Impulse response of linear disturbances in a skewed Stokes layer

The spatiotemporal development of impulsively excited two-dimensional linear disturbances in acceleration-skewed and velocity-skewed Stokes layers is investigated using numerical simulations of the linearized Navier–Stokes equations. This study focuses on the long-term behavior of linearly unstable disturbances within these skewed flows. The onset of linear instability in the symmetric Stokes layer is known to coincide with absolute instability, with disturbances forming family tree structures, characterized by multiple wavepackets spread across the spatiotemporal plane, coupled with pointwise subharmonic temporal growth [Ramage et al., “Numerical simulation of the spatiotemporal development of linear disturbances in Stokes layers: Absolute instability and the effects of high-frequency harmonics,” Phys. Rev. Fluids 5, 103901 (2020)]. However, the introduction of acceleration and velocity skewness disrupts the formation of the family tree structure. Instead, the onset of linearly unstable behavior is matched to convective instability, with disturbances predominantly propagating in the direction of the maximum acceleration or maximum velocity. As the Reynolds number increases, absolute instability emerges, albeit with pointwise temporal growth less than the growth obtained by the disturbance maximum.