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Bore-generated macrovortices on erodible beds

Published online by Cambridge University Press:  11 October 2013

M. Brocchini
M. Brocchini*
Affiliation:
Department I.C.E.A., Università Politecnica delle Marche, 60131 Ancona, Italy
*
†Email address for correspondence: m.brocchini@univpm.it
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Abstract

The interaction of free-surface bores and an erodible porous channel bed in a shallow-water flow is analysed based on the assumption of weak coupling between free-surface discontinuities and bed discontinuities and on the simplest closure for the sediment transport rate (cubic with the mean flow velocity). It is shown that free-surface bores with finite cross-stream extent can evolve over the erodible bed by generating vertically oriented macrovortices in a manner similar to, but more complex than, that of free-surface bores of finite cross-stream extent over a rigid channel bottom. An equation for the potential vorticity is derived, which shows that on an erodible bed the vortices are generated by a combination of various mechanisms related to energy dissipation of both surface bores and bed discontinuities. The model is verified and the physics explored by comparison with a number of numerical simulations, typical of both riverine (dam-break test and pit test) and nearshore (bore on a beach test) flows, and with previously published experimental results. For all cases a fairly good agreement is found between the analytically estimated potential vorticity and that computed numerically.

JFM classification

Geophysical and Geological Flows: Sediment transport Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 734 , 10 November 2013 , pp. 486 - 508
Copyright
©2013 Cambridge University Press 

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References

Best, J. 2005 The fluid dynamics of river dunes: a review and some future research directions. J. Geophys. Res. 110, F04S02.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. & Colombini, M. 2004 A note on the decay of vorticity in shallow flows. Phys. Fluids 16 (7), 2469–2475.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
Chanson, H. 2004 The Hydraulics of Open Channel Flow: An Introduction, 2nd edn. Elsevier.Google Scholar
Fraccarollo, L. & Capart, H. 2002 Riemann wave description of erosional dam-break flows. J. Fluid Mech. 461, 183–228.Google Scholar
Goutiere, L., Soares-Frazao, S. & Zech, Y. 2011 Dam-break flow on mobile bed in abruptly widening channel: experimental data. J. Hydraul. Res. 49 (3), 367–371.Google Scholar
Grass, A. J. 1981 Sediment transport by waves and currents. Tech. Rep. FL29. London Centre for Marine Technology, University College London.Google Scholar
Hudson, J. & Sweby, P. K. 2003 Formulations for numerically approximating hyperbolic systems governing sediment transport. J. Sci. Comput. 19 (8), 225–252.Google Scholar
Kelly, D. M. & Dodd, N. 2010 Beach-face evolution in the swash zone. J. Fluid Mech. 661, 316–340.Google Scholar
Kennedy, A., Brocchini, M., Soldini, L. & Mancinelli, A. 2006 Topographically-controlled, breaking wave-induced macrovortices. Part 2. Changing geometries. J. Fluid Mech. 559, 57–80.Google Scholar
Nadaoka, K., Hino, M. & Koyano, Y. 1989 Structure of the turbulent-flow field under breaking waves in the surf zone. J. Fluid Mech. 204, 359–387.Google Scholar
Nadaoka, K., Ueno, S. & Igarashi, T. 1988 Sediment suspension due to large-scale eddies in the surf zone. In Proceedings of 21st International Conference on Coastal Engineering, pp. 1646–1660. ASCE.Google Scholar
Noguchi, K., Nezu, I. & Sanjou, M. 2008 Turbulence structure and fluid particle interaction in sediment-laden flows over developing sand dunes. Environ. Fluid Mech. 8, 569–578.Google Scholar
Peregrine, D. H. 1998 Surf zone currents. Theor. Comput. Fluid Dyn. 10, 295–309.Google Scholar
Postacchini, M., Brocchini, M., Mancinelli, A. & Landon, M. 2012 A multi-purpose, intra-wave, shallow water hydro-morphodynamic solver. Adv. Water Resour. 38, 13–26.Google Scholar
Pratt, L. J. 1983 On inertial flow over topography. Part 1. Semigeostrophic adjustment to an obstacle. J. Fluid Mech. 131, 195–218.Google Scholar
van Prooijen, B. C., Battjes, J. A. & Uijttewaal, W. S. J. 2005 Momentum exchange in straight uniform compound channel flow. J. Hydraul. Engng 131 (3), 175–183.Google Scholar
Provenzale, A. 1999 Transport by coherent barotropic vortices. Annu. Rev. Fluid Mech. 31, 55–93.CrossRefGoogle Scholar
Rosatti, G. & Fraccarollo, L. 2006 A well-balanced approach for flows over mobile-bed with high sediment-transport. J. Comput. Phys. 220, 312–338.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
Soldini, L., Piattella, A., Brocchini, M., Mancinelli, A. & Bernetti, R. 2004 Macrovortices-induced horizontal mixing in compound channels. Ocean Dyn. 54 (3/4), 333–339.Google Scholar
Stoesser, T., Braun, C., Garcia-Villalba, M. & Rodi, W. 2008 Turbulence structures in flow over two-dimensional dunes. J. Hydraul. Engng ASCE 134 (1), 42–55.Google Scholar
Tambroni, N., Pittaluga, M. B. & Seminara, G. 2005 Laboratory observations of the morphodynamic evolution of tidal channels and tidal inlets. J. Geophys. Res.-Earth Surf. 110 (F4), F04009.Google Scholar
Toro, E. F. 1992 Riemann problems and the WAF method for solving two-dimensional shallow water equations. Phil. Trans. R. Soc. Lond. A 338, 43–68.Google Scholar
Zhang, H., Nakagawa, H. & Mizutani, H. 2012 Bed morphology and grain size characteristics around a spur dyke. Intl J. Sedim. Res. 27, 141–157.Google Scholar