Viscous effects on a rotating imploding cylindrical liquid liner

The effect of viscosity on the inner surface of a rotating imploding cylindrical liquid metal liner is analyzed in the limit of high Reynolds number Re. The condition of vanishing tangential stress on the free surface leads to the formation of a boundary layer of thickness approx. 1/sq. root Re. Within this layer the zonal velocity v is reduced by an amount delta v such that delta v/v approx. 1/sq. root Re. This results in a requirement of slightly increased rotation in order to satisfy the criterion for suppression of the Rayleigh-Taylor instability on the free surface. For Reynolds numbers appropriate to liquid metals and parameters of current experimental interest, the correction to the rotation required for stability is less than one percent. Calculations are presented for a model linear trajectory.