The classical unsteady boundary layer: A numerical study

Abstract The transition process from a laminar to turbulent flow near solid wall (e.g., at the suction side of slender airfoil) is still not fully understood. We focus on early stage based boundary layer (BL) theory, that is, high Reynolds number asymptotic expansions, which reduce Navier–Stokes equations into simplified forms. While steady solutions resulting classical BL and corresponding regularisations viscous–inviscid interaction theory are studied quite extensively, there only few information about time‐dependent scenario. Hence, we numerically study unsteady its breakdown structure, Van Dommelen–Shen singularity, simplest example can imagine, incompressible planar fluid through rectangular channel with suction. depicted builds lower follows initially generic Blasius behaviour, gets temporally modulated by means slot located upper wall. As usual, main part inviscid governed Laplace's equation. Remarkably, wall‐slip velocity, or alternatively pressure gradient imposed BL, be calculated in closed form have full control temporal dependency variation applied strength. This specific configuration allows us split off initial solution promises high‐accuracy remaining equation scaled stream function formulation. Chebyshev collocation used wall‐normal direction, where infinite domain mapped onto [ − 1, 1]. On contrary, discretise mainstream direction finite difference scheme second‐order accuracy, proved more precise build‐up singularities. In order trigger dynamic equations, increase rate continuously zero level slightly above critical value (obtained case). consequence, system cannot relax instead blows up time some position. try resolve this resolution final goal verify inner structure (the two‐dimensional blow‐up profile) singularity role separation transition.