Journal of Fluid Mechanics



Evolution of a wave packet into vortex loops in a laminar separation bubble


JONATHAN H. WATMUFF a1
a1 MCAT Inc., NASA Ames Research Center, Moffett Field, CA 94035, USA

Abstract

A laminar boundary layer develops in a favourable pressure gradient where the velocity profiles asymptote to the Falkner & Skan similarity solution. Flying-hot-wire measurements show that the layer separates just downstream of a subsequent region of adverse pressure gradient, leading to the formation of a thin separation bubble. In an effort to gain insight into the nature of the instability mechanisms, a small-magnitude impulsive disturbance is introduced through a hole in the test surface at the pressure minimum. The facility and all operating procedures are totally automated and phase-averaged data are acquired on unprecedently large and spatially dense measurement grids. The evolution of the disturbance is tracked all the way into the reattachment region and beyond into the fully turbulent boundary layer. The spatial resolution of the data provides a level of detail that is usually associated with computations.

Initially, a wave packet develops which maintains the same bounded shape and form, while the amplitude decays exponentially with streamwise distance. Following separation, the rate of decay diminishes and a point of minimum amplitude is reached, where the wave packet begins to exhibit dispersive characteristics. The amplitude then grows exponentially and there is an increase in the number of waves within the packet. The region leading up to and including the reattachment has been measured with a cross-wire probe and contours of spanwise vorticity in the centreline plane clearly show that the wave packet is associated with the cat's eye pattern that is a characteristic of Kelvin–Helmholtz instability. Further streamwise development leads to the formation of roll-ups and contour surfaces of vorticity magnitude show that they are three-dimensional. Beyond this point, the behaviour is nonlinear and the roll-ups evolve into a group of large-scale vortex loops in the vicinity of the reattachment. Closely spaced cross-wire measurements are continued in the downstream turbulent boundary layer and Taylor's hypothesis is applied to data on spanwise planes to generate three-dimensional velocity fields. The derived vorticity magnitude distribution demonstrates that the second vortex loop, which emerges in the reattachment region, retains its identity in the turbulent boundary layer and it persists until the end of the test section.

(Received March 31 1998)
(Revised March 8 1999)



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