The calculation of a sea‐breeze circulation in terms of the differential heating across the coastline

A method is derived for calculating the velocity, temperature and pressure distributions of the sea-breeze produced when an initially isothermal and static atmosphere is heated differentially across a long straight coastline. Heat is assumed to be distributed vertically from the land surface by convection currents; internal friction is included but surface drag is taken as zero. The motion is separated into two parts, a rotational non-divergent component near the coast and a mainly irrotational large-scale tidal motion transferring mass from land to sea. The former is considered first and a numerical method devised to enable the non-linear equations to be solved. The solutions are given as a set of diagrams each showing values of velocity, temperature and pressure calculated over a network of points, and each referring to a particular time in the development of the motion. In Section 5 the tidal motion is considered and an analytical solution obtained since the equations can be linearized. The rotational solution represents the spread inland of a tongue of cold air; well inland the wind rises some hours after heating has started, and is accompanied by a fall in temperature. An upper return current occurs in all the diagrams as well as subsidence over the sea and upper cooling inland. The vertical temperature profiles show a sharpening of the discontinuity in lapse rate at the top of the convection layer produced by the vertical velocity component. Conditions for convective instability are found to be produced dynamically in a shallow layer of the upper return current. Comments are made on the formation of ‘heat lows’ and ‘cold highs’ over continents.