Paththage A. Priyadarshana

Statistical structure of turbulent-boundary-layer velocity–vorticity products at high and low Reynolds numbers

The mean wall-normal gradients of the Reynolds shear stress and the turbulent kinetic energy have direct connections to the transport mechanisms of turbulent-boundary-layer flow. According to the Stokes–Helmholtz decomposition, these gradients can be expressed in terms of velocity–vorticity products. Physical experiments were conducted to explore the statistical properties of some of the relevant velocity–vorticity products. The high-Reynolds-number data ( R θ ≃ O (10 6 ), where θ is the momentum thickness) were acquired in the near neutrally stable atmospheric-surface-layer flow over a salt playa under both smooth- and rough-wall conditions. The low- R θ data were from a database acquired in a large-scale laboratory facility at 1000 > R θ > 5000. Corresponding to a companion study of the Reynolds stresses (Priyadarshana & Klewicki, Phys. Fluids , vol. 16, 2004, p. 4586), comparisons of low- and high- R θ as well as smooth- and rough-wall boundary-layer results were made at the approximate wall-normal locations y p /2 and 2 y p , where y p is the wall-normal location of the peak of the Reynolds shear stress, at each Reynolds number. In this paper, the properties of the v ω z , w ω y and u ω z products are analysed through their statistics and cospectra over a three-decade variation in Reynolds number. Here u , v and w are the fluctuating streamwise, wall-normal and spanwise velocity components and ω y and ω z are the fluctuating wall-normal and spanwise vorticity components. It is observed that v –ω z statistics and spectral behaviours exhibit considerable sensitivity to Reynolds number as well as to wall roughness. More broadly, the correlations between the v and ω fields are seen to arise from a ‘scale selection’ near the peak in the associated vorticity spectra and, in some cases, near the peak in the associated velocity spectra as well.

Reynolds Number Scaling of Wall Layer Velocity-Vorticity Products

The wall normal gradients of Reynolds stress and turbulent kinetic energy are important in analyzing momentum transport in the turbulent boundary layer. These gradients can be expressed in terms of velocity- vorticity correlations. In this paper, properties of velocity-vorticity products over a three decade variation in Reynolds number are analyzed. Data were acquired in the near neutral atmospheric surface layer in the western desert of Utah and in a laboratory boundary layer. A custom made six-wire hot wire probe was employed to measure axial and wall normal velocities as well as spanwise vorticity. It is observed that the co-spectra of velocity and vorticity generally follows the vorticity spectrum at both high and low Reynolds number. Thus, it is concluded that the vortical motions dictate the scales over which the net correlation occurs. Normalization of vorticity spectra using the Taylor time scale appears to effectively remove Reynolds number variations.

Reynolds Number Dependencies in Boundary Layer Axial Stress and Scalar Variance Transport

Boundary layer axial stress, (u 2), and scalar variance, (c 2), transport were investigated using custom hot-wire/photoionization probes. The probes allow instantaneous measurement of all the terms in the evolution equations for (u 2) and (c 2), excluding molecular diffusion and pressure-strain. Of particular interest are the dominant length scales participating in the transport. Turbulent transport in the wall normal direction was found to prevail over other terms in the evolution equations. Independent of Reynolds number, the peak in the spectra of the turbulent transport term was found to occur near λu, the Taylor microscale associated with u.