Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-19T03:23:24.845Z Has data issue: false hasContentIssue false
  • English
  • Français

Dispersal by randomly varying currents

Published online by Cambridge University Press:  20 April 2006

G. T. Csanady
G. T. Csanady
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543
Get access Rights & Permissions [Opens in a new window]

Abstract

The long-term oceanic dispersal of persistent contaminants is approached as a problem in turbulent diffusion, with tidal, wind-driven, and other variable currents relegated to turbulence. The mean advection velocity in this problem is typically small compared with the r.m.s. fluctuation. Therefore, close to a continuous concentrated source, puffs of contaminant of all ages are present and have significant effects. Old puffs, i.e. those released a long time previously, give rise to a background concentration field. Young puffs affect the local contaminant concentration p.d.f. according to the probability of their presence, quantified by the visitation frequency.

The behaviour of young puffs is governed by variable advection and may be described approximately in terms of probability distributions obtainable from current-meter data. The visitation frequency can be calculated from the distribution of escape probability density, a Lagrangian equivalent of flux. A long-term effect of variable advection is the distribution of the contaminant over an ‘extended’ source, which serves as a starting point for the random walk of old puffs. The conventional approach of using the diffusion equation to describe this random walk is therefore valid as a description of the near-source background concentration field, provided that the extended source is used in place of the physical source.

A sample calculation for a typical open coastal case shows that the background concentration plume becomes wide compared with source dimensions, of order KH/U, with KH horizontal (eddy and shear) diffusivity, U mean advection velocity. The near-source value of the background concentration is correspondingly low, of order m/hKn, with m the mass-release rate and h the water depth. Visitation frequencies calculated with the aid of current statistics drop rapidly with distance from the source, especially in the cross-shore direction. The typical cross-shore diameter of the extended source region is a few kilometres.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 132 , July 1983 , pp. 375 - 394
Copyright
© 1983 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bartlett, M. S. 1956 An Introduction to Stochastic Processes. Cambridge University Press.
Batchelor, G. K. 1949 Diffusion in a field of homogeneous turbulence. I. Eulerian analysis. Austral. J. Sci. Res.Google Scholar
Batchelor, G. K. 1952 Diffusion in a field of homogeneous turbulence: The relative motion of particles. Proc. Camb. Phil. Soc. 48A, 345–362.Google Scholar
Brooks, N. H. 1960 Diffusion of sewage effluent in an ocean current. In Waste Disposal in the Marine Environment (ed. Pearson), pp. 246–267. Pergamon.
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids, 2nd edn. Oxford University Press.
Csanady, G. T. 1973 Turbulent Diffusion in the Environment. Reidel.
Feller, W. 1950 An Introduction to Probability Theory and Its Applications. Wiley.
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic.
Ketchum, B. H. & Keen, D. J. 1955 The accumulation of river water over the continental shelf between Cape Cod and Chesapeake Bay. Deep-Sea Res. 3 (suppl.), 346–357.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, vol. I. MIT Press.
Pasquill, F. 1974 Atmospheric Diffusion, 2nd edn. Halstead/Wiley.
Roberts, P. H. 1961 Analytical theory of turbulent diffusion J. Fluid Mech. 11, 257–283.Google Scholar
Snooks, J. H. & Jacobson, J. P. 1979 Currents and Residual Drift in Block Island Sound During the Period February Through December 1978 Yankee Atomic Electric Co., Westborough, Mass.
Spencer, D. W., Bacon, M. P. & Brewer, P. G. 1981 Models of the distribution of 210Pb in a section across the North Equatorial Atlantic Ocean. J. Mar. Res. 39, 119–138.Google Scholar
Taylor, G. I. 1922 Diffusion by continuous movements Proc. Lond. Math. Soc. A20, 196–212.Google Scholar