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Solution of Howells’ model of the scalar spectrum and comparison with experiment

Published online by Cambridge University Press:  19 April 2006

R. J. Hill
R. J. Hill*
Affiliation:
Wave Propagation Laboratory, Environmental Research Laboratories, National Oceanic and Atmospheric Administration, Boulder, Colorado 80302
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Abstract

Howells’ model of the scalar spectrum for isotropic turbulent flow is simplified using a restriction to large Péclet number and statistically stationary turbulence at high wavenumbers, and is generalized by introducing Batchelor's constant as a free parameter. The resulting model is compared with data from the atmospheric surface layer, ocean, and liquid mercury. It is found that Howells’ model, which is applicable for arbitrary Prandtl number (Pr), does not compare well with data for large and intermediate Pr at wavenumbers higher than those in the inertial-convective range. The model implies that the inertial-diffusive range asymptotic form, , cannot appear even for Pr as small as that of mercury (Pr = 0·018).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 96 , Issue 4 , 27 February 1980 , pp. 705 - 722
Copyright
Copyright © 1980 Cambridge University Press

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References

Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113–133.10.1017/S002211205900009XCrossRefGoogle Scholar
Batchelor, G. K., Howells, I. D. & Townsend, A. A. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 2. The case of large conductivity. J. Fluid Mech. 5, 134–139.10.1017/S0022112059000106CrossRefGoogle Scholar
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, 515–550.10.1175/1520-0469(1977)034<0515:FMFETA>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
Clay, J. P. 1973 Turbulent mixing of temperature in water, air and mercury. Ph.D. thesis, University of California at San Diego.Google Scholar
Gibson, C. H. 1968 Fine structure of scalar fields mixed by turbulence. II. Spectral theory. Phys. Fluids 11, 2316–2327.10.1063/1.1691821CrossRefGoogle Scholar
Grant, H. L., Hughes, B. A., Vogel, W. M. & Moilliet, A. 1968 The spectrum of temperature fluctuations in turbulent flow. J. Fluid Mech. 34, 423–492.10.1017/S0022112068001990CrossRefGoogle Scholar
Hill, R. J. 1978 Models of the scalar spectrum for turbulent advection. J. Fluid Mech. 88, 541–562.10.1017/S002211207800227XCrossRefGoogle Scholar
Howells, I. D. 1960 An approximate equation for the spectrum of a conserved scalar quantity in a turbulent fluid. J. Fluid Mech. 9, 104–106.10.1017/S0022112060000943CrossRefGoogle Scholar
McConnell, S. 1976 The fine structure of velocity and temperature measured in the laboratory and atmospheric marine boundary layer. Ph.D. thesis, University of California at San Diego.Google Scholar
Pao, Y. H. 1965 Structure of turbulent velocity and scalar fields at large wavenumbers. Phys. Fluids 8, 1063–1075.10.1063/1.1761356CrossRefGoogle Scholar
Schmitt, K. F., Friehe, C. A. & Gibson, C. H. 1978 Humidity sensitivity of atmospheric temperature sensors by salt contamination. J. Phys. Oceanog. 8, 151–161.10.1175/1520-0485(1978)008<0151:HSOATS>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
Williams, R. M. & Paulson, C. A. 1977 Microscale temperature and velocity spectra in the atmospheric boundary layer. J. Fluid Mech. 83, 547–567.10.1017/S0022112077001335CrossRefGoogle Scholar
Wyngaard, J. C. 1971 The effects of velocity sensitivity on temperature derivative statistics in isotropic turbulence. J. Fluid Mech. 48, 763–769.10.1017/S0022112071001836CrossRefGoogle Scholar