Thermally driven motions in a rotating stratified fluid: theory and experiment

Abstract

A radial temperature distribution is applied to the top of a cylinder of rotating stably stratified fluid. Thermal wind shear drives the interior flow. Linearized theory predicts, and laboratory experiments confirm, that when the stratification is large enough it completely suppresses the Ekman pumping into the interior. The interior velocity field, which is primarily azimuthal, responds by satisfying the no-slip boundary conditions without the need of Ekman layers on the horizontal surfaces. Moreover, for large stratification a thermal boundary layer beneath the top surface traps the thermal disturbance applied at the upper surface. The greatest azimuthal velocity occurs at the base of this layer. Below this layer the azimuthal velocity viscously diffuses downward with thermal wind adjusting the temperature. The Rossby radius of deformation based on this layer depth is the cylinder's radius divided by the square root of the Prandtl number. Detailed measurements of the velocity field generated in the cylinder by the heating are compared with the theory in the case where the Ekman layers are eliminated by stratification. The theory and experiments agree qualitatively well over a range of four orders of magnitude of imposed parameters and over a large parameter range the quantitative comparison is also very good.

Thermally Driven Circulations in Small Oceanic Basins*

“…The model used here is the linear model of Barcilon and Pedlosky (1967) as altered by Pedlosky (1974) to include distinct mixing coefficients for vertical and horizontal mixing of mass and momentum. (See also Pedlosky et. al.…”

“…The motion is no longer hydrostatic in this layer and the thermal wind equation no longer applies. The reader is referred to Barcilon and Pedlosky (1967) and Pedlosky et. al.…”

Ocean circulations driven by meridional density gradients

“…More recent, relevant laboratory experiments (Pedlosky et al 1997, Rayer et al 1998) have received rather less attention. A large number of investigations have been devoted to analysis of coarse resolution ocean circulation models using simplified geometrical configurations and forcing.…”

Basic Regularities of the Haline Stratification Long-Term Evolution in the Black Sea

“…В развитие этих исследований в работе [12] аналитическое решение задачи о течениях во вращающемся цилиндрическом бассейне, вызываемых потоками плавучести на границах, было получено в рамках линеаризованной модели. Аналитическое решение сопоставлялось с результатами лабораторного моделирования, что продемонстрировало удивительное соответствие теории и эксперимента.…”