An Analytical Study of the Sea Breeze

Gianni A. Dalu Cooperative Institute for Research in the Atmosphere (CIRA), Fort Collins, Colorado, and Institute for Atmospheric Physics (IFA-CNR), Rome

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Roger A. Pielke Department of Atmospheric Science, Colorado State University (CSU), Fort Collins, Colorado

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Abstract

In this paper we present theoretical results concerning the sea breeze intensity and its inland penetration as a function of latitude and friction. We produce solutions for the spatial structure of the streamfunction and momentum components and for their Line behavior in the case of a step function forcing of finite duration, and in the case of periodic forcing. Results show that the sea breeze initially has an aspect ratio equal to unity and that earth rotation and friction aged its intensity but they are unimportant in determining its early geometry. The sea breeze has a characteristic time scale which is a combination of the inertial period and the e-folding time due to friction. For a time larger than this characteristic time scale, the inland penetration of the sea breeze is confined by a Rossby deformation radius, which includes a frictional effect. In fact, friction and inertia reduce, not only the intensity, but also the horizontal scale of motion; at the equator the controlling parameter for the intensity and penetration of the sea breeze is friction. When the friction is small, periodicity in the forcing enhances the intensity and the horizontal scale; however when the friction efolding time is of the order of one day, the opposite is true. The existence of wave structure below 30 degrees of latitude, suggested by Rotunno, strongly depends on relative values of periodicity and friction, i.e., periodicity tends to make the governing partial differential equation for the streamfunction hyperbolic while friction tends to keep it eliptical; from the competition of these two contrasting effects waves may or may not result.

Abstract

In this paper we present theoretical results concerning the sea breeze intensity and its inland penetration as a function of latitude and friction. We produce solutions for the spatial structure of the streamfunction and momentum components and for their Line behavior in the case of a step function forcing of finite duration, and in the case of periodic forcing. Results show that the sea breeze initially has an aspect ratio equal to unity and that earth rotation and friction aged its intensity but they are unimportant in determining its early geometry. The sea breeze has a characteristic time scale which is a combination of the inertial period and the e-folding time due to friction. For a time larger than this characteristic time scale, the inland penetration of the sea breeze is confined by a Rossby deformation radius, which includes a frictional effect. In fact, friction and inertia reduce, not only the intensity, but also the horizontal scale of motion; at the equator the controlling parameter for the intensity and penetration of the sea breeze is friction. When the friction is small, periodicity in the forcing enhances the intensity and the horizontal scale; however when the friction efolding time is of the order of one day, the opposite is true. The existence of wave structure below 30 degrees of latitude, suggested by Rotunno, strongly depends on relative values of periodicity and friction, i.e., periodicity tends to make the governing partial differential equation for the streamfunction hyperbolic while friction tends to keep it eliptical; from the competition of these two contrasting effects waves may or may not result.

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