New Theory for Zonal and Meridional Flows in the Solar Convection Zone; and a Simple Model for Secular Orbit Oscillations
type: CreativeWork
description: This theoretical work first studies the fundamental force balances associated with the rotation and internal motion of the Sun. The relative motions take place in the convection zone. They include the dominant global mean zonal circulation, and the order of magnitude smaller mean meridional circulation. The observed zonal circulation is shown to be consistent with a dynamic equilibrium between global pressure gradients, centrifugal forces and Coriolis forces. This force balance is revealed only by using the most precise observations of global shape and by avoiding the effective gravity approximation. The latter is the more challenging conceptual task, as it has become an almost universally applied assumption in geophysical and astrophysical fluid dynamics. Explanation of the meridional circulation requires a similar theoretical advance. A generalized astrophysical Ekman theory is developed in spherical polar coordinates, and in the absence of the customary approximations for geostrophic balance, in order to remain consistent with the dynamic equilibrium of the zonal flow. Observed zonal velocity anomalies, departures from the dynamic equilibrium, are interpreted as the effects of friction forces retarding the bulk flow at the top and bottom boundaries. Astrophysical Ekman theory shows how friction then forces a meridional overturning consistent with observations. For both zonal and meridional circulations the forces governing internal fluid motions are shown to be strongly influenced by the inertial forces of rotation - Coriolis and centrifugal forces. Next the precise global shape is explained by returning to the friction free dynamic equilibrium model. A new equipotential surface is derived from first principles. The radial force, and the associated potential function, now include contributions from the Coriolis forces of relative motion - as well as the typical gravity and centrifugal terms. Using an empirical description of the observed relative motions leads to…
abstract: This theoretical work first studies the fundamental force balances associated with the rotation and internal motion of the Sun. The relative motions take place in the convection zone. They include the dominant global mean zonal circulation, and the order of magnitude smaller mean meridional circulation. The observed zonal circulation is shown to be consistent with a dynamic equilibrium between global pressure gradients, centrifugal forces and Coriolis forces. This force balance is revealed only by using the most precise observations of global shape and by avoiding the effective gravity approximation. The latter is the more challenging conceptual task, as it has become an almost universally applied assumption in geophysical and astrophysical fluid dynamics. Explanation of the meridional circulation requires a similar theoretical advance. A generalized astrophysical Ekman theory is developed in spherical polar coordinates, and in the absence of the customary approximations for geostrophic balance, in order to remain consistent with the dynamic equilibrium of the zonal flow. Observed zonal velocity anomalies, departures from the dynamic equilibrium, are interpreted as the effects of friction forces retarding the bulk flow at the top and bottom boundaries. Astrophysical Ekman theory shows how friction then forces a meridional overturning consistent with observations. For both zonal and meridional circulations the forces governing internal fluid motions are shown to be strongly influenced by the inertial forces of rotation - Coriolis and centrifugal forces. Next the precise global shape is explained by returning to the friction free dynamic equilibrium model. A new equipotential surface is derived from first principles. The radial force, and the associated potential function, now include contributions from the Coriolis forces of relative motion - as well as the typical gravity and centrifugal terms. Using an empirical description of the observed relative motions leads to…
author: Hester, Richard
keywords: differential rotation, equilibrium shape, meridional circulation, orbit oscillations, secular frequencies, zonal circulation
date published: 2025
date modified: 2026-07-27T19:52:02Z
provider: George Mason University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: George Mason University