The Sea-Breeze Forerunner

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Abstract
The response of a stably stratified atmosphere to differential heating across a coastline is studied. A linear, inviscid, Boussinesq theory is used to analyze the growth caused by switching on a small temperature contrast at an initial time. The propagation of the disturbance is interpreted in terms of internal gravity waves. The outer part of the disturbance, where the linearization is always valid, arrives ahead of the main nonlinear overturning, the sea breeze proper, and can therefore be described as the sea-breeze forerunner. Solutions are obtained and discussed for three different assumed model atmospheres, illustrating the influence of thermal stratification upon the structure of the forerunner. Some modifications are introduced to enable the effects of viscosity to be described. Reasonable values of internal viscosity and of surface drag are inserted into the modified theory, and these effects, respectivly, are found to limit the amplitude of the forerunner at moderate distances inland to a few meters per second and to limit the inland penetration distance to about 60 km. Implications of the results of this study for a more general nonlinear theory are emphasized. In particular, the role of the upper boundary condition in a model of the sea-breeze circulation is clarified. The momentum balance argument advanced here should also be valid in the nonlinear case.

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