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A simple model of wave–current interaction

Published online by Cambridge University Press:  23 June 2015

Nicoletta Tambroni ,
Paolo Blondeaux  and
Giovanna Vittori
Nicoletta Tambroni
Affiliation:
Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy
Paolo Blondeaux*
Affiliation:
Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy
Giovanna Vittori
Affiliation:
Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy
*
†Email address for correspondence: blx@dicat.unige.it
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Abstract

The interaction between a steady current and propagating surface waves is investigated by means of a perturbation approach, which assumes small values of the wave steepness and considers current velocities of the same order of magnitude as the amplitude of the velocity oscillations induced by wave propagation. The problems, which are obtained at the different orders of approximation, are characterized by a further parameter which is the ratio between the thickness of the bottom boundary layer and the length of the waves and turns out to be even smaller than the wave steepness. However, the solution is determined from the bottom up to the free surface, without the need to split the fluid domain into a core region and viscous boundary layers. Moreover, the procedure, which is employed to solve the problems at the different orders of approximation, reduces them to one-dimensional problems. Therefore, the solution for arbitrary angles between the direction of the steady current and that of wave propagation can be easily obtained. The theoretical results are compared with experimental measurements; the fair agreement found between the model results and the laboratory measurements supports the model findings.

JFM classification

Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 775 , 25 July 2015 , pp. 328 - 348
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Copyright
© 2015 Cambridge University Press 

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References

Bakker, W. T. & Van Doorn, T. 1978 Near-bottom velocities in waves with a current. In Proceedings of 16th International Conference on Coastal Engineering, pp. 1394–1413. ASCE.Google Scholar
Blondeaux, P. 1987 Turbulent boundary layer at the bottom of gravity waves. J. Hydraul. Res. 25 (4), 447–464.Google Scholar
Blondeaux, P. & Vittori, G. 1994 Wall imperfections as a triggering mechanism for Stokes-layer transition. J. Fluid Mech. 264, 107–135.Google Scholar
Blondeaux, P. & Vittori, G. 1999 Boundary layer and sediment dynamics under sea waves. Adv. Coast. Ocean Engng 4, 133–190.CrossRefGoogle Scholar
Davies, A. G., Soulsby, R. L. & King, H. L. 1988 A numerical model of the combined wave and current bottom boundary layer. J. Geophys. Res. 93 (C1), 491–508.Google Scholar
Dingemans, M. W., Van Kester, J. A. T. M., Radder, A. C. & Uittenbogaard, R. E. 1996 The effect of the CL-vortex force in 3D wave–current interaction. In Proceedings of 25th International Conference on Coastal Engineering, Orlando, FL, pp. 4821–4832.Google Scholar
Fredsøe, J. 1984 Turbulent boundary layer in wave–current motion. ASCE J. Hydraul. Engng 110, 1103–1120.Google Scholar
Fredsøe, J. & Deigaard, R. 1992 Mechanics of Coastal Sediment Transport, Adv. Series on Ocean Engng, vol. 3. World Scientific.Google Scholar
Grant, W. D. & Madsen, O. S. 1979 Combined wave and current interaction with a rough bottom. J. Geophys. Res. 84 (C4), 1797–1808.Google Scholar
Grant, W. D. & Madsen, O. S. 1986 The Continental-Shelf Bottom Boundary Layer. Annu. Rev. Fluid Mech. 18, 265–305.Google Scholar
Groeneweg, J. & Battjes, J. 2003 Three-dimensional wave effects on a steady current. J. Fluid Mech. 478, 325–343.Google Scholar
Groeneweg, J. & Klopman, G. 1998 Changes of the mean velocity profiles in the combined wave–current motion described in a GLM formulation. J. Fluid Mech. 370, 271–296.Google Scholar
Huang, Z. & Mei, C. C. 2003 Effects of surface waves on a turbulent current over a smooth or rough seabed. J. Fluid Mech. 497, 253–287.Google Scholar
Kemp, P. H. & Simons, R. R. 1982 The interaction between waves and a turbulent current: waves propagating with the current. J. Fluid Mech. 116, 227–250.Google Scholar
Kemp, P. H. & Simons, R. R. 1983 The interaction between waves and a turbulent current: waves propagating against the current. J. Fluid Mech. 130, 73–89.Google Scholar
Kim, H., O’Conner, B. A., Park, I & Lee, Y. 2001 Modeling effect of intersection angle on near-bed flows for waves and currents. ASCE J. Waterway Port Coastal Ocean Engng 127 (6), 308–318.Google Scholar
Klopman, G.1994, Vertical structure of the flow due to waves and currents. Tech. Rep. H840.32. Part II. Delft Hydraulics.Google Scholar
Klopman, G.1997, Secondary circulation of the flow due to waves and current. Tech. Rep. Z2249. Delft Hydraulics.Google Scholar
Marchi, E. 1961a Il moto uniforme delle correnti liquide nei condotti chiusi e aperti. Parte I. L’Energia Elettrica 38 (4), 289–301.Google Scholar
Marchi, E. 1961b Il moto uniforme delle correnti liquide nei condotti chiusi e aperti. Parte II. L’Energia Elettrica 38 (5), 393–413.Google Scholar
Musumeci, R. E., Cavallaro, L., Foti, E., Scandura, P. & Blondeaux, P. 2006 Waves plus currents crossing at a right angle: experimental investigation. J. Geophys. Res. 111 (C7), C07019.Google Scholar
Nezu, I. & Rodi, W. 1986 Open-channel flow measurements with a laser Doppler anemometer. ASCE J. Hydraul. Engng 112 (5), 335–354.Google Scholar
Nielsen, P. 1992 Coastal Bottom Boundary Layers and Sediment Transport. World Scientific.CrossRefGoogle Scholar
Nielsen, P. & You, Z. 1996 Eulerian mean velocity under non-breaking waves on horizontal bottom. In Proceedings of 25th International Conference on Coastal Engineering, Orlando, FL, pp. 4066–4078.Google Scholar
Olabarrieta, M., Medina, R. & Castanedo, S. 2010 Effects of wave–current interaction on the current profile. Coast. Engng 57 (7), 643–655.Google Scholar
Soulsby, R. L. 1997 Dynamics of Marine Sands, vol. 21, p. 249. Thomas Telford.Google Scholar
Soulsby, R. L., Hamm, L., Klopman, G., Myrhaug, D., Simons, R. R. & Thomas, G. P. 1993 Wave–current interaction within and outside the bottom boundary layer. Coast. Engng 21, 41–69.Google Scholar
Umeyama, M. 2005 Reynolds stresses and velocity distributions in a wave–current coexisting environment. J. Waterways Port Coast. Ocean Engng 131 (5), 203–212.Google Scholar
Vittori, G. 2003 Sediment suspension due to waves. J. Geophys. Res. Oceans 108 (C6), 3173.Google Scholar