Direct numerical simulation of H-type transition in stratified horizontal boundary layers

Thermal stratification in boundary layers occurs in many natural phenomena and industrial applications, such as atmospheric boundary layers and heat exchangers. In these cases, the stratification can significantly affect hydrodynamic stability. While buoyancy effects on fully developed turbulence have been widely investigated, laminar-to-turbulent transition of horizontal boundary layers is mostly unexplored. In this study, we conduct direct numerical simulations of H-type breakdown in flat-plate boundary layers with weak wall-heating (T_w/T_∞=1.05) at a Mach number of 0.2. We examine a range of Richardson numbers, based on the inlet boundary-layer thickness, wall density, and gravitational acceleration, from 0.01 to -0.02. First, primary and secondary perturbation growth rates in stably- and unstably-stratified configurations are analyzed. Buoyancy forces either decrease or increase primary and secondary instability growth rates and thus either delay or promote the transition to turbulence. We propose a scaling law as a function of the Richardson number that successfully predicts the primary and secondary growth rates. The physical mechanisms of non-neutral stratification on the instability growth are then investigated based on the vorticity fluctuation equation. As for the primary instability, the buoyancy term exhibits a peak near the critical layer, where it is in phase with the spanwise vorticity fluctuation.