Numerical simulations of disturbance development on a rotating disk with time-periodic motion

The rotating disk or von K´arm´an (1921) boundary layer is the archetypical flow for the study of laminar-turbulent transition processes that occur naturally on the wings of aircraft (Gregory et al. 1955) and is often used to demonstrate laminar flow control applications. Morgan et al. (2022) developed the novel approach of controlling linear disturbance development via a time-periodic modulation of the otherwise steady disk rotation rate; a three-dimensional oscillatory boundary layer forms that couples a Stokes layer with the von K´arm´an flow. Results of recent numerical simulations are reviewed that demonstrate the significant control benefits brought about by disk modulation for both local and global forms of linear instability (Lingwood 1995; Thomas & Davies 2018).