STUDY OF TURBULENT BOUNDARY-LAYER STRUCTURE USING THE INVARIANTS OF THE VELOCITY-GRADIENT TENSOR

The geometry of the velocity field in a numerically simulated incompre ssible turbulent boundary layer over a flat plate at Re-theta = 670 is studied with the use of the invariants of the velocity gradient tenso r (P, Q, and R). These invariants are computed at every grid point in the flow and used to form the discriminant (D = 27R(2)/4 + Q(3)). Of p rimary interest are those regions in the flow where the discriminant i s positive-regions where, according to the characteristic equation, th e eigenvalues of the velocity gradient tensor are complex. An observer moving with a frame of reference that is attached to a fluid particle lying within such a region would see a local flow pattern of the type stable-focus-stretching or unstable-focus-compressing. When the flow is visualized in this way, continuous, connected, large-scale structur es are revealed that extend from just below the buffer layer (y(+) app roximate to 1.0) out into the beginning of the wake region. These stru ctures are aligned with the mean shear close to the wall and arch in t he cross-stream direction away from the wall. In some cases, the struc tures observed are very similar to the hairpin eddy vision of boundary -layer structure proposed by Theodorsen [1]. Recently, this conceptual picture has been used by Ferry et al. [2] to develop a successful mod el of the turbulent boundary layer based on an extension of the attach ed eddy hypothesis first proposed by Townsend [3]. That the structure of the flow is revealed more effectively by the discriminant rather th an by the vorticity is important and adds support to the recent analys is of channel flow structure by Blackburn et al. [4]. Of particular im portance (and also in contrast with the use of the vorticity) is the f act that the procedure does not require the use of an arbitrary thresh old in the discriminant. Further analysis using computer flow visualiz ation shows a high degree of spatial correlation between the regions o f positive discriminant, extreme negative pressure fluctuations, and l arge instantaneous values of Reynolds shear stress (u'v'). (C) Elsevie r Science Inc., 1996