SIMULATION OF CYLINDRICAL COUETTE FLOW

We have developed, tested, and implemented a numerical code for calculating the viscous, three dimensional flow between two differentially rotating cylinders (cylindrical Couette flow). In this paper we describe the methods that we have used to apply efficiently pseudo-spectral techniques to a complicated (i.e. non-Cartesian) geometry with real (i.e. viscous, no-slip) boundaries and the tests that we have used to determine the accuracy of our code. I. OBSERVED STATES OF COUETTE FLOW When the inner cylinder is rotating and the outer cylinder is held station-ary, four non-chaotic flows have been observed experimentally. We define the Rey-nolds number as RE = ~ R I (R2- Rl)/V where v is the viscosity, ~ is the angu-lar velocity of the inner cylinder, and R I and R 2 are the radii of the inner and outer cylinders. We also define the radius ratio ~ to be R I /R 2. For a given geometry, as the Reynolds number is increased to RE.x, the stable flow changes •.. crlt. from its laminar proflle to N axlsyu~etrlc Taylor vortlces stacked on top o