Abstract
Lagrangian integral time scales were calculated from crosswind concentration distributions of oil-fog smoke released from a continuous point source over the ocean during stable atmospheric conditions assuming an exponential correlation function. Variance of the lateral velocity fluctuations, Σ v 2, and the energy dissipation rate, ɛ, were obtained from simultaneous Eulerian measurements at the beach. An Eulerian energy dissipation scale defined as Σ v 2/ɛ was then computed. The ratio of the Lagrangian integral scale to the Eulerian energy dissipation scale was found to be close to 1. This ratio was also estimated to be 1 based on physical and dimensional considerations regarding the cascade of energy. Length scales for longitudinal, lateral and vertical directions were interpreted with a model based on similarity considerations applicable for over-water atmospheric flows.
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References
Angell, J. K.: 1964, ‘Measurements of Lagrangian and Eulerian Properties of Turbulence at a Height of 2500 ft’, Quart. J. Roy. Meteorol. Soc. 90, 57–71.
Angell, J. K., Pack, D. H., Hoecker, W. H., and Delver, N.: 1971, ‘Lagrangian-Eulerian Time-Scale Ratios Estimated from Constant Volume Balloon Flights Past a Tall Tower’, Quart. J. Roy. Meteor. Soc. 97, 87–92.
Barad, M. E.: 1959, ‘Analysis of Diffusion Studies at O'Neill’, Adv. Geophys. 6, 389–398.
Blackman, R. B. and Tukey, J. W.: 1958, The Measurement of Power Spectra, Dover Publications, New York.
Danielson, D., Mizuno, T., Moravek, D., Sullivan, D., Thompson, D. W., and Panofsky, H. A.: 1974, Two-point Statistics over Lake Ontario. Final Report, Department of Meteorology, The Pennsylvania State University, University Park, Pa., 88 pp.
Draxler, R. R.: 1976, ‘Determination of Atmospheric Diffusion Parameters’, Atmos. Environ. 10, 99–105.
Ellison, T. H.: 1957, ‘Turbulent Transport of Heat and Momentum from an Infinite Rough Plane’, J. Fluid Mech. 2, 456–466.
Gifford, F. A.: 1955, ‘A Simultaneous Lagrangian-Eulerian Turbulence Experiment’, Mon. Weath. Rev. 83, 293–301.
Gifford, F. A.: 1967, ‘Variation of the Lagrangian-Eulerian Time Scale Relationship with Stability’, USAEC Meteorological Information Meeting, Chalk River, Canada (AECL-2787), pp. 485–499.
Haugen, D. A.: 1966, ‘Some Lagrangian Properties of Turbulence Deduced from Atmospheric Experiments’, J. Appl. Meteor. 5, 646–652.
Hay, J. S. and Pasquill, F.: 1959, ‘Diffusion from a Continuous Source in Relation to the Spectrum and Scale of Turbulence’, Adv. Geophys. 6, 345–365.
Hinze, J. O.: 1959, Turbulence, McGraw-Hill, New York, 586 pp.
Inoue, E.: 1959, ‘The Effects of Thermal Stratification on Turbulent Diffusion in the Atmospheric Surface Layer’, Adv. Geophys. 6, 319–329.
Lumley, J. L. and Panofsky, H. A.: 1964, The Structure of Atmospheric Turbulence, Interscience Publishers, New York, 239 pp.
Miyake, M., Stewart, R. W., and Burling, R. W.: 1970, ‘Spectra and Co-spectra of Turbulence over Water’, Quart. J. Roy. Meteorol. Soc. 96, 138–143.
Monin, A. S. and Yaglom, A. M.: 1971, Statistical Fluid Mechanics: Mechanics of Turbulence, The MIT Press, Cambridge, Mass., 769 pp.
Panofsky, H. A.: 1962, ‘Scale Analysis of Atmospheric Turbulence at 2 m’, Quart. J. Roy. Meteorol. Soc. 88, 57–69.
Pasquill, F.: 1974, Atmospheric Diffusion, 2nd Ed., John Wiley, New York, 429 pp.
Philip, J. R.: 1967, ‘atRelation Between Eulerian and Lagrangian Statistics’, The Phys. of Fluids Supplement, 69–71.
Pond, S., Phelps, G. T., Pasquin, J. E., McBean, G., and Stewart, R. W.: 1971, ‘Measurements of the Turbulent Fluxes of Momentum, Moisture and Sensible Heat over the Ocean’, J. Atmos. Sci. 28, 901–907.
Raynor, G. S., Michael, P., Brown, R. M., and Sethuraman, S.: 1975, ‘Studies of Atmospheric Diffusion from a Nearshore Oceanic Site’, J. Appl. Meteorol. 14, 1080–1094.
SethuRaman, S. and Brown, R. M.: 1976, ‘A Comparison of Turbulence Measurements Made by a Hot-Film Probe, a Bivane, and a Directional Vane in the Atmospheric Surface Layer’, J. Appl. Meteorol. 15, 138–144.
SethuRaman, S., Brown, R. M., and Tichler, J.: 1974, Spectra of Atmospheric Turbulence over the Sea During Stably Stratified Conditions, Preprints Symp. Atmospheric Diffusion and Air Pollution, Santa Barbara, Calif., 9–13 Sept., Am. Meteor. Soc., pp. 71–76.
Taylor, R. J.: 1952, ‘The Dissipation of Kinetic Energy in the Lowest Layers of the Atmosphere’, Quart. J. Roy. Meteorol. Soc. 78, 179.
Tennekes, H. and Lumley, J. L.: 1972, A First Course in Turbulence, The MIT Press, Cambridge, Mass., 300 pp.
Thompson, N.: 1965, ‘Short-Range Vertical Diffusion in Stable Conditions’, Quart. J. Roy. Meteorol. Soc. 91, 175–183.
Thompson, N.: 1966, ‘The Estimation of Vertical Diffusion over Medium Distances of Travel’, Quart. J. Roy. Meteorol. Soc. 92, 270–276.
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Authored under contract EY-76-C-02-0016 with the U.S. Department of Energy. Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes.
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Sethuraman, S., Meyers, R.E. & Brown, R.M. A comparison of a Eulerian and a Lagrangian time scale for over-water atmospheric flows during stable conditions. Boundary-Layer Meteorol 14, 557–565 (1978). https://doi.org/10.1007/BF00121894
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DOI: https://doi.org/10.1007/BF00121894