Flow and Reynolds number dependencies of one-dimensional vorticity fluctuations

Although significant attention has been given to the evolution of various characteristics of turbulent velocity and scalar fields with R _λ, the Taylor microscale Reynolds number, there is a scarcity of data relating to the dependence of vorticity statistics on R _λ. In this paper, we examine the dependence on R _λ (= 27–1067) of the statistics of the spanwise (or lateral) vorticity component ω _z , obtained in different types of flows. Measurements in grid turbulence, circular cylinder wakes and plane and square jets issued from different geometry nozzles were made using a 4-hot-wire vorticity probe. The vorticity variance, normalized by Kolmogorov scales, satisfies local isotropy closely and does not depend on R _λ or the type of flow. Vorticity spectra in grid and wake flows agree with isotropic calculations and evolve with R _λ at low wavenumbers. In wakes, the spectra do not change significantly even at low wavenumbers when R _λ is greater than about 160. By contrast, the vorticity spectra in jets show a significant departure from local isotropy at low wavenumbers, irrespectively of R _λ. The pdf of the vorticity fluctuation exhibits good symmetry with single exponential tails for R _λ < 160, independently of the flow. The tails stretch out to larger amplitudes and have a double exponential structure at largerR _λ. Although the pdf depends on R _λ, its dependence on the flow is small.

Acknowledgment

We acknowledge Dr. Y. Li's contribution to the experimental work on square jets. RAA is grateful for the support of the Australian Research Council.