Pattern formation and anomalous modes in axisymmetic, compressible Taylor-Couette Flow

Abstract

Taylor-Couette flow is the annular flow between two concentric, differentially rotating cylinders. Figure 1.1 shows the geometry of the setup and is taken from Taylor [39]. Due to its geometric simplicity, this flow has been a topic of scientific investigation for centuries - for example, Newton [30] used the setup to describe the flow of rotating fluids in his Principia in 1687. In 1880, Stokes [36] made an attempt of investigation of the flow and realized the difficulty lied in the treatment of boundary conditions. The advent of Navier-Stokes equations led to a debate on how one can determine the viscosity of a fluid. Both Mallock [25] and Couette [10] independently came up with the idea of resolving this question by studying the flow of a fluid using differentially rotating concentric cylinders. Couette only rotated the outer cylinder, keeping the inner cylinder fixed. In addition to the experiments on the same lines as Couette, Mallock also rotated the inner cylinder, keeping the outer cylinder fixed.