Experimental investigation of the instantaneous connection between freestream turbulence wavenumber and Klebenoff modes during bypass transition

Delaying the transition from laminar flow to turbulent flow in a boundary layer has many advantages for aerospace systems, the principal one being a significant reduction in wall shear stress and thereby skin friction drag. As such, understanding the mechanisms by which this transition occurs has been of fundamental scientific interest since Osborne Reynolds' classic dye experiment in the 19th century. Traditionally, the study of laminar-turbulent transition has focussed on the boundary layers forming along a nominally zero pressure gradient flat plat immersed in a disturbancefree flow. In such conditions, the transition process has been viewed as consisting offour steps (Morkovin et al., 1994; Fasel, 2002; Sarec et al., 2002): (1) receptivity, by which unsteady disturbances external to the boundary layer enter the boundary layer; (2) linear instability, by which growth of these disturbances can be determined using the linearized, unsteady, NavierStokes equations; (3) secondary instability, during which nonlinear interactions occur and the amplitude of the disturbances grow three-dimensionally; and (4) breakdown, involving the formation of local bursts and spots of turbulence which rapidly merge to form a fully turbulent boundary layer. The transition process described above is only observed under ideal conditions where the freestream turbulence intensity is quite low, u' jUoo of the order of 0.01%, where u' is the mean amplitude of the velocity fluctuations and Uoo is the mean velocity of the free stream. Whereas this magnitude of freestream turbulence is potentially possible in free flight conditions, in a large majority of engineering flows, freestream turbulence levels can be considerably higher. Under these conditions, the boundary layer undergoes what is referred to as "bypass transition" (Morkovin, 1993). During bypass transition, transition occurs much earlier and the actual transition to turbulence is often preceded by the appearance of streamwise streaks of low momentum fluid within the boundary layer (Klebenoff, 1971) associated with spanwise distortion of the boundary layer thickness. Commonly referred to as "Klebenoff modes" , these structures are long in the streamwise direction and narrow in the spanwise direction (with a width on the order of the boundary layer thickness). The amplitude of the fluctuations of the Klebenoff modes peaks at a location approximately half the boundary layer thickness away from the wall and grows algebraically in the streamwise direction. As such, these streaks differ from both the linear disturbances occurring in disturbance-free conditions (a.k.a. the TollmienSchlichting waves (Schlichting & Gersten, 2000)) and longitudinal streaks observed in fully turbulent boundary layers (Kline et al., 1967; Hutchins et al., 2009). It as yet, unclear what role the Klebenoff modes play in the ultimate transition turbulence, although it's been