The three-dimensional impulse response of a boundary layer to different types of wall excitation

Abstract

Here we report a study of the physical mechanism behind the creation of perturbation of a boundary layer by direct numerical simulation (DNS) of an incompressible Navier-Stokes equation (NSE) that leads to eventual three-dimensional (3D) transition. By considering two different types of impulsive wall-excitations which are similar to dip-slip and strike-slip events in the seismological terminology for a zero pressure gradient (ZPG) boundary layer, we show that initial events and the evolution of the resultant wave-packet bear a close resemblance with the physical mechanism for the creation of tsunamis. This is due to the significant differences in the characteristics and dynamics of the wall-bounded and oceanic boundary layer at deep-ocean. Here we particularly seek out the impulse response of a ZPG boundary layer as demonstrated recently in the work of S. Bhaumik and T. K. Sengupta [“Impulse response and spatio-temporal wave-packets: The common feature of rogue waves, tsunami, and transition to turbulence,” Phys. Fluids 29, 124103 (2017)], by considering a specific boundary motion similar to dip-slip events for the creation of tsunamis. The precursor of flow transition, noted as the spatiotemporal wave front, has been shown to be very effectively created by the dip-slip type of boundary motion, first reported in the work of Sengupta et al. [“Spatiotemporal growing wave-fronts in spatially stable boundary layers,” Phys. Rev. Lett. 96, 224504 (2006)], from both linear and nonlinear analyses of NSE. In this study, receptivity of the boundary layer to these two types of subduction motions is contrasted. This is performed for the first time using 3D DNS of NSE. It is shown that the dip-slip event displays stronger receptivity than the strike-slip event.