The sidewall-localized mode in a resonant precessing cylinder

Abstract

We investigate, via direct numerical simulation using a finite-element method, the precessionally driven flow of a homogeneous fluid confined in a fluid-filled circular cylinder that rotates rapidly about its symmetry axis and precesses about a different axis that is fixed in space. Our numerical simulation, after validating with the asymptotic analytical solution for a weakly precessing cylinder and with the constructed exact solution for the strongly nonlinear problem, focuses on the strongly precessing flow at asymptotically small Ekman numbers. An unusual form of the resonant precessing flow is found when the precessing rate is sufficiently large and the corresponding nonlinearity is sufficiently strong. The nonlinear precessing flow is marked by a sidewall-localized non-axisymmetric traveling wave and a wall-localized axisymmetric shear together with an overwhelmingly dominant interior rigid-body rotation whose direction and magnitude substantially reduce the angular momentum of the rotating fluid system.