Vorticity, strain-rate and dissipation characteristics in the near-wall region of turbulent boundary layers

Abstract

Experimental results are presented that reveal the structure of a two-dimensional turbulent boundary layer which has been investigated by measuring the timedependent vorticity flux at the wall, vorticity vector, strain-rate tensor and dissipationrate tensor in the near-wall region with spatial resolution of the order of 7 Kolmogorov viscous length scales. Considerations of the structure function of velocity and pressure, which constitute vorticity flux and vorticity, indicated that, in the limit of vanishing distance, the maximum attainable content of these quantities which corresponds to unrestricted resolution, is determined by Taylor's microscale. They also indicated that most of the contributions to vorticity or vorticity flux come from the uncorrelated part of the two signals involved. The measurements allowed the computation of all components of the vorticity stretching vector, which indicates the rate of change of vorticity on a Lagrangian reference frame if viscous effects are negligible, and several matrix invariants of the velocity gradient or strain-rate tensor and terms appearing in the transport equations of vorticity, strain rate and their squared fluctuations. The orientation of vorticity revealed several preferential directions. During bursts or sweeps vorticity is inclined at 35m to the longitudinal direction. It was also found that there is high probability of the vorticity vector aligning with the direction of the intermediate extensive strain corresponding to the middle eigenvector of the strain-rate matrix. The results of the joint probability distributions of the vorticity vector orientation angles showed that these angles may be related to those of hairpin vortex structures. All invariants considered exhibit a very strong intermittent behaviour which is characterized by large-amplitude bursts which may be of the order of 10 r.m.s. values. Small-scale motions dominated by high rates of turbulent kinetic energy dissipation and high enstrophy density are of particular interest. It appears that the fluctuating strain field dominates the fluctuations of pressure more than enstrophy. Local high values of the invariants are also often associated with peaks in the shear stress.

Application of a Novel Laser-Doppler Velocimeter for Turbulence: Structural Measurements in Turbulent Boundary Layers

“…Similar studies to Klebanoff's were repeated with elaborate hot-wire arrangements by Balint et al (1991) and Honkan and Andreopoulos (1997) among others. These studies measured all-nine components of the velocity gradient tensor in low Reynolds number turbulent boundary layer flows, but with probe-sizes that were several times the Kolmogorov length scales in the low Reynolds number flows.…”

“…Several researchers have utilized HWA in multiple-wire configurations to achieve velocity gradient measurements (Balint et al 1991, Wallace and Foss 1995, Honkan and Andreopoulos 1997, Wang and Sen 1999, Honkan and Andreopoulos 2001, and Kholmyansky et al 2001. Although able to measure three components of vorticity, these techniques are intrusive, thus preventing near-wall measurements, and spatially unresolved, with probe sizes no smaller than twice the size of the smallest scales of turbulence in their flows.…”

“…For each case, the ratios of the span-wise or normal-to-wall direction gradient variance to the stream-wise gradient variance are about 120-150. To make the magnitudes of these values clearer, they are compared to the 2D flat-plate turbulent boundary layer results of Honkan and Andreopoulos (1997) in viscous wall scaling. To note is that the variance for the x-direction derivative from the simulation is much smaller than the measurement variance in the 2D turbulent boundary layer indicating that this derivative may be confidently measured with the CompLDV3.…”

“…The probability distributions for the turbulence were all taken to be Gaussian with statistics values given in Table 2.6. The data of Honkan and Andreopoulos (1997) were used as estimates for the velocity gradient variances. The ranges of y-and z-positions were based upon experimentally determined ranges for the CompLDV3.…”

Near Wall Velocity and Vorticity Measurements, In A Very High R(theta) Turbulent Boundary Layer

“…Ong and Wallace (1998) explored the joint probability of velocity and vorticity components at relatively low Reynolds numbers. Andreopoulos and Honkan (1997) measured near-wall vorticity, strain-rate and dissipation and in 2001 they examined vorticity stretching, and the velocity-gradient tensor (Andreopoulos and Honkan 2001).…”