Spin-up from rest in a cylinder

The problem of impulsive spin-up from rest of a fluid of kinematic viscosity ν in a closed cylindrical container is examined numerically and experimentally. The shape of the velocity profiles is found to depend upon a parameter α0=h (ν/Ω1/2/a2, where h is the height, a is the radius, and Ω is the angular speed of the container. When α0 is less than 0.005, the numerical profiles agree well with the solutions of Wedemeyer and Venezian, and the fractional spin-up time (the time to reach some fraction of solid body rotation) is proportional to h (ν/Ω)−1/2. When α0 is larger than 1, the numerical profiles agree well with the solution of the diffusion equation, and the fractional spin-up time is proportional to a2/ν. For intermediate values of α0, the numerical profiles agree well with experiment, and the dependence of the fractional spin-up time on Ω, ν, h, and a varies with α0, with radial position r, and with the dimensionless angular velocity W=v/rΩ, where v is the azimuthal velocity.