Numerical solutions and laser-Doppler measurements of spin-up

The spin-up flow in a cylinder of homogeneous fluid has been examined both experimentally and numerically. A series of laser-Doppler measurements was made of the zonal flow over a range of Ekman numbers and Rossby numbers at various locations in the interior of the flow. These measurements exceed previous ones in accuracy. The weak inertial modes excited by the impulsive start are detectable. The numerical simulations used the primitive equations in axisymmetric form and employed finite-difference techniques on both constant and variable grids. The number of grid points necessary to resolve the Ekman layers was determined. A thorough comparison of the simulations and the experimental measurements is made which includes the details of the amplitude and frequency of the inertial modes. Agreement to within the experimental tolerance is achieved. Analytical results for conditions identical to those in the experiments are not available but some similar linear and nonlinear theories are also compared with the experiments.