Abstract
Spectral corrections, which are based on local isotropy, are presented for all the spatial derivatives of velocity and temperature fluctuations which feature in the average dissipations of turbulent energy and temperature. The corrections, which compensate for the spectral attenuation due to the separation between sensors, depend only weakly on the choice of the three-dimensional energy (or temperature) spectrum and therefore on the turbulence Reynolds number. Corrections are also obtained for the variances of velocity and temperature derivatives. The diagonal velocity derivatives require smaller corrections than either the off-diagonal velocity derivatives or the temperature derivatives. Corrections of comparable magnitude are required for the average dissipations of turbulent energy and temperature.
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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
Antonia, R. A.; Shah, D. A.; Browne, L. W. B. 1987: Spectra of velocity derivatives in a turbulent wake. Phys. Fluids 30, 3455–3462
Antonia, R. A.; Shah, D. A.; Browne, L. W. B. 1988a: Dissipation and vorticity spectra in a turbulent wake. Phys. Fluids 31, 1805–1807
Antonia, R. A.; Browne, L. W. B.; Shah, D. A. 1988b: Characteristics of vorticity fluctuations in a turbulent wake. J. Fluid Mech. 189, 349–365
Antonia, R. A.; Browne, L. W. B.; Kim, J. 1991: Some characteristics of small scale turbulence in a turbulent duct flow. J. Fluid Mech. 233, 369–388
Batchelor, G. K. 1953: The theory of homogeneous turbulence. Cambridge: Cambridge University Press
Browne, L. W. B.; Antonia, R. A.; Chambers, A. J. 1983: Effect of the separation between cold wires on the spatial derivatives of temperature in a turbulent flow. Boundary-Layer Meteorol. 27, 129–140
Champagne, R. H. 1978: The fine-scale structure of the turbulent velocity field. J. Fluid Mech. 86, 67–108
Champagne, F. H.; Friehe, C. A.; LaRue, J. C.; Wyngaard, J. C. 1977: Flux measurements, flux estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land. J. Atmos. Sci. 34, 515–530
Corrsin, S. 1964: Further generalization of Onsager's cascade model for turbulent spectra. Phys. Fluids 7, 1156–1159
Domaradzky, J. A.; Rogallo, R. S. 1991: Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence. Phys. Fluids A, 2, 413–426
Durbin, P. A.; Speziale, C. G. 1991: Local anisotropy in strained turbulence at high Reynolds numbers. J. Fluids Eng. 113, 707–709
Hinze, J. O. 1959: Turbulence — an introduction to its mechanism and theory. New York: McGraw-Hill
Kolmogorov, A. N. 1941: The local structure of turbulence in an incompressible fluid with very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 30, 301–305
Mestayer, P.; Chambaud, P. 1979: Some limitation to measurements of turbulence micro-structure with hot- and cold-wires. Boundary-Layer Meteorol. 16, 311–329
Pao, Y.-H. 1965: Structure of turbulent velocity and scalar fields in large wavenumbers. Phys. Fluids 8, 1063–1075
Roberts, J. B. 1973: On the correction of hot wire turbulence measurements for spatial resolution errors. Aero. Jnl. 77, 406–412
Smith, L. M.; Reynolds, W. C. 1991: The dissipation-range spectrum and the velocity-derivative skewness in turbulent flows. Phys. Fluids A 3, 992–994
Uberoi, M. S.; Kovasznay, L. S. G. 1953: On mapping and measurement of random fields. Q. Appl. Math. 10, 375–393
Wyngaard, J. C. 1968: Measurements of small-scale turbulence structure with hot wires. J. Sci. Instrum. 1, 1105–1108
Wyngaard, J. C. 1969: Spatial resolution of the vorticity meter and other hot-wire arrays. J. Sci. Instrum. 2, 983–987
Wyngaard, J. C. 1971: Spatial resolution of a resistance wire temperature sensor. Phys. Fluids 14, 2052–2054
Yeung, P. K.; Brasseur, J. G. 1991: The response of isotropic turbulence to isotropic and anisotropic forcing at the large scales. Phys. Fluids A 3, 884–897
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Antonia, R.A., Mi, J. Corrections for velocity and temperature derivatives in turbulent flows. Experiments in Fluids 14, 203–208 (1993). https://doi.org/10.1007/BF00189511
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DOI: https://doi.org/10.1007/BF00189511