Prof. Peter Read

Abstract:

A series of numerical simulations of steady, thermally stratified flow of a Boussinesq, incompressible fluid in a rotating, cylindrical fluid annulus were carried out over ranges of spatial resolution, grid stretch, and rotation rate. A range of different numerical advection schemes were used for the representation of heat transport, including a conventional conservative second-order Eulerian scheme and three different variants of a semi-Lagrangian scheme used either for temperature advection alone, or for both thermal and momentum advection. The resulting simulations were compared both with each other, and with high precision measurements of velocity, temperature, and total heat transport in the laboratory. The performance of the semi-Lagrangian scheme was found to be quite strongly sensitive to the spatial interpolation algorithm. A basic tensor cubic scheme generally produced good simulations of steady 2D and 3D flows, although the somewhat more accurate tensor quintic scheme (which is, however, also significantly more expensive) appeared to offer some detectable improvements in accuracy and performance in some cases. A split cubic scheme (which is computationally cheaper but formally less accurate) gave generally poor results in practice and is not recommended. In all cases considered, both the fully Eulerian and most forms of the semi-Lagrangian schemes gave good quantitative agreement with the laboratory measurements when extrapolated to very high resolution. Some significant systematic errors in the simulated heat transport and zonal momentum were found with all schemes, however, when run at moderate (though by no means very low) resolution. The semi-Lagrangian schemes had a tendency to overestimate heat transport relative to the laboratory measurements compared with the Eulerian schemes, but the latter tended to overestimate zonal momentum relative to the laboratory flows compared with the fully semi-Lagrangian simulations.

Abstract:

Results from an experimental study of vortices in a rotating shear layer will be presented. Through the rotation of circular sections in the base and lid of a circular tank, a vertical shear layer is created in the fluid interior. In supercritical conditions, the flow is in the form of a regular string of two-dimensional, vertically uniform, vortices along the now wavy shear layer. Once established, the vortices are very stable flow structures that persist as long as the shear is maintained. Under most conditions the vortices were steady, but quasi-periodic and chaotic flows were also observed. The data from the experiments are in the form of maps of the instantaneous horizontal velocity field obtained by a particle tracking technique similar to Particle Image Velocimetry (PIV). The data would be useful validate both the spatial and temporal behaviour of numerical models.

Abstract:

The Proper Orthogonal Decomposition (POD) is a procedure to compute an orthogonal basis from a time series of spatial fields. This basis is optimal among all linear decompositions, in the sense that for a given number of modes, the projection of the original signal onto the subspace will contain the most variance on average. This algorithm is applied to streamfunction fields derived from measurements of the flow in the thermally forced rotating annulus experiment. Results of this analysis are presented, and a method to derive low-dimensional models of the flow by projecting the equations of motion onto these empirical eigenfunctions is discussed.