Summary
In a new kind of random walk, displaying both Lagrangian and Eulerian statistical properties1), calculations were made previously of the Eulerian and Lagrangian velocity auto-correlations. Now the characteristic function of particle displacement has been calculated, and possible continuum limit forms for the probability density equation have been deduced. One of these turns out to be the telegraph equation, given by Goldstein2) as the limit of a different kind of random walk. For this case the auto-correlation functions have been determined.
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References
Lumley, J. and S. Corrsin, Proc. Int. Symp. on atm. Diffusion and Air Pollution, Advances in Geophysics, Vol. 6, Academic Press, 1949.
Goldstein, S., Quart. J. Mech. Appl. Math. 4 (1951) Pt 2.
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This work was supported by the Mechanics Branch, U.S. Office of Naval Research, under contract Nonr 248 (38) and was presented in Session F of the 1959 Annual Meeting of the American Physical Society at New York under the title “A Random Walk with both Lagrangian and Eulerian Statistics.”
Associate Professor of Engineering Research, Ordnance Research Laboratory, The Pennsylvania State University. This work was done as Research Associate, Post-Doctoral Fellow, Mechanical Engineering Department, The Johns Hopkins University.
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Lumley, J.L. Distribution and dispersion in the Euler-Lagrange random walk. Appl. sci. Res. 10, 153 (1961). https://doi.org/10.1007/BF00411907
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DOI: https://doi.org/10.1007/BF00411907