Skip to main content
Log in

Transverse velocity and temperature derivative measurements in grid turbulence

  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

The same probe, comprising two parallel wires, is used to measure either velocity or temperature derivatives in shearless grid turbulence at a Taylor microscale Reynolds number of about 40. The aerodynamic interference of the probe affects the mean velocity when the transverse separation Δy between the wires is smaller than about 3η, where η (≃0.4 mm for the present experiments) is the Kolmogorov length scale, but not the mean temperature. Spectra and corresponding moments of transverse velocity and temperature derivatives are significantly but similarly affected when Δy≤3η, thus suggesting that this effect is more likely to be caused by electronic noise than aerodynamic interference. Indeed, after noise corrections are applied, the resulting derivative variances are brought into alignment with values inferred from two-point correlations with respect to y. Transverse derivative variances and their corresponding spectra satisfy isotropy closely but second-order structure functions satisfy it only when the separation is less than about 10η, i.e. the dissipative range scales.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.

Similar content being viewed by others

References

  • Anselmet F, Antonia RA (1985) Joint statistics between temperature and its dissipation in a turbulent jet. Phys Fluids 28:1048–1051

    Article  Google Scholar 

  • Anselmet F, Djeridi H, Fulachier L (1994) Joint statistics of a passive scalar and its dissipation in turbulent flows. J Fluid Mech 280:173–197

    Google Scholar 

  • Antonia RA, Anselmet F, Chambers AJ (1986) Assessment of local isotropy using measurements in a turbulent plane jet. J Fluid Mech 163:365–391

    Google Scholar 

  • Antonia RA, Browne LWB, Chambers AJ (1984) On the spectrum of the transverse derivatives of the streamwise velocity in a turbulent flow. Phys Fluids 27:2628–2631

    Google Scholar 

  • Antonia RA, Kim J, Browne LWB (1991) Some characteristics of small-scale turbulence in a turbulent duct flow. J Fluid Mech 233:369–399

    CAS  Google Scholar 

  • Antonia RA, Mi J (1993a) Temperature dissipation in a turbulent round jet. J Fluid Mech 250:531–551

    CAS  Google Scholar 

  • Antonia RA, Mi J (1993b) Corrections for velocity and temperature derivatives in turbulent flows. Exp Fluids 14:203–208

    CAS  Google Scholar 

  • Antonia RA, Pearson BR, Zhou T (2000) Reynolds number dependence of second-order velocity structure functions. Phys Fluids 12:3000–3006

    Article  CAS  Google Scholar 

  • Antonia RA, Zhou T, Zhu Y (1998) Three-component vorticity measurements in a turbulent grid flow. J Fluid Mech 374:29–57

    Article  Google Scholar 

  • Antonia RA, Zhu Y, Kim J (1993) On the measurement of lateral velocity derivatives in turbulent flows. Exp Fluids 15:65–69

    CAS  Google Scholar 

  • Browne LWB, Antonia RA, Shah DA (1987) Turbulent energy dissipation in a wake. J Fluid Mech 179:307–326

    CAS  Google Scholar 

  • Champagne FH (1978) The fine-scale structure of the turbulent velocity field. J Fluid Mech 86:67–108

    Google Scholar 

  • Comte-Bellot G, Strohl A, Alcaraz E (1971) On aerodynamic disturbances caused by single hot-wire probes. J Appl Mech 38: 767–774

    Google Scholar 

  • Corrsin S (1951) On the spectrum of isotropic temperature fluctuations in isotropic turbulence. J Appl Phys 22:469–473

    Google Scholar 

  • Danaila L, Zhou T, Anselmet F, Antonia RA (2000) Calibration of a temperature dissipation probe in decaying grid turbulence. Exp Fluids 28:45–50

    Article  Google Scholar 

  • Durbin PA (1982) Analysis of the decay of temperature fluctuations in isotropic turbulence. Phys Fluids 25:1328–1332

    Google Scholar 

  • Ewing D, Hussein HJ, George WK (1995) Spatial resolution of parallel hot-wire probes for derivative measurements. Exp Thermal Fluid Sci 11:155–173

    Article  Google Scholar 

  • Ferchichi M, Tavoularis S (2000) Reynolds number effects on the fine structure of uniformly sheared turbulence. Phys Fluids 12:2942–2953

    Article  CAS  Google Scholar 

  • George WK, Hussein HJ (1991) Locally axisymmetric turbulence. J Fluid Mech 233:1–23

    CAS  Google Scholar 

  • Hou Y, Wu XH, Chen S, Zhou Y (1998) Effect of finite computational domain on turbulence scaling law in both physical and spectral spaces. Phys. Rev E 58:5841–5844

    Article  CAS  Google Scholar 

  • Jimenez J (1994) Resolution requirements for velocity gradients in turbulence. In: Annual research briefs. Center for Turbulence Research, Stanford University, pp 357–364

  • Jimenez J, Wray AA, Saffman PG, Rogallo RS (1993) The structure of intense vorticity in isotropic turbulence. J Fluid Mech 255:65–90

    CAS  Google Scholar 

  • Kolmogorov AN (1941) The local structure of turbulence in an incompressible fluid with very large Reynolds numbers. Dokl Akad Nauk SSSR 30:301

    Google Scholar 

  • Lasserre JJ (2000) Méthodes pratiques de détermination du taux de dissipation de l'énergie cinétique de la turbulence par anémométrie à fils chauds. PhD thesis, University of Aix-Marseille II

  • Mestayer P (1982) Local isotropy and anisotropy in a high-Reynolds-number turbulent boundary layer. J Fluid Mech 125:475–503

    Google Scholar 

  • Mestayer P, Chambaud P (1979) Some limitations to measurements of turbulence micro-structure with hot and cold wires. Boundary-Layer Meteorol 19:311–329

    Google Scholar 

  • Monin AS, Yaglom AM (1975) Statistical fluid mechanics, vol 2. MIT Press, Cambridge, Mass.

  • Mydlarski L, Warhaft Z (1996) On the onset of high-Reynolds-number grid-generated wind tunnel turbulence. J Fluid Mech 320:331–368

    Google Scholar 

  • Mydlarski L, Warhaft Z (1998) Passive scalar statistics in high-Peclet-number grid turbulence. J Fluid Mech 358:135–175

    Article  Google Scholar 

  • Obukhov AM (1949) Structure of the temperature field in turbulent flows. Izv Akad Nauk SSSR, Geogr Geofiz 13:58–69

    Google Scholar 

  • Phan-Thien N, Antonia RA (1994) Isotropic Cartesian tensors of arbitrary even orders and velocity gradient correlation functions. Phys Fluids 6:3818–3822

    Article  CAS  Google Scholar 

  • Pumir A (1994) A numerical study of the mixing of a passive scalar in three dimensions in the presence of a mean gradient. Phys Fluids 6:2118–2132

    Article  CAS  Google Scholar 

  • Shafi HS, Antonia RA (1997) Statistics of ∂u/∂y in a turbulent wake. Fluid Dyn Res 19:169–183

    Article  Google Scholar 

  • Shen X, Warhaft Z (2000) The anisotropy of the small scale structure in high Reynolds number (R λ ~1000) turbulent shear flow. Phys Fluids 12:2976–2989

    Article  CAS  Google Scholar 

  • Sreenivasan KR (1991) On local isotropy of passive scalars in turbulent shear flows. Proc Roy Soc Lond A434:165–182

    Google Scholar 

  • Sreenivasan KR, Antonia RA (1997) The phenomenology of small-scale turbulence. Ann Rev Fluid Mech 29:435–472

    Article  Google Scholar 

  • Sreenivasan KR, Antonia RA, Danh HQ (1977) Temperature dissipation fluctuations in a turbulent boundary layer. Phys Fluids 20:1238–1249

    Google Scholar 

  • Sreenivasan KR, Tavoularis S, Henry R, Corrsin S (1980) Temperature fluctuations and scales in grid-generated turbulence. J Fluid Mech 100:597–621

    Google Scholar 

  • Stolovitzky G, Sreenivasan KR, Juneja A (1993) Scaling functions and scaling exponents in turbulence. Phys Rev E 48:R3217

    Google Scholar 

  • Strohl A, Comte-Bellot G (1973) Aerodynamic effects due to configuration of X-wire anemometers. J Appl Mech 40:661–666

    Google Scholar 

  • Van Atta CW, Antonia RA (1980) Reynolds number dependence of skewness and flatness factors of turbulent velocity derivatives. Phys Fluids 23:252–257

    Google Scholar 

  • Wallace JM, Foss JF (1995) The measurement of vorticity in turbulent flows. Ann Rev Fluid Mech 27:467–514

    Article  Google Scholar 

  • Warhaft Z, Lumley JL (1978) An experimental study of the decay of temperature fluctuations in grid-generated turbulence. J Fluid Mech 88:659–684

    Google Scholar 

  • Warhaft Z, Shen X (2001) Some comments on the small scale structure of turbulence at high Reynolds number. Phys Fluids 13:1532–1533

    Article  CAS  Google Scholar 

  • Wyngaard JC (1969) Spatial resolution of the vorticity meter and other hot wire arrays. J Sci Instrum 2:983–987

    Article  Google Scholar 

  • Zhou T, Antonia RA (2000a) Approximation for turbulent energy and temperature dissipation rates in grid turbulence. Phys Fluids 12:335–344

    CAS  Google Scholar 

  • Zhou T, Antonia RA (2000b) Reynolds number dependence of the small-scale structure of grid turbulence. J Fluid Mech 406:81–107

    CAS  Google Scholar 

  • Zhou T, Danaila L, Antonia RA, Anselmet F (2000) Transport equations for the mean energy and temperature dissipation rates in grid turbulence. Exp Fluids 28:143–151

    Article  Google Scholar 

  • Zhu Y, Antonia RA, Kim J (1993) Velocity and temperature derivative measurements in the near-wall region of a turbulent duct flow. In: So RMC, Speziale CG, Launder BE (eds) Near-wall turbulent flows. Elsevier Science, Amsterdam, pp 549–561

Download references

Acknowledgements

RAA gratefully acknowledges the support of the Australian Research Council. An IREX grant support J-J. Lasserre's visit to Newcastle.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. A. Antonia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, T., Antonia, R.A., Lasserre, JJ. et al. Transverse velocity and temperature derivative measurements in grid turbulence. Exp Fluids 34, 449–459 (2003). https://doi.org/10.1007/s00348-002-0566-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-002-0566-9

Keywords

Navigation