Different Routes of Transition by Spatio-Temporal Wave-Front

Here, we demonstrate by DNS of 3D zero-pressure gradient boundary layer that both K-and H- or N-types of transition, as described in Kachanov (Ann. Rev. Fluid Mech., 26, 1994) are consequences of low amplitude monochromatic deterministic excitation caused by the growth of spatio-temporal wave-front (STWF). In Bhaumik & Sengupta (Phys. Rev. E, 89, 043018, 2014), STWF has been established as the precursor of 3D routes of transition. One of the main feature of present DNS is the extreme accuracy of the used compact schemes over a significantly longer computational domain, including the leading edge of the plate. The velocity-vorticity ((V) over right arrow,(Omega) over right arrow)-formulation used here helps achieving higher accuracy, maintain solenoidality of the vorticity vector and reduce aliasing error for solving Navier-Stokes equation (NSE). Results show that the H-type transition occurs for lower frequency of excitation, while K-type is seen to occur for higher frequency cases. This is in contrast to the theoretical view-point in the literature for H-type transition, which is claimed to occur via triad resonant interaction of spatial TS waves.