Three-dimensional transition of zero-pressure-gradient boundary layer by impulsively and nonimpulsively started harmonic wall excitation

Abstract

A three-dimensional (3D) transition route for zero-pressure-gradient boundary layer over a flat plate is computationally investigated, for impulsive and nonimpulsive startup of harmonic wall excitation. A monochromatic frequency of excitation is chosen to perturb the boundary layer. The exciter placed near the leading edge of the flat plate is stapled in the spanwise direction, as in the classical experiment by Klebanoff, Tidstrom, and Sargent [J. Fluid Mech. 12, 1 (1962)]. The computational domain includes the leading edge and the 3D Navier-Stokes equation is solved first for the equilibrium flow without any excitation. This is followed by computing the disturbed flow with the exciter started in either an impulsive or in a nonimpulsive manner. Detailed description of the transition process is provided for the startup cases, which shows that the transition is essentially caused by the spatiotemporal wave front for the moderate frequency of excitation. The present investigation follows the formulation and methodology given by Bhaumik and Sengupta [Phys. Rev. E 89, 043018 (2014)], which specifically reported only the impulsive startup of harmonic wall Gaussian circular patch excitation for a moderate frequency that led to the aligned pattern of $\mathrm{\ensuremath{\Lambda}}$ vortices.