Physics Seminar

Rotating Fluids and Taylor-Proudman Theorem
by Dr. Kiran Chilakamarri, Texas Southern University
2007-11-28, 10:00 AM in NSB 148

Abstract

The rotational effects are felt by the fluid in the form of a fictitious force called Coriolis force. When the Coriolis force dominates both the inertial force and the viscous force, then the flow becomes two-dimensional. If the axis of rotation is z-axis, then the velocity vector is independent of the variable z. This is the Taylor-Proudman theorem. Fluid motion is not only a function of internal balances but also of the imposed boundary conditions. If the imposed boundary conditions are designed to violate the Taylor- Proudman restriction, then the Fluid exhibits striking behavior. For instance, suppose we pull a short solid cylinder along the bottom of a rotating tank of fluid, then the entire column of fluid on the top of the cylinder will move as a solid column with the short cylinder. This is known as Taylor column. At the boundaries the viscous forces dominate then Taylor-Proudman restriction does not apply and the structure of the boundary layers is complex. The method of matched asymptotics is used to study the fluid motion. This is an expository talk.