Receptivity and non-uniqueness of turbulent boundary layer flows

The classical theory of firmly attached time-mean turbulent boundary layers, exhibiting fully developed broadband turbulence, in the limit of large Reynolds numbers, Re, is extended in two ways, where the focus lies on their stability and receptivity. At first, the description of non-unique equilibrium flows having a so-called moderately large velocity deficit is generalised as weak spanwise variations and unsteadiness is taken into account. Here the time period of filtering the flow tends to infinity such that conventional Reynolds averaging is obtained as Re → ∞. Secondly, the method of matched asymptotic expansions is supplemented with a suitable multiple-scales approach so as to capture the global effect of pronounced surface waviness on the time-mean velocity profile of the boundary layer in a self-consistent manner in terms of a memory decaying exponentially from the surface. Remarkably, the results of the asymptotic analysis are qualitatively independent of any turbulence closure.