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Vorticity generation due to cross-sea

Published online by Cambridge University Press:  11 March 2014

M. Postacchini ,
M. Brocchini  and
L. Soldini
M. Postacchini*
Affiliation:
Department I.C.E.A., Università Politecnica delle Marche, 60131 Ancona, Italy
M. Brocchini
Affiliation:
Department I.C.E.A., Università Politecnica delle Marche, 60131 Ancona, Italy
L. Soldini
Affiliation:
Department I.C.E.A., Università Politecnica delle Marche, 60131 Ancona, Italy
*
†Email address for correspondence: [email protected]
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Abstract

Similarly to shore-parallel waves interacting with submerged obstacles, two wave trains, approaching the shore with different angles, generate breakers of finite cross-flow length and an intense vorticity at their edges. The dynamics of crossing wave trains in shallow waters is studied by means of a simple theoretical approach that is used to inspect the flow characteristics at breaking. The post-breaking dynamics, with specific focus on the vorticity generation and evolution processes, is described on the basis of the analytical results of Brocchini et al. (J. Fluid Mech., vol. 507, 2004, pp. 289–307). Ad hoc numerical simulations, performed by means of a nonlinear shallow-water equations (NSWE) solver, are used to support the analytical findings and detail the post-breaking flow evolution. Comparisons between numerical and analytical findings confirm that: (i) the cross-sea theory successfully predicts the breaking position when a finite-length breaker stems from two crossing wave trains and (ii) the dynamics induced by such a breaking (i.e. vorticity generation, mutual-advection and self-advection mechanisms) is similar to that occurring after the breaking event of a shore-parallel wave over a submerged obstacle: vortices generated at the breaker edges are first subjected to wave forcing and self-advection, these pushing the vortices shoreward; then, oppositely-signed vortices pair and the mutual interaction enables them to invert the motion and move seaward. Useful relationships have been found to describe the main features of such a dynamics (i.e. breaker length, vortex trajectories, etc.).

JFM classification

Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Wave breaking
Type
Papers
Information
Journal of Fluid Mechanics , Volume 744 , 10 April 2014 , pp. 286 - 309
Copyright
© 2014 Cambridge University Press 

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References

Antuono, M., Soldini, L. & Brocchini, M. 2012 On the role of the Chezy frictional term near the shoreline. Theor. Comput. Fluid Dyn. 26, 105–116.Google Scholar
Brocchini, M. 2013 Bore-generated macrovortices on erodible beds. J. Fluid Mech. 734, 486–508.Google Scholar
Brocchini, M., Bernetti, R., Mancinelli, A. & Albertini, G. 2001 An efficient solver for nearshore flows based on the WAF method. Coast. Engng. 43, 105–129.Google Scholar
Brocchini, M., Kennedy, A., Soldini, L. & Mancinelli, A. 2004 Topographically-controlled, breaking wave-induced macrovortices. Part 1. Widely separated breakwaters. J. Fluid Mech. 507, 289–307.Google Scholar
Bühler, O. & Jacobson, T. E. 2001 Wave-driven currents and vortex dynamics on barred beaches. J. Fluid Mech. 449, 313–339.Google Scholar
Clark, D. B., Elgar, S. & Raubenheimer, B. 2012 Vorticity generation by short-crested wave breaking. Geophys. Res. Lett. 39, L24604.Google Scholar
Dean, R. G. 1968 Breaking wave criteria; a study employing a numerical wave theory. International Conference on Coastal Engineering. pp. 108–123, ASCE.Google Scholar
Kennedy, A., Brocchini, M., Soldini, L. & Gutierrez, E. 2006 Topographically-controlled, breaking wave-induced macrovortices. Part 2. Changing geometries. J. Fluid Mech. 559, 57–80.Google Scholar
Kharif, C., Pelinovsky, E. & Slunyaev, A. 2009 Rogue waves in the ocean. Springer.Google Scholar
Le Méhauté, B. 1976 An introduction to hydrodynamics and water waves. Springer-Verlag.Google Scholar
Mei, C. C. 1983 The applied dynamics of ocean surface waves. Wiley-Interscience.Google Scholar
Mori, N. 2012 Freak waves under typhoon conditions. J. Geophys. Res. Oceans 117, C00J07.Google Scholar
Onorato, M., Osborne, A. & Serio, M. 2006 Modulational instability in crossing sea states: A possible mechanism for the formation of freak waves. Phys. Rev. Lett. 96, 014503.Google Scholar
Peregrine, D. H. 1998 Surf zone currents. Theor. Comput. Fluid Dyn. 10, 295–309.Google Scholar
Postacchini, M., Brocchini, M. & Soldini, L. 2012 Bore-induced macrovortices over a planar beach: the cross-sea condition case. International Conference on Coastal Engineering. ASCE, DOI: 10.9753/icce.v33.waves.18.Google Scholar
Schär, C. & Smith, R. B. 1993 Shallow-water flow past isolated topography. Part I. Vorticity production and wake formation. J. Atmos. Sci. 50, 1373–1400.Google Scholar
Shukla, P. K., Marklund, M. & Stenflo, L. 2007 Modulational instability of nonlinearly interacting incoherent sea states. JETP Lett. 84 (12), 645–649.Google Scholar
Whitham, G. B. 1974 Linear and nonlinear waves. John Wiley & Sons.Google Scholar