Characteristics of the Lamb Vector in the Outer Region of a Turbulent Boundary Layer

Abstract

A characteristic feature of wall-turbulence is the presence of ‘sweeps’, u1 > 0, u2 0, Q2 events (low momentum fluid transported away from the wall). These sweep and ejection events are found to make substantial contributions to turbulence production. In other words, these Reynolds shear stress generating events act as a source for kinetic energy to sustain turbulence. In this study, the streamwise, wall-normal and spanwise directions are along the x1 , x2 and x3 axes respectively. The mean and fluctuating velocity components along those three directions are represented by (U1, U2, U3) and (u1, u2, u3), respectively. The flow fields that contribute to Reynolds shear stress are well documented in the literature. Theodorsen and Offen & Kline explained the presence of sweeps and ejections using a hairpin model. Bandyopadhyay and Head & Bandyopadhyay found visual evidence for the existence of large structures with characteristic inclined interface. Adrian et al. called these large scale structures as hairpin packets that comprise a group of individual hairpin type vortices, whereas Na et al. classified large-scale low-momentum regions that produce Reynolds stress as superbursts. Ganapathisubramani et al. found that a signature consistent with hairpin packets, contributes close to 25% of Reynolds shear stress and yet occupy only a fraction of the area. Guala et al. found that very large scale motions (which can be understood as a collection of hairpin packets) are very active and contain more than half the Reynolds shear stress. While the focus on Reynolds shear stress is warranted, inspection of the mean momentum equation indicates that in fact it is the gradient of Reynolds shear stress that is of primary importance to the rate of change of momentum. The mean momentum equation along the streamwise direction (equation 1) for a zero pressure gradient turbulent boundary layer shows that the wall-normal gradient of Reynolds shear stress (T ) is a force that acts as a momentum source/sink.