On the origins of steady streaming in precessing fluids

The nite-amplitude space-time mean ows that are precessionally forced in rotating nite circular cylinders are examined. The ndings show that in addition to conventional Reynolds-stress-type source terms for streaming in oscillatory forced ows, a set of Coriolis-type source terms due the the background rotation also contribute. These terms result from the interaction between the equatorial component of the total rotation vector and the overturning ow that is forced by the precession, both of which have azimuthal wavenumbers m = 1. The interaction is particular to precessing ows in axisymmetric vessels and does not exist in rotating ows driven by libration (m = 0 forcing) or tides (m = 2 forcing). By examining typical example ows in the quasi- linear weakly forced streaming regime, we are able to consider the contributions from the Reynolds stress terms and the equatorial Coriolis terms separately, and nd that they are of similar magnitude. In the cases examined, the azimuthal component of streaming ow driven by the equatorial Coriolis terms is everywhere retrograde, whereas that driven by Reynolds stresses may have both retrograde and prograde regions, but the total streaming ows are everywhere retrograde. Even when the forcing frequency is larger than twice the background rotation rate, we nd that there is a streaming ow driven by both the Reynolds stress and the equatorial Coriolis terms. For cases forced at precession frequencies in near resonance with the eigenfrequencies of the intrinsic inertial modes of the linear inviscid unforced rotating cylinder ow, we quantify theoretically how the amplitude of streaming ow scales with respect to variations in Reynolds number, cylinder tilt angle and aspect ratio, and compare these with numerical simulations.