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Vorticity effects on nonlinear wave–current interactions in deep water

Published online by Cambridge University Press:  31 July 2015

R. M. Moreira  and
J. T. A. Chacaltana
R. M. Moreira*
Affiliation:
Computational Fluid Dynamics Laboratory, Fluminense Federal University, Rua Passo da Pátria 156, bl.D, sl.563A, Niterói, RJ 24210-240, Brazil
J. T. A. Chacaltana*
Affiliation:
Free-Surface Flow Laboratory, Espírito Santo Federal University, Av. Fernando Ferrari 514, CT-4, sl.24, Vitória, ES 29075-910, Brazil
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

The effects of uniform vorticity on a train of ‘gentle’ and ‘steep’ deep-water waves interacting with underlying flows are investigated through a fully nonlinear boundary integral method. It is shown that wave blocking and breaking can be more prominent depending on the magnitude and direction of the shear flow. Reflection continues to occur when sufficiently strong adverse currents are imposed on ‘gentle’ deep-water waves, though now affected by vorticity. For increasingly positive values of vorticity, the induced shear flow reduces the speed of right-going progressive waves, introducing significant changes to the free-surface profile until waves are completely blocked by the underlying current. A plunging breaker is formed at the blocking point when ‘steep’ deep-water waves interact with strong adverse currents. Conversely negative vorticities augment the speed of right-going progressive waves, with wave breaking being detected for strong opposing currents. The time of breaking is sensitive to the vorticity’s sign and magnitude, with wave breaking occurring later for negative values of vorticity. Stopping velocities according to nonlinear wave theory proved to be sufficient to cause wave blocking and breaking.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave breaking Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 778 , 10 September 2015 , pp. 314 - 334
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Copyright
© 2015 Cambridge University Press 

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References

Barnes, T. C. D., Brocchini, M., Peregrine, D. H. & Stansby, P. K. 1996 Modelling post-wave breaking turbulence and vorticity. In Proceedings of the 25th International Conference on Coastal Engineering, pp. 186–199. ASCE.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Benjamin, T. B. 1962 The solitary wave on a stream with an arbitrary distribution of vorticity. J. Fluid Mech. 12, 97–116.Google Scholar
Brevik, I. 1979 Higher-order waves propagating on constant vorticity currents in deep water. Coast. Engng 2, 237–259.Google Scholar
Choi, W. 2009 Nonlinear surface waves interacting with a linear shear current. Maths Comput. Simul. 80, 29–36.Google Scholar
Constantin, A. & Escher, J. 2004 Symmetry of steady periodic surface water waves with vorticity. J. Fluid Mech. 498, 171–181.Google Scholar
Dabiri, D. & Gharib, M. 1997 Experimental investigation of the vorticity generation within a spilling water wave. J. Fluid Mech. 330, 113–139.Google Scholar
Dalrymple, R. A. 1974 A finite amplitude wave on a linear shear current. J. Geophys. Res. 79, 4498–4504.CrossRefGoogle Scholar
Dold, J. W. 1992 An efficient surface-integral algorithm applied to unsteady gravity waves. J. Comput. Phys. 103, 90–115.Google Scholar
Jonsson, I. G. 1990 Wave–current interactions. In The Sea: Ocean Engineering Science 9A (ed. Le Méhauté, B. & Hanes, D. M.), pp. 65–120. Wiley Interscience.Google Scholar
Kharif, C., Giovanangeli, J.-P., Touboul, J., Grare, L. & Pelinovsky, E. 2008 Influence of wind on extreme wave events: experimental and numerical approaches. J. Fluid Mech. 594, 209–247.CrossRefGoogle Scholar
Kishida, N. & Sobey, R. J. 1988 Stokes theory for waves on a linear shear current. J. Engng Mech. ASCE 114, 1317–1334.Google Scholar
Ko, J. & Strauss, W. 2008 Effect of vorticity on steady water waves. J. Fluid Mech. 608, 197–215.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1998 Vorticity and curvature at a free surface. J. Fluid Mech. 356, 149–153.CrossRefGoogle Scholar
Lundgren, T. & Koumoutsakos, P. 1999 On the generation of vorticity at a free surface. J. Fluid Mech. 382, 351–366.Google Scholar
Miche, R. 1944 Mouvements ondulatoires de la mer en profondeur constante ou décroissante. Ann. des Ponts et Chaussées 114, 369–406.Google Scholar
Moreira, R. M.2001 Nonlinear interactions between water waves, free-surface flows and singularities. PhD thesis, University of Bristol, UK.CrossRefGoogle Scholar
Moreira, R. M. & Chacaltana, J. T. A. 2012 Nonlinear interactions between water waves and currents with constant vorticity. In Proceedings of the 33rd International Conference on Coastal Engineering. ASCE; abstract no. 1172.Google Scholar
Moreira, R. M. & Peregrine, D. H. 2010 Nonlinear interactions between a free-surface flow with surface tension and a submerged cylinder. J. Fluid Mech. 648, 485–507.Google Scholar
Moreira, R. M. & Peregrine, D. H. 2012 Nonlinear interactions between deep-water waves and currents. J. Fluid Mech. 691, 1–25.Google Scholar
Novikov, Y. A. 1981 Generation of surface waves by discrete vortices. Izv. Atmos. Ocean. Phys. 17, 709–714.Google Scholar
Nwogu, O. G. 2009 Interaction of finite-amplitude waves with vertically sheared current fields. J. Fluid Mech. 627, 179–213.CrossRefGoogle Scholar
Pak, O. S. & Chow, K. W. 2009 Free surface waves on shear currents with non-uniform vorticity: third-order solutions. Fluid Dyn. Res. 41, 1–13.Google Scholar
Peirson, W. L. & Banner, M. L. 2003 Aqueous surface layer flows induced by microscale breaking wind waves. J. Fluid Mech. 479, 1–38.Google Scholar
Peregrine, D. H. 1976 Interaction of water waves and currents. Adv. Appl. Mech. 16, 9–117.Google Scholar
Peregrine, D. H. 1999 Large-scale vorticity generation by breakers in shallow and deep water. Eur. J. Mech. (B/Fluids) 18, 403–408.Google Scholar
Peregrine, D. H. & Thomas, G. P. 1979 Finite-amplitude deep-water waves on currents. Phil. Trans. R. Soc. Lond. A 292, 371–390.Google Scholar
Simmen, J. A.1984 Steady deep-water waves on a linear shear current. PhD thesis, California Institute of Technology, USA.Google Scholar
Simmen, J. A. & Saffman, P. G. 1985 Steady deep-water waves on a linear shear current. Stud. Appl. Maths 75, 35–57.CrossRefGoogle Scholar
Swan, C., Cummins, I. P. & James, R. L. 2001 An experimental study of two-dimensional surface water waves propagating on depth-varying currents. Part 1. Regular waves. J. Fluid Mech. 428, 273–304.CrossRefGoogle Scholar
Taylor, G. I. 1955 The action of a surface current used as a breakwater. Proc. R. Soc. Lond. A 231, 466–478.Google Scholar
Teles da Silva, A. F.1989 Application of boundary integral methods to the study of steep free surface waves. PhD thesis, University of Bristol, UK.Google Scholar
Teles da Silva, A. F. & Peregrine, D. H. 1988 Steep, steady surface waves on water of finite depth with constant vorticity. J. Fluid Mech. 195, 281–302.Google Scholar
Thomas, G. P. & Klopman, G. 1997 Wave–current interactions in the nearshore region. In Gravity Waves in Water of Finite Depth (ed. Hunt, J. N.), pp. 215–319. Computational Mechanics Publications.Google Scholar
Thomas, R., Kharif, C. & Manna, M. 2012 A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity. Phys. Fluids 24, 127102.Google Scholar
Toffoli, A., Waseda, T., Houtani, H., Kinoshita, T., Collins, K., Proment, D. & Onorato, M. 2013 Excitation of rogue waves in a variable medium: an experimental study on the interaction of water waves and currents. Phys. Rev. E 87, 051201(R).CrossRefGoogle Scholar
Tsao, S. 1959 Behaviour of surface waves on a linearly varying flow. Tr. Mosk. Fiz.-Tekh. Inst. Issled. Mekh. Prikl. Mat. 3, 66–84.Google Scholar
Vasan, V. & Oliveras, K. 2014 Pressure beneath a traveling wave with constant vorticity. Discr. Contin. Dyn. Syst. 34, 3219–3239.Google Scholar