Direct numerical simulation of K-type and H-type transitions to turbulence in a low Mach number flat plate boundary layer

Transition to turbulence via spatially evolving secondary instabilities in compressible, zero-pressure-gradient flat plate boundary layers is numerically simulated for both the Klebanoff K-type and Herbert H-type disturbances. The objective of this work is to evaluate the universality of the breakdown process between different routes through transition in wall-bounded shear flows. Each localized linear disturbance is amplified through weak non-linear instability that grows into lambda-vortices and then hairpin-shaped eddies with harmonic wavelength, which become less organized in the late-transitional regime once a fully populated spanwise turbulent energy spectrum is established. For the H-type transition, the computational domain extends from $Re_x = 10^5$, where laminar blowing and suction excites the most unstable fundamental and a pair of oblique waves, to fully turbulent stage at $Re_x = 10.6\times10^5$. The computational domain for the K-type transition extends to $Re_x = 9.6\times 10^5$. The computational algorithm employs fourth-order central differences with non-reflective numerical sponges along the external boundaries. For each case, the Mach number is 0.2.