches correspond to the prior no-wind solution of Rotunno, except with Doppler shifting and associated wave dispersion. The third branch exists only for non-zero U and is shown to be broadly similar to flow past a steady heat source or a topographic obstacle. The relative importance of this third branch is determined largely by the parameter combination U/L. For sufficiently large U/L, the third branch becomes the dominant part of the solution.

The spatial structures of the three branches are described in terms of group velocity arguments combined with a desingularized quadrature method.