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On relating Eulerian and Lagrangian velocity statistics: single particles in homogeneous flows

Published online by Cambridge University Press:  20 April 2006

Russ E. Davis
Russ E. Davis
Affiliation:
Scripps Institution of Oceanography, La Jolla, California 92093
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Abstract

Various theories seeking to relate the velocity statistics of Lagrangian particles to the statistics of the Eulerian flow in which they are embedded are examined. Mean particle drift, mean-square particle velocity and the frequency spectrum of velocity are examined for stationary, homogeneous and joint-normally distributed Eulerian fields. Predictions based on a third-order weak-interaction expansion, the successive approximation procedure of Phythian (1975), the quasi-normal approximation of Saffman (1969), the parametrized model of Saffman (1962), and a new procedure based on a statistical estimator of the kinematic equation are compared with simulations of particle motion in one-dimensional flow. Only the statistical estimator produces both acceptable mean-drift and frequency-spectrum predictions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 114 , January 1982 , pp. 1 - 26
Copyright
© 1972 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions, Chap. 7. Nat. Bureau of Standards, Washington, D.C.
Corrsin, S. 1960 Progress report on some turbulent diffusion research. In Proc. Symp. on Atmospheric Diffusion and Air Pollution, pp. 161–164. Academic.
Davis, R. E. 1977 Techniques for statistical analysis and prediction of geophysical fluid systems. Geophys. Astrophys. Fluid Dyn. 8, 245–277.Google Scholar
Hasselman, K. 1966 Feynman diagrams and interaction rules of wave — wave scattering processes. Rev. Geophys. Space Phys. 4, 1–32.Google Scholar
Hinze, J. O. 1959 Turbulence, Chap. 5. McGraw-Hill.
Hoult, D. P. 1968 Euler-Lagrange relationship for random dispersive waves. Phys. Fluids 11, 2082–2086.Google Scholar
Kenyon, K. E. 1969 Stokes drift for random gravity waves. J. Geophys. Res. 74, 6991–6994.Google Scholar
Kraichnan, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497–543.Google Scholar
Kraichnan, R. H. 1965 Lagrangian — history closure approximation for turbulence. Phys. Fluids 8, 575–598.Google Scholar
Kraichnan, R. H. 1970 Diffusion by a random velocity field. Phys. Fluids 13, 22–31.Google Scholar
Kraichnan, R. H. 1977 Lagrangian velocity covariance in helical turbulence. J. Fluid Mech. 81, 385–398.Google Scholar
Liu, H. & Thompson, R. 1974 Conversion of Eulerian to Lagrangian statistics in one dimension. Utilitas Math. 10, 109–128.Google Scholar
Lorenz, E. N. 1977 An experiment in nonlinear statistical weather forecasting. Mon. Wea. Rev. 105, 590–602.Google Scholar
Lundgren, T. S. & Pointin, Y. B. 1976 Turbulent self-diffusion. Phys. Fluids 19, 355–358.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.
Phythian, R. 1975 Dispersion by random velocity fields. J. Fluid Mech. 67, 145–153.Google Scholar
Richardson, L. F. 1926 Atmospheric diffusion shown on a distance — neighbour graph. Proc. R. Soc. Lond. A 110, 709–727.Google Scholar
Roberts, P. H. 1961 Analytical theory of turbulent diffusion. J. Fluid Mech. 11, 257–283.Google Scholar
Saffman, P. G. 1962 An approximate calculation of the Lagrangian autocorrelation coefficient for stationary homogeneous turbulence. Appl. Sci. Res. A 11, 245–255.Google Scholar
Saffman, P. G. 1969 An application of the Weiner — Hermite expansion to diffusion of a passive scalar in a homogeneous turbulent flow. Phys. Fluids 12, 1786–1798.Google Scholar
Stommel, H. 1949 Horizontal diffusion due to oceanic turbulence. J. Mar. Res. 8, 199–225.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196–212.Google Scholar