Abstract
The Lagrangian diffusion equation appropriate for the dispersion of current followers (e. g., floats, drogues, drifters) is proposed. The analytical solution to the equation is obtained for a uniform deformation field, characterized by Lagrangian deformations and anisotropic eddy diffusivities both varying with time. Expressions are derived for the patch area and its elongation and rotation. For small values of elapsed time after the initial release the patch area can be accounted for by the exponential of the cumulative value of the horizontal divergence; the relative rate of change of the patch area can be accounted for by the horizontal divergence.
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References
Attermeyer, M. (1974): Models for viscous dissipation of energy obtained from the Lagrangian form of the equations of motion. Phys. Fluids,17, 679–687.
Batchelor, G. K. (1952): Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc. Cambridge Phil. Soc.,48, 345–362.
Chevray, R. and K. S. Venkataramani (1979): Total dispersion of a scalar quantity in turbulent flow. Phys. Fluids,22, 2284–2288.
Chew, F. and G. A. Berberian (1971): A determination of horizontal divergence in the Gulf Stream off Cape Lookout. J. Phys. Oceanogr.,1, 39–44.
Corrsin, S. (1962): Theories of turbulent dispersion. Mechanics of Turbulence, Proc. Intern. Symp. National Science Research Center, Marseille, 28 August – 28 September, 1961, Gordon and Breach, 27–52.
Kawai, H. (1976): Convergence, divergence, and particulate physics in the sea. In: Lectures in Oceanography, vol. 2, Physical Oceanography II, ed. by T. Teramoto, University of Tokyo Press, p. 103–155 (in Japanese).
Kawai, H. (1979): Examples of observation on fine current-structures and their influence on the aggregation of floating particles. Fishery Civil Engineering (“Suisan Doboku”)16, 25–32 (in Japanese).
Kirwan, A. D. (1975): Oceanic velocity gradients. J. Phys. Oceanogr.,5, 729–735.
Monin, A. S. (1962): On the Lagrangian equations of the hydrodynamics of an incompressible viscous fluid. J. Appl. Math. and Mech.,26, 458–468 (English edition).
Okubo, A. (1966): A note on horizontal diffusion from an instantaneous source in a nonuniform flow. J. Oceanogr. Soc. Japan,22, 35–40.
Okubo, A. (1967): Study of turbulent dispersion by use of Lagrangian diffusion equation. Phys. Fluids, Suppl. 1967, S 72–75.
Okubo, A., C. C. Ebbesmeyer and J. M. Helseth, (1976a): Determination of Lagrangian deformations from analysis of current followers. J. Phys. Oceanogr.,6, 524–527.
Okubo, A., C. C. Ebbesmeyer, J. M. Helseth, and A. S. Robbins. (1976b): Reanalysis of the Great Lakes drogue studies data. Special Report No. 2, Marine Sciences Research Center, State University of New York, Stony Brook (Reference 76–2), 84 pp.
Reed, R. K. (1971): An observation of divergence in the Alaskan Stream. J. Phys. Oceanogr.,1, 282–283.
Richardson, L. F. (1926): Atmospheric diffusion shown on a distance-neighbour graph. Proc. Roy. Soc. London,A110, 709–727.
Taylor, G. I. (1921): Diffusion by continuous movements. Proc. London Math. Soc., Ser. 2,20, 196–211.
Yanagi, T., K. Murashita and H. Higuchi (1982): Horizontal turbulent diffusivity in the sea. Deep-Sea Res.,29A, 217–226.
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Contribution No. 379 of Marine Sciences Research Center, State University of New York at Stony Brook.
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Okubo, A., Ebbesmeyer, C.C. & Sanderson, B.G. Lagrangian diffusion equation and its application to oceanic dispersion. Journal of the Oceanographical Society of Japan 39, 259–266 (1983). https://doi.org/10.1007/BF02070396
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DOI: https://doi.org/10.1007/BF02070396