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Lateral vorticity measurements in a turbulent wake

Published online by Cambridge University Press:  26 April 2006

R. A. Antonia ,
Y. Zhu  and
H. S. Shafi
R. A. Antonia
Affiliation:
Department of Mechanical Engineering, University of Newcastle, NSW, 2308, Australia
Y. Zhu
Affiliation:
Department of Mechanical Engineering, University of Newcastle, NSW, 2308, Australia
H. S. Shafi
Affiliation:
Department of Mechanical Engineering, University of Newcastle, NSW, 2308, Australia
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 323 , 25 September 1996 , pp. 173 - 200
Copyright
© 1996 Cambridge University Press

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References

Antonia, R. A., Anselmet, F. & Chambers, A. J. 1986 Assessment of local isotropy using measurements in a turbulent plane jet. J. Fluid Mech. 163, 365–391.Google Scholar
Antonia, R. A., Browne, L. W. B. & Chambers, A. J. 1984 On the spectrum of the transverse derivatives of the streamwise velocity in a turbulent flow. Phys. Fluids 27, 2628–2631.Google Scholar
Antonia, R. A., Browne, L. W. B. & Fulachier, L. 1987 Average wavelength of organised structures in the turbulent far wake of a cylinder. Exps. Fluids 5, 298–304.Google Scholar
Antonia, R. A., Browne, L. W. B. & Shah, D. A. 1988a Characteristics of vorticity fluctuations in a turbulent wake. J. Fluid Mech. 189, 349–365.Google Scholar
Antonia, R. A. & Kim, J. 1994 A numerical study of local isotropy of turbulence. Phys. Fluids A 6, 834–841.Google Scholar
Antonia, R. A. & Mi, J. 1993a Corrections for velocity and temperature derivatives in turbulent flows. Exps. Fluids 14, 203–208.Google Scholar
Antonia, R. A. & Mi, J. 1993b Temperature dissipation in a turbulent round jet. J. Fluid Mech. 250, 531–551.Google Scholar
Antonia, R. A. & Rajagopalan, S. 1990 Performance of lateral vorticity probe in a turbulent wake. Exps. Fluids 9, 118–120.Google Scholar
Antonia, R. A., Satyaprakash, B. R. & Hussain, A. K. M. F. 1982 Statistics of fine-scale velocity in turbulent plane and circular jets. J. Fluid Mech. 119, 55–80.Google Scholar
Antonia, R. A., Shah, D. A. & Browne, L. W. B. 1988b Dissipation and vorticity spectra in a turbulent wake. Phys. Fluids 31, 1805–1807.Google Scholar
Antonia, R. A., Zhu, Y. & Kim, J. 1993 On the measurement of lateral velocity derivatives in turbulent flows. Exps. Fluids 15, 65–69.Google Scholar
Antonia, R. A., Zhu, Y. & Kim, J. 1994 Corrections for spatial velocity derivatives in a turbulent shear flow. Exps. Fluids 16, 411–413.Google Scholar
Balint, J.-L., Wallace, J. M. & Vukoslavcevic, P. 1989 The statistical properties of the vorticity field of a two-stream turbulent mixing layer. Advances in Turbulence II (ed. H. H. Fernholz & H. E. Fiedler), pp. 74–78. Springer.
Balint, J.-L., Wallace, J. M. & Vukoslavcevic, P. 1991 The velocity and vorticity vector fields of a turbulent boundary layer. Part 2. Statistical properties. J. Fluid Mech. 228, 53–86.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Browne, L. W. B., Antonia, R. A. & Chua, L. P. 1989 Calibration of X-probes for turbulent flow measurements. Exps. Fluids 7, 201–208.Google Scholar
Browne, L. W. B., Antonia, R. A. & Shah, D. A. 1987 Turbulent energy dissipation in a wake. J. Fluid Mech. 179, 307–326.Google Scholar
Champagne, F. H. 1978 The fine-scale structure of the turbulent velocity field. J. Fluid Mech. 86, 67–108.Google Scholar
Corrsin, S. & Kistler, A. L. 1955 Free-stream boundaries of turbulent flows. NACA Rep. 1244.
Ewing, D., Hussein, H. J. & George, W. K. 1995 Spatial resolution of parallel hot wire probes for derivative measurements. Exptl Thermal Fluid Sci. 11, 155–173.Google Scholar
Fan, M. 1991 Features of vorticity in fully turbulent flows. PhD thesis, Yale University.
Foss, J. F. 1979 Transverse vorticity measurements. In Proc. Dynamic Flow Conference 1978 (ed. B. W. Hansen), pp. 983–1001. DISA.
Foss, J. F. & Wallace, J. M. 1989 The measurement of vorticity in transitional and fully developed turbulent flows. In Advances in Fluid Mechanics Measurements (ed. M. Gad-el-Hak). Lecture Notes in Engineering, vol. 45, pp. 263–321. Springer.
Frenkiel, F. N. & Klebanoff, P. S. 1975 On lognormality of small-scale structure of turbulence. Boundary-Layer Met. 8, 173–200.Google Scholar
Frenkiel, F. N., Klebanoff, P. S. & Huang, T. 1979 Grid turbulence in air and water. Phys. Fluids 22, 1606–1617.Google Scholar
Haw, R. C., Foss, J. K. & Foss, J. F. 1988 Vorticity based intermittency measurements in a single stream shear layer. In Advances in Turbulence II (ed. H. H. Fernholz & H. E. Fiedler), pp. 90–95. Springer.
Jimenez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.Google Scholar
Kastrinakis, E. G. & Eckelmann, H. 1983 Measurement of streamwise vorticity fluctuations in a turbulent channel flow. J. Fluid Mech. 137, 165–186.Google Scholar
Kastrinakis, E. G., Eckelmann, H. & Willmarth, W. W. 1979. Influence of the flow velocity on a Kovasznay type vorticity probe. Rev. Sci. Instrum. 50, 759–767.Google Scholar
Kerr, R. M. 1985 High-order derivative correlations and the alignments of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31–58.Google Scholar
Kida, S. & Murakami, Y. 1989 Statistics of velocity gradients in turbulence at moderate Reynolds numbers. Fluid Dyn. Res. 4, 347–370.Google Scholar
Kim, J. & Antonia, R. A. 1993 Isotropy of the small scales of turbulence at low Reynolds number. J. Fluid Mech. 251, 219–238.Google Scholar
Klewicki, J. C. & Falco, R. E. 1990 On accurately measuring statistics associated with small-scale structure in turbulent boundary layers using hot-wire probes. J. Fluid Mech. 219, 119–142.Google Scholar
Kolmogorov, A. N. 1941 Local structure of turbulence in an incompressible fluid for very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 30, 299–303.Google Scholar
Kovasznay, L. S. G. 1954 Turbulence measurements in physical measurements. In Gas Dynamics and Combustion (ed. R. W. Landenbuerg, B. Lewis, R. N. Pease & H. S. Taylor), vol. 10, p. 213.
Kuo, A. Y. & Corrsin, S. 1971 Experiments on internal intermittency and fine structure distribution functions in fully turbulent fields. J. Fluid Mech. 50, 285–319.Google Scholar
Lemonis, G. C. 1995 An experimental study of the vector fields of velocity and vorticity in turbulent flows. PhD thesis, Swiss Federal Institute of Technology, Zurich.
Marasli, B., Nguyen, P. & Wallace, J. M. 1993 A calibration technique for multiple-sensor hotwire probes and its application to vorticity measurements in the wake of a circular cylinder. Exps. Fluids 15, 209–218.Google Scholar
Meneveau, C., Sreenivasan, K. R., Kailasnath, P. & Fan, M. S. 1990 Joint multifractal measures: theory and applications to turbulence. Phys. Rev. A 41, 894–913.Google Scholar
Mi, J. & Antonia, R. A. 1996 Vorticity characteristics of the turbulent intermediate wake. Exps. Fluids 20, 383–392.Google Scholar
Mi, J. & Antonia, R. A. 1994 Scaling of spanwise vorticity in turbulent plane wakes. Rep. TN - FM 94/4. Department of Mechanical Engineering, University of Newcastle, NSW.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, Vol. 2. MIT Press.
Ong, L. 1992 Visualization of turbulent flows with simultaneous velocity and vorticity measurements. PhD thesis, University of Maryland.
Ong, L. & Wallace, J. M. 1995 Local isotropy of the vorticity field in a boundary layer at high Reynolds number. Advances in Turbulence V (ed. R. Benzi), pp. 392–397. Kluwer.
Perry, A. E., Lim, K. L. & Henbest, S. M. 1987 An experimental study of the turbulence structure in smooth and rough-wall boundary layers. J. Fluid Mech. 177, 437–466.Google Scholar
Phan-Thien, N. & Antonia, R. A. 1994 Isotropic Cartesian tensors of arbitrary even orders and velocity gradient correlation functions. Phys. Fluids 6, 3818–3822.Google Scholar
Rajagopalan, S. & Antonia, R. A. 1993 Structure of the velocity field associated with the spanwise vorticity in the wall region of a turbulent boundary layer. Phys. Fluids A 5, 2502–2510.Google Scholar
Rose, W. G. 1966 Results of an attempt to generate a homogeneous turbulent shear flow. J. Fluid Mech. 25, 97–120.Google Scholar
Siggia, E. D. 1981 Invariants for the one point vorticity and strain rate correlation functions. Phys. Fluids 24, 1934–1936.Google Scholar
Silverman, B. A. 1968 The effect of spatial averaging on spectrum estimation. J. Appl. Met. 7, 168–172.Google Scholar
Sreenivasan, K. R. 1995 Small-scale intermittency in turbulence. Proc. Twelfth Australasian Fluid Mechanics Conference, Sydney (ed. R. W. Bilger), Vol. 2, pp. 549–556.
Taylor, G. I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. A 151, 421–478.Google Scholar
Tsinober, A., Kit, E. & Dracos, T. 1992 Experimental investigation of the field of velocity gradients in turbulent flows. J. Fluid Mech. 242, 169–192.Google Scholar
Van Atta, C. W. 1979 Multi-channel measurements and high-order statistics. In Proc. Dynamic Flow Conference 1978 (ed. B. W. Hansen), pp. 919–941. DISA.
Van Atta, C. W. 1991 Local isotropy of the smallest scales of turbulent scalar and velocity fields. Proc. R. Soc. Lond. A 434, 139–147.Google Scholar
Van Atta, C. W. & Antonia, R. A. 1980 Reynolds number dependence of skewness and flatness factors of turbulent velocity derivatives. Phys. Fluids 23, 252–257.Google Scholar
Verollet, E. 1977 Etude d'une couche limite turbulente avec aspiration et chauffage à la paroi. Rapport CEA-R-4861. CEN, Saclay.
Wallace, J. M. 1986 Methods of measuring vorticity in turbulent flows. Exps. Fluids 4, 61–71.Google Scholar
Wallace, J. M. & Foss, J. F. 1995 The measurement of vorticity in turbulent flows. Ann. Rev. Fluid Mech. 27, 467–514.Google Scholar
Wallace, J. M. & Vukoslavcevic, P. 1982 Measurement of the structure of the streamwise vorticity field in a turbulent boundary layer. In Structure of Turbulence in Heat and Mass Transfer (ed. Z. P. Zaric), pp. 29–41. Hemisphere.
Willmarth, W. W. 1979 Nonsteady vorticity measurements : survey and new results. In Proc. Dynamic Flow Conference 1978 (ed. B. W. Hansen), pp. 1003–1012. DISA.
Wyngaard, J. C. 1968 Measurement of small-scale turbulence structure with hot wires. J. Phys. E: J. Sci. Instrum. 1, 1105–1108.Google Scholar
Wyngaard, J. C. 1969 Spatial resolution of the vorticity meter and other hot-wire arrays. J. Phys. E: J. Sci. Instrum. 2, 983–987.Google Scholar
Wyngaard, J. C. & Pao, Y. H. 1972 Some measurements of the fine structure of large Reynolds number turbulence. In Statistical Models of Turbulence. Lecture Notes in Physics, vol. 12, pp. 384–401. Springer.
Yaglom, A. M. 1981 Laws of small-scale turbulence in atmosphere and ocean (in Commemoration of the 40th Anniversary of the theory of locally isotropic turbulence). Izv. Atmos. Oceanic Phys. 17, 919–935.Google Scholar
Zhu, Y. & Antonia, R. A. 1995a Spatial resolution of two X-probes for velocity derivative measurements. Meas. Sci. & Tech. 6, 538–549.Google Scholar
Zhu, Y. & Antonia, R. A. 1995b Effect of wire separation on the X-probe measurement in a turbulent flow. J. Fluid Mech. 287, 199–223.Google Scholar
Zhu, Y., Antonia, R. A. & Kim, J. 1993 Velocity and temperature derivative measurements in the near-wall region of a turbulent duct flow. In Near Wall Turbulent Flows (ed. R. M. C. So, C. G. Speziale & B. E. Launder), pp. 549–561. Elsevier.