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Mass transport in two-dimensional water waves

Published online by Cambridge University Press:  26 April 2006

Mohamed Iskandarani  and
Philip L.-F. Liu
Mohamed Iskandarani
Affiliation:
Joseph Defrees Hydraulics Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
Philip L.-F. Liu
Affiliation:
Joseph Defrees Hydraulics Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

Mass transport in various kind of two-dimensional water waves is studied. The characteristics of the governing equations for the mass transport depend on the ratio of viscous lengthscale to the amplitude of the free-surface displacement. When this ratio is small, the nonlinearity is important and the mass transport flow acquires a boundary-layer character. Numerical schemes are developed to investigate mass transport in a partially reflected wave and above a hump in the seabed. When the mass transport is periodic in the horizontal direction, a spectral scheme based on a Fourier–Chebyshev expansion, is presented for the solution of the equations. For the ease of a hump on the seabed, the flow domain is divided into three regions. Using the spectral scheme, the mass transport in the uniform-depth regions is calculated first. and the results are used to compute the steady flow in the inhomogeneous flow region which encloses the hump on the seabed.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 231 , October 1991 , pp. 395 - 415
Copyright
© 1991 Cambridge University Press

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References

Baker, A. J. 1983 Finite Element Computational Fluid Mechanics. Hemisphere.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bertelsen, A., Svardal, A. & Tjotta, S. 1973 Nonlinear streaming effects associated with oscillating cylinders. J. Fluid Mech. 59, 493–511.Google Scholar
Boyd, J. P. 1989 Chebyshev and Fourier Spectral Methods (ed. C. A. Brebbia & S. A. Orszag), Lecture Notes in Engineering. Springer.
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer Series in Computational Physics. Springer.
Dore, B. D. 1976 Double boundary layer in standing surface waves. Pure Appl. Geophys. 114, 629–637.Google Scholar
Duck, P. W. & Smith, F. T. 1979 Steady streaming induced between, oscillating cylinders. J. Fluid Mech. 91, 93–110.Google Scholar
Gottlieb, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Applications. Philadelphia: SIAM-CBMS.
Haddon, E. W. & Riley, N, 1983 A note on the mean circulation in standing waves. Wave Motion 5, 43–48.Google Scholar
Iskandarani, M. 1991 Mass transport in two- and three-dimensional water waves. PhD thesis, Cornell University.
Iskandarani, M. & Liu, P. L.-F. 1991 Mass transport in three-dimensional water waves. J. Fluid Mech. 231, 417–437.Google Scholar
Liu, P. L.-F. & Abbaspour, M. 1982 An integral equation method for the diffraction of oblique waves by an infinite cylinder. Intl J. Numer. Method. Engng 18, 1497–1504.Google Scholar
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245, 535–581.Google Scholar
Longuet-Higgins, M. S. 1960 Mass transport in the boundary layer at a free oscillating surface. J. Fluid Mech. 8, 293–306.Google Scholar
Riley, N. 1965 Oscillating viscous flows. Mathematika 12, 161–175.Google Scholar
Riley, N. 1984 Progressing surface waves on a liquid of non-uniform depth. Wave Motion 6, 15–22.Google Scholar
Roache, P. J. 1982 Computational Fluid Dynamics.
Hermosa. Russell, R. C. H. & Osorio, J. D. C. 1958 An experimental investigation of drift profiles in a closed channel. In Proc. Sixth Con/, on Coastal Engng, pp. 171–193. ASCE.
Stuart, J. T. 1966 Double boundary layer in oscillatory viscous flow. J. Fluid Mech. 24, 673–687.Google Scholar
Ünlüuata, Ü. & Mei, C. C. 1970 Mass transport in water waves. J. Geophys. Res. 75, 7611–7618.Google Scholar