The Taylor-Couette problem is a fundamental example in bifurcation theory and hydrodynamic stability, and has been the subject of over 1500 papers. This thesis treats a generalization of this problem in which the rigid outer cylinder is replaced by a deformable (nonlinearly viscoelastic) cylinder whose motion is not prescribed, but responds to the forces exerted on it by the moving liquid. The inner cylinder is rigid and rotates at a prescribed angular velocity, driving the liquid, which in turn drives the deformable cylinder. The motion of the outer cylinder is governed by a geometrically exact theory of shells and the motion of the liquid by the Navier-Stokes equations, where the domain occupied by the liquid depends on the deformation of the outer cylinder.

Seldom does a physical system, particularly one as apparently simple as the flow of a Newtonian fluid between concentric rotating cylinders, retain the interest of scientists, applied mathematicians and engineers for very long. Yet, as this volume goes to press it has been nearly 70 years since G. I. Taylor's outstanding experimental and theoretical study of the linear stability of this flow was published, and a century since the first experiments were performed on rotating cylinder viscometers. Since then, the study of this system has progressed enormously, but new features of the flow patterns are still being uncovered. Interesting variations on the basic system abound. Connections with open flows are being made. More complex fluids are used in some experiments. The vigor of the research going on in this particular example of nonequilibrium systems was very apparent at the NATO Advanced Research Workshop on "Ordered and Turbulent Patterns in Taylor Couette Flow," held in Columbus, Ohio, USA May 22-24, 1991. A primary goal of this ARW was to bring together those interested in pattern formation in the classic Taylor Couette problem with those looking at variations on the basic system and with those interested in related systems, in order to better define the interesting areas for the future, the open questions, and the features common (and not common) to closed and open systems. This volume contains many of the contributions presented during the workshop.

Excerpt from Stabilization of Taylor-Couette Flow Due to Time-Periodic Outer Cylinder Oscillation We next choose dimensionless variables. The length scale is chosen to be the fluid gap width d R2 ri, the time scale is chosen to be dz/v, and the velocity scale is chosen to be v/d. We retain the same notation for all variables, which Will henceforth be dimensionless. The choice of scaling introduces the Reynolds number in the boundary condition, which is given by R8 Qld2/v. The fluid region then occupies the range n/(l 77) r n), where 7] rl/rg. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.