'WHHIT)1TY IXFFUSION BY SHEAR EFTTC'T
337
terms being
(31)
As oiie might expect, this creates numerical difficulties and required ;L
careful test of several techniques before a reliable one was perfected (Adam
and Runfola, 1973).
In many cases, when one is only interested in a prediction of the pollutant's concentration every one or two tidal periods, it is advantageous first to
average Eq. (30) over a tidal period. This generally reduces considerably the
numerical difficulties and it is easy to see why it should be so. Indeed, if, in
Eq. (31), 5 was independent of time, the integration over a tidal period
would make the operator elliptic by virtue of Swam's inequality. Of course
E is not independent of time in general and in particular in the case of
dispersion from an instantaneous source simulating a dumping. However it
is usually possible to separate u and 5 into slowly varying parts (over a tidal
period) and rapidly oscillating parts (with the tidal period) and to apply the
averaging technique of Krylov. Bogoliubov, and Mitropolsky with the same
benefit (Nihoul, 1972).
The most important limitation of the model is due in most cases to the
lack of precision in the observed or calculated values of U. In situations
where the velocity field was known with great accuracy, the spreading and
distortion of the pollutant patches were always faithfully depicted by the
model; confirming the importance of the shear effect dispersion in shallow
open seas.
ACKNOWLEDGMENTS
This study was supported by the Department of Scientific Politics in the scope of the
Programnil, N(irinn(i1 Brlyr sur I' Eni3ironmcni Physique ri Biologique.
REFERENCES
Atkim, Y.. and Runfola. Y. (1973). Projct Mcr, N / 4 . Programme Nat. Environ. Phys. Riot..
Bowdcii. K . F. (1Y65). 1. Fluid Mech. 21. 83-95,
Bowden. K. F.. :ind Fairbuirn, L. A. (1952). Pror. Roy. Soc., Ser. .4 214. 371 392.
IMer. J. W. (1959). J . I.lrticl Much. 5, 544-5643.
Ellison. T. M. (1957). J . Fluid Mech. 2, 456466.
Nihoul, J. <'. J. (1971). Proc. North SPU Sci. C-mj:. Ai*irniorc., Scotland 1. 89-108.
Nihoul, J. c'. J. (1972). Bull. Soc. Sci. Liege 10. 521VS26.
Nihoul, J. C . J. (1973). Proc. Liege Colloy. Oceun Hydrcdyn., 5th pp. 1-10.
Taylor. G . I. (1953). Proc. Roy. Soc.. Ser. A 219, 186- 201.
Taylor, G . I. (1954). Proc. Roy. Soc., Sur. A 223, 4.16-468.
Van Veen, J. (1938). J . Cons.. Cons. Permu. In!. Explor. Mer 13, 7-36.
Dcp. Sri. I'oliiics, Liege.
337
terms being
(31)
As oiie might expect, this creates numerical difficulties and required ;L
careful test of several techniques before a reliable one was perfected (Adam
and Runfola, 1973).
In many cases, when one is only interested in a prediction of the pollutant's concentration every one or two tidal periods, it is advantageous first to
average Eq. (30) over a tidal period. This generally reduces considerably the
numerical difficulties and it is easy to see why it should be so. Indeed, if, in
Eq. (31), 5 was independent of time, the integration over a tidal period
would make the operator elliptic by virtue of Swam's inequality. Of course
E is not independent of time in general and in particular in the case of
dispersion from an instantaneous source simulating a dumping. However it
is usually possible to separate u and 5 into slowly varying parts (over a tidal
period) and rapidly oscillating parts (with the tidal period) and to apply the
averaging technique of Krylov. Bogoliubov, and Mitropolsky with the same
benefit (Nihoul, 1972).
The most important limitation of the model is due in most cases to the
lack of precision in the observed or calculated values of U. In situations
where the velocity field was known with great accuracy, the spreading and
distortion of the pollutant patches were always faithfully depicted by the
model; confirming the importance of the shear effect dispersion in shallow
open seas.
ACKNOWLEDGMENTS
This study was supported by the Department of Scientific Politics in the scope of the
Programnil, N(irinn(i1 Brlyr sur I' Eni3ironmcni Physique ri Biologique.
REFERENCES
Atkim, Y.. and Runfola. Y. (1973). Projct Mcr, N / 4 . Programme Nat. Environ. Phys. Riot..
Bowdcii. K . F. (1Y65). 1. Fluid Mech. 21. 83-95,
Bowden. K. F.. :ind Fairbuirn, L. A. (1952). Pror. Roy. Soc., Ser. .4 214. 371 392.
IMer. J. W. (1959). J . I.lrticl Much. 5, 544-5643.
Ellison. T. M. (1957). J . Fluid Mech. 2, 456466.
Nihoul, J. <'. J. (1971). Proc. North SPU Sci. C-mj:. Ai*irniorc., Scotland 1. 89-108.
Nihoul, J. c'. J. (1972). Bull. Soc. Sci. Liege 10. 521VS26.
Nihoul, J. C . J. (1973). Proc. Liege Colloy. Oceun Hydrcdyn., 5th pp. 1-10.
Taylor. G . I. (1953). Proc. Roy. Soc.. Ser. A 219, 186- 201.
Taylor, G . I. (1954). Proc. Roy. Soc., Sur. A 223, 4.16-468.
Van Veen, J. (1938). J . Cons.. Cons. Permu. In!. Explor. Mer 13, 7-36.
Dcp. Sri. I'oliiics, Liege.