Lateral vorticity measurements in a turbulent wake

Abstract

The accurate measurement of vorticity has proven difficult because of the difficulty of estimating spatial derivatives of velocity fluctuations reliably. A method is proposed for correcting the lateral vorticity spectrum measured using a four-wire probe. The attenuation of the measured spectrum increases as the wavenumber increases but does not vanish when the wavenumber is zero. Although the correction procedure assumes local isotropy, the major contributor to the high-wavenumber part of the vorticity spectrum is the streamwise derivative of the lateral velocity fluctuation, and the correction of this latter quantity does not depend on local isotropy. Satisfactory support for local isotropy is provided by the high-wavenumber parts of the velocity, velocity derivative and vorticity spectra measured on the centreline of a turbulent wake. Second- and fourth-order moments of vorticity show departures from local isotropy but the degree of departure seems unaffected by the turbulence Reynolds number Rλ. The vorticity probability density function is approximately exponential and has tails which stretch out to larger amplitudes as Rλ increases. The vorticity flatness factor, which is appreciably larger than the flatness factor of the streamwise velocity derivative, also increases with Rλ. When Rλ is sufficiently large for velocity structure functions to indicate a r2/3 inertial range, two-point longitudinal correlations of lateral vorticity fluctuations give encouraging support for the theoretical r−4/3 behaviour.