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A numerical study of the wave-induced solute transport above a rippled bed

Published online by Cambridge University Press:  26 April 2006

K. T. Shum
K. T. Shum
Affiliation:
Maurice Lamontagne Institute, Department of Fisheries & Oceans, Mont-Joli, Québec, Canada G5H 3Z4 Present address: Contra Costa Water District, 1331 Concord Avenue, PO Box H20, Concord, CA 94524, USA.
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Abstract

The role of wave-induced separated flow in solute transport above a rippled bed is studied from numerical solutions to the two-dimensional Navier–Strokes equations and the advection-diffusion equation. A horizontal ambient flow that varies sinusoidally in time is imposed far above the bed, and a constant concentration difference between the upper and lower boundaries of computation is assumed. The computed flow field is the sum of an oscillatory rectilinear flow and a vortical flow which is periodic both in time and in the horizontal. Poincaré sections of this flow suggest chaotic mixing. Vertical lines of fluid particles above the crest and above the trough deform into whorls and tendrils, respectively, in just one wave period. Horizontal lines near the bottom deform into Smale horseshoe patterns. The combination of high shear and vortex-induced normal velocity close to the sediment surface results in large net displacements of fluid particles in a period. The resulting advective transport normal to the bed can be higher than molecular diffusion from well within the viscous boundary layer up to a few ripple heights above the bed. When this flow field is applied to the transport equation of a passive scalar, two distinct features – regular temporal oscillations in concentration and a linear time-averaged vertical concentration profile – are found immediately above the bed. These features have also been observed previously in field measurements on oxygen concentration. Advective transport is shown to be dominant even in the region where the time-averaged concentration profile is linear, a region where vertical solute transport has often been estimated using diffusion-type models in many field studies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 299 , 25 September 1995 , pp. 267 - 288
Copyright
© 1995 Cambridge University Press

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References

Anderson, D. A., Tannehill, J. C. & Pletcher, R. H. 1984 Computational Fluid Mechanics and Heat Transfer. Hemisphere.
Benjamin, T. B. 1959 Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161–205.Google Scholar
Blondeaux, P. & Vittori, G. 1991a Vorticity dynamics in an oscillatory flow over a rippled bed. J. Fluid Mech. 226, 257–289.Google Scholar
Blondeaux, P. & Vittori, G. 1991b A route to chaos in an oscillatory flow: Feigenbaum scenario. Phys. Fluids A 3, 2492–2495.Google Scholar
Carslaw, H. S. & Jaeger, J. C. 1963 Operational Methods in Applied Mathematics. Dover.
Dingler, J. R. & Inman, D. L. 1976 Wave-formed ripples in nearshore sands. In Proc. 14th ASCE Coastal Engineering Conference, pp. 2109–2126.
Du Toit, C. G. & Sleath, J. F. A. 1981 Velocity measurements close to rippled beds in oscillatory flows. J. Fluid Mech. 112, 71–96.Google Scholar
Einstein, A. 1905 Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen.. Annln Phys. 17, (47), 549–560 (In German).Google Scholar
Ghaddar, N. K., Magen, M., Mikic, B. B. & Patera, A. T. 1986 Numerical investigation of incompressible flow in grooved channels. Part 2. Resonance and oscillatory heat-transfer enhancement. J. Fluid Mech. 168, 541–567.Google Scholar
Gundersen, J. K. & JöSrgensen, B. B. 1990 Microstructure of diffusive boundary layers and the oxygen uptake of the sea floor. Nature 345, 604–607.Google Scholar
Hara, T. & Mel, C. C. 1992 Oscillating flows over periodic ripples of finite slope. Phys. Fluids A 4, 1373–1384.Google Scholar
Lazier, J. R. N. & Mann, K. H. 1989 Turbulence and the diffusive layers around small organisms. Deep-Sea Res. 36, 1721–1733.Google Scholar
Mei, C. C. & Liu, P. L.-F. 1993 Surface waves and coastal dynamics. Ann. Rev. Fluid Mech. 25, 215–240.Google Scholar
Ottino, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge University Press.
Rom-Kedar, V., Leonard, A. & Wiggins, S. 1990 An analytical study of transport, mixing and chaos in an unsteady vortical flow. J. Fluid Mech. 214, 347–394.Google Scholar
Schlichting, H. 1968 Boundary Layer Theory. McGraw Hill.
Shum, K. T. 1988 A numerical study of vortex dynamics over rigid ripples. Doctoral thesis, MIT.
Shum, K. T. 1992 Wave-induced advective transport below a rippled water-sediment interface.. J. Geophys. Res. 97, 789–808; and Corrections, 97 14475–14477.Google Scholar
Shum, K. T. 1993 The effects of wave-induced pore water circulation on the transport of reactive solutes below a rippled sediment bed. J. Geophys. Res. 98, 10289–10301.Google Scholar
Sobey, I. J. 1985 Dispersion caused by separation during oscillatory flow through a furrowed channel. Chem. Engng Sci. 40, 2129–2134.Google Scholar
Ta Phuoc Loc 1980 Numerical analysis of unsteady secondary vortices generated by an impulsively started circular cylinder. J. Fluid Mech. 160, 93–117.Google Scholar
Thorsness, C. B. & Hanratty, T. J. 1979 Mass transfer between a flowing fluid and a solid wavy surface. Am. Inst. Chem. Engng J. 25, 686–697.Google Scholar
Vittori, G. & Tanda, G. 1991 Study of separated flow and heat transfer in two-dimensional channels with wavy walls. In Proc. 24th Congress of Intl Assoc of Hydraulic Res. Madrid, Spain, pp. C203–C210.