Session Cd - Interfacial & Thin-Film Instabilities.
ORAL session, Sunday, November 23
304, Moscone Center
We investigate the axial instability of the free-surface of a viscous fluid in a horizontal cylinder rotating about its major axis. At low rotation rates, the shape of the free-surface appears to be determined by the balance between gravitational and viscous forces. Following earlier work (Benjamin, Pritchard and Tavener), we use an asymptotic expansion in the small parameter \alpha = \sqrtØmega \nu øver g R where \nu is viscosity, Ømega is angular velocity, g is gravity and R is the radius of the cylinder, to derive a simplified evolution equation for the free-surface. This equation is solved numerically to determine the base state with no axial variation, which is then perturbed to examine the onset of unstable axial modes. Various computational results will be presented for the shape of the free-surface and the wavelength of the axial instability. We show that inertia plays an important role in the onset of the instability and we derive the power law \lambda = \gamma^1/3 where \lambda is the wavelength of the axial instability and \gamma is surface tension.