Lake currents associated with the thermal bar

Abstract

A time-dependent theoretical study of the thermal bar is presented. The temperature and velocity distributions are obtained for a system consisting of water contained in a rotating annulus with a horizontally varying heat flux applied at the free upper surface. An equation of state is used that shows a parabolic dependence of density on temperature, the maximum density occurring at 4°C. The analysis assumes small Rossby and Ekman numbers and allows for different values of vertical and horizontal eddy viscosities and conductivities. The temperature field is found from the time-dependent heat conduction equation. An interior flow field is found utilizing the ‘thermal-wind’ balance and is matched to Ekman layers. Side boundary layers are found, the form of which depends on the relative sizes of the Ekman number and the ratio of eddy viscosities or conductivities, but their contributions are small compared to the interior. Both of the lines of zero meridional velocity and stream function proceed from the shore to the center of the lake, marking a change in direction of all velocity components as they go. As time elapses, the magnitudes of the velocity components get larger in the shoreward water and smaller in the seaward water. Eventually the shoreward regime encompasses the entire lake.