Experimental Study of Absolute Instability over a Rotating Disk

A series of experiments were performed to study the absolute instability of Type I traveling cross-flow modes in the boundary layer on a smooth disk rotating at constant speed. The basic flow agreed with analytic theory, and the growth of natural disturbances matched linear theory predictions. Controlled temporal disturbances were introduced by a short-duration air pulse from a hypodermic tube located above the disk and outside the boundary layer. The air pulse was positioned just outboard of the critical radius for Type I cross-flow modes. A hot-wire sensor primarily sensitive to the azimuthal velocity component, was positioned at different spatial locations on the disk to document the growth of disturbances produced by the air pulses. Ensemble averages conditioned on the air pulses revealed wave packets that evolved in time and space. Two amplitudes of air pulses were used. The lower amplitude produced wave packets with linear amplitude characteristics that agreed with linear-theory wall-normal eigenfunction distributions and spatial growth rates. The higher amplitude pulse produced wave packets that had nonlinear amplitude characteristics. The space-time evolution of the leading and trailing edges of the wave packets were followed well past the critical radius for the absolute instability based on Lingwood (1995). With the linear amplitudes, the absolute instability was dominated by the convective modes, agreeing with the linear DNS simulations of Davies and Carpenter (2003). With the nonlinear amplitudes, larger temporal growth of the wave packets existed which supports the finite amplitude analysis of Pier (2003), and more closely resembles the wave packet evolution in the experimental study of Lingwood (1996). This suggests that the disturbance levels in the experiment that was intended to demonstrate the linear analysis, were likely finite.