Inertial waves in a spherical shell induced by librations of the inner sphere: experimental and numerical results
- Journal Article
We begin with an experimental investigation of the flow induced in a rotating spherical shell. The shell globally rotates with angular velocity Ω. A further periodic oscillation with angular velocity 0 ω 2Ω, a so-called longitudinal libration, is added on the inner sphere's rotation. The primary response is inertial waves spawned at the critical latitudes on the inner sphere, and propagating throughout the shell along inclined characteristics. For sufficiently large libration amplitudes, the higher harmonics also become important. Those harmonics whose frequencies are still less than 2Ω behave as inertial waves themselves, propagating along their own characteristics. The steady component of the flow consists of a prograde zonal jet on the cylinder tangent to the inner sphere and parallel to the axis of rotation, and increases with decreasing Ekman number. The jet becomes unstable for larger forcing amplitudes as can be deduced from the preliminary particle image velocimetry observations. Finally, a wave attractor is experimentally detected in the spherical shell as the pattern of largest variance. These findings are reproduced in a two-dimensional numerical investigation of the flow, and certain aspects can be studied numerically in greater detail. One aspect is the scaling of the width of the inertial shear layers and the width of the steady jet. Another is the partitioning of the kinetic energy between the forced wave, its harmonics and the mean flow. Finally, the numerical simulations allow for an investigation of instabilities, too local to be found experimentally. For strong libration amplitudes, the boundary layer on the inner sphere becomes unstable, triggering localized Görtler vortices during the prograde phase of the forcing. This instability is important for the transition to turbulence of the spherical shell flow. © 2013 The Japan Society of Fluid Mechanics and IOP Publishing Ltd. Show more
Journal / seriesFluid dynamics research
Pages / Article No.
PublisherInstitute of Physics
Organisational unit03734 - Jackson, Andrew / Jackson, Andrew
MoreShow all metadata