Transition to turbulence in rotating-disk boundary layers—convective and absolute instabilities

Abstract

This work is an experimental study of mechanisms for transition to turbulence in the boundary layer on a rotating disk. In one case, the focus was on a triad resonance between pairs of traveling cross-flow modes and a stationary cross-flow mode. The other was on the temporal growth of traveling modes through a linear absolute instability mechanism first discovered by Lingwood (1995, J Fluid Mech 314:373–405). Both research directions made use of methods for introducing controlled initial disturbances. One used a distributed array of ink dots placed on the disk surface to enhance a narrow band of azimuthal and radial wave numbers of both stationary and traveling modes. The size of the dots was small so that the disturbances they produce were linear. Another approach introduced temporal disturbances by a short-duration air pulse from a hypodermic tube located above the disk and outside the boundary layer. Hot-wire sensors primarily sensitive to the azimuthal velocity component, were positioned at different spatial (r,θ) locations on the disk to document the growth of disturbances. Spatial correlation measurements were used with two simultaneous sensors to obtain wavenumber vectors. Cross-bicoherence was used to identify three-frequency phase locking. Ensemble averages conditioned on the air pulses revealed wave packets that evolved in time and space. The space–time evolution of the leading and trailing edges of the wave packets were followed past the critical radius for the absolute instability, r _{c A} . With documented linear amplitudes, the spreading of the disturbance wave packets did not continue to grow in time as r _{c A} was approached. Rather, the spreading of the trailing edge of the wave packet decelerated and asymptotically approached a constant. This result supports the linear DNS simulations of Davies and Carpenter (2003, J Fluid Mech 486:287–329) who concluded that the absolute instability mechanism does not result in a global mode, and that linear-disturbance wave packets are dominated by the convective instability. In contrast, wave-number matching between traveling cross-flow modes confirmed a triad resonance that lead to the growth of a low azimuthal number (n = 4) stationary mode. At transition, this mode had the largest amplitude. Signs of this mechanism can be found in past flow visualization of transition to turbulence in rotating disk flows.