Three-component vorticity measurements in a turbulent grid flow

Abstract

All components of the fluctuating vorticity vector have been measured in decaying grid turbulence using a vorticity probe of relatively simple geometry (four X-probes, i.e. a total of eight hot wires). The data indicate that local isotropy is more closely satisfied than global isotropy, the r.m.s. vorticities being more nearly equal than the r.m.s. velocities. Two checks indicate that the performance of the probe is satisfactory. Firstly, the fully measured mean energy dissipation rate 〈ε〉 is in good agreement with the value inferred from the rate of decay of the mean turbulent energy 〈q²〉 in the quasi-homogeneous region; the isotropic mean energy dissipation rate 〈ε_iso〉 agrees closely with this value even though individual elements of 〈ε〉 indicate departures from isotropy. Secondly, the measured decay rate of the mean-square vorticity 〈ω²〉 is consistent with that of 〈q²〉 and in reasonable agreement with the isotropic form of the transport equation for 〈ω²〉. Although 〈ε〉≃〈ε_iso〉, there are discernible differences between the statistics of ε and ε_iso; in particular, ε_iso is poorly correlated with either ε or ω². The behaviour of velocity increments has been examined over a narrow range of separations for which the third-order longitudinal velocity structure function is approximately linear. In this range, transverse velocity increments show larger departures than longitudinal increments from predictions of Kolmogorov (1941). The data indicate that this discrepancy is only partly associated with differences between statistics of locally averaged ε and ω², the latter remaining more intermittent than the former across this range. It is more likely caused by a departure from isotropy due to the small value of R_λ, the Taylor microscale Reynolds number, in this experiment.