On flows having constant vorticity

Constant vorticity flows of a uniform fluid in a rigid ellipsoidal container rotating at a variable rate are considered. These include librationally driven and precessionally driven flows. The well-known Poincaré solution for precessionally driven flow in a spheroid is generalized to an ellipsoid with unequal principal axes. The dynamic stability of these flows is investigated, and of other flows in which the angular velocity of the container is constant in time. Solutions for the Chandler wobble are discussed. The role of an invariant, called here the Helmholtzian, is examined.

► We study constant vorticity fluid flows in a rigid rotating ellipsoidal container.
► We generalize the Poincaré solution for precessionally driven flow to an ellipsoid.
► We investigate the dynamic stability of these flows and of other related flows.
► We discuss solutions for the Chandler wobble and examine the role of an invariant.