No abstract

The snapshot form of the Karhunen-Loéve (K–L) expansion has been applied to twodimensional, two-component hot-wire data from the region of a weakly pertubed free shear layer that includes the first pairing process. Low-level external perturbation was provided by a loudspeaker driven by a computer-generated signal composed of two sine waves of equal amplitude at the frequencies of the naturally developing fundamental instability wave and its first subharmonic, separated by a controllable initial phase angle difference. It was found that a large fraction of the fluctuation energy is carried by the first few modes. A low-dimensional empirical eigenfunction space is obtained which describes the shear-flow coherent structures well. Galerkin projection of the Navier-Stokes equations onto this basis set of principal eigenfunction modes results in a low-order system of dynamical equations, and solution of this system of equations describes the dynamics of the coherent structures associated with eigenfunctions. Finally the simulation, as obtained from the system of dynamical equations, is shown to compare reasonably well with the experiments.

An experimental study has been made of the hydrodynamic stability of viscous flow between coaxial rotating cylinders with a superposed radial thermal gradient. For the data presented, the outer cylinder is at rest and the annulus is small. The axis of the cylinders is vertical; the fluid is water. There is a qualitative difference between the type of instability which first sets in when the thermal gradient is zero or nonzero: the secondary motion when the gradient is nonzero does not consist of toroidal Taylor cells. However, there is a transition to Taylor cells at a higher Taylor number. Free convection affects the results strongly. Quantitative data concerning the transition to Taylor cells are presented along with a qualitative description of the cells which first cause instability.