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Transport by breaking internal gravity waves on slopes

  • Robert S. Arthur (a1) (a2) and Oliver B. Fringer (a1)


We use the results of a direct numerical simulation (DNS) with a particle-tracking model to investigate three-dimensional transport by breaking internal gravity waves on slopes. Onshore transport occurs within an upslope surge of dense fluid after breaking. Offshore transport occurs due to an intrusion of mixed fluid that propagates offshore and resembles an intermediate nepheloid layer (INL). Entrainment of particles into the INL is related to irreversible mixing of the density field during wave breaking. Maximum onshore and offshore transport are calculated as a function of initial particle position, and can be of the order of the initial wave length scale for particles initialized within the breaking region. An effective cross-shore dispersion coefficient is also calculated, and is roughly three orders of magnitude larger than the molecular diffusivity within the breaking region. Particles are transported laterally due to turbulence that develops during wave breaking, and this lateral spreading is quantified with a lateral turbulent diffusivity. Lateral turbulent diffusivity values calculated using particles are elevated by more than one order of magnitude above the molecular diffusivity, and are shown to agree well with turbulent diffusivities estimated using a generic length scale turbulence closure model. Based on a favourable comparison of DNS results with those of a similar two-dimensional case, we use two-dimensional simulations to extend our cross-shore transport results to additional wave amplitude and bathymetric slope conditions.


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Aghsaee, P., Boegman, L. & Lamb, K. G. 2010 Breaking of shoaling internal solitary waves. J. Fluid Mech. 659, 289317.
Arthur, R. S. & Fringer, O. B. 2014 The dynamics of breaking internal solitary waves on slopes. J. Fluid Mech. 761, 360398.
Boegman, L., Ivey, G. N. & Imberger, J. 2005 The degeneration of internal waves in lakes with sloping topography. Limnol. Oceanogr. 50 (5), 16201637.
Bogucki, D., Dickey, T. & Redekopp, L. G. 1997 Sediment resuspension and mixing by resonantly generated internal solitary waves. J. Phys. Oceanogr. 27 (7), 11811196.
Bourgault, D. & Kelley, D. E. 2007 On the reflectance of uniform slopes for normally incident interfacial solitary waves. J. Phys. Oceanogr. 37 (5), 11561162.
Bourgault, D., Kelley, D. E. & Galbraith, P. S. 2005 Interfacial solitary wave run-up in the St Lawrence Estuary. J. Mar. Res. 63 (6), 10011015.
Bourgault, D., Morsilli, M., Richards, C., Neumeier, U. & Kelley, D. E. 2014 Sediment resuspension and nepheloid layers induced by long internal solitary waves shoaling orthogonally on uniform slopes. Cont. Shelf Res. 72, 2133.
Canuto, V. M., Howard, A., Cheng, Y. & Dubovikov, M. S. 2001 Ocean turbulence. Part I: one-point closure model-momentum and heat vertical diffusivities. J. Phys. Oceanogr. 31 (6), 14131426.
Carter, G. S., Gregg, M. C. & Lien, R. 2005 Internal waves, solitary-like waves, and mixing on the Monterey Bay shelf. Cont. Shelf Res. 25 (12), 14991520.
Cheriton, O. M., McPhee-Shaw, E. E., Shaw, W. J., Stanton, T. P., Bellingham, J. G. & Storlazzi, C. D. 2014 Suspended particulate layers and internal waves over the southern Monterey Bay continental shelf: an important control on shelf mud belts? J. Geophys. Res. 119 (1), 428444.
Chou, Y. J. & Fringer, O. B. 2010 A model for the simulation of coupled flow-bed form evolution in turbulent flows. J. Geophys. Res. 115, C10041.
Cui, A.1999 On the parallel computation of turbulent rotating stratified flows. PhD thesis, Stanford University.
Davis, K. A. & Monismith, S. G. 2011 The modification of bottom boundary layer turbulence and mixing by internal waves shoaling on a barrier reef. J. Phys. Oceanogr. 41 (11), 22232241.
Fringer, O. B.2003 Numerical simulations of breaking interfacial waves. PhD thesis, Stanford University.
Gil, G. T. C. & Fringer, O. B. 2015 Particle drift due to nonlinear internal gravity waves and emerging wave trains. J. Geophys. Res. (in preparation).
Helfrich, K. R. 1992 Internal solitary wave breaking and run-up on a uniform slope. J. Fluid Mech. 243, 133154.
Helfrich, K. R. & Melville, W. K. 2006 Long nonlinear internal waves. Annu. Rev. Fluid Mech. 38, 395425.
Hosegood, P., Bonnin, J. & van Haren, H. 2004 Solibore-induced sediment resuspension in the Faeroe–Shetland channel. Geophys. Res. Lett. 31, L09301.
Hosegood, P. & van Haren, H. 2004 Near-bed solibores over the continental slope in the Faeroe–Shetland channel. Deep-Sea Res. II 51 (25), 29432971.
Ivey, G. N. & Nokes, R. I. 1989 Vertical mixing due to the breaking of critical internal waves on sloping boundaries. J. Fluid Mech. 204, 479500.
Kennel, M. B.2004 KDTREE 2: Fortran 95 and C++ software to efficiently search for near neighbors in a multi-dimensional Euclidean space. arXiv:physics/0408067 [].
Klymak, J. M. & Moum, J. N. 2003 Internal solitary waves of elevation advancing on a shoaling shelf. Geophys. Res. Lett. 30 (20), 2045.
Lamb, K. G. 1997 Particle transport by nonbreaking, solitary internal waves. J. Geophys. Res. 102 (C8), 1864118660.
Lamb, K. G. 2002 A numerical investigation of solitary internal waves with trapped cores formed via shoaling. J. Fluid Mech. 451, 109144.
Lamb, K. G. 2003 Shoaling solitary internal waves: on a criterion for the formation of waves with trapped cores. J. Fluid Mech. 478, 81100.
Leichter, J. J., Wing, S. R., Miller, S. L. & Denny, M. W. 1996 Pulsed delivery of subthermocline water to Conch Reef (Florida Keys) by internal tidal bores. Limnol. Oceanogr. 41 (7), 14901501.
Lien, R. C., D’Asaro, E. A., Henyey, F., Chang, M. H., Tang, T. Y. & Yang, Y. J. 2012 Trapped core formation within a shoaling nonlinear internal wave. J. Phys. Oceanogr. 42 (4), 511525.
Lien, R. C., Henyey, F., Ma, B. & Yang, Y. J. 2014 Large-amplitude internal solitary waves observed in the northern South China sea: properties and energetics. J. Phys. Oceanogr. 44 (4), 10951115.
McPhee-Shaw, E. E. 2006 Boundary–interior exchange: reviewing the idea that internal-wave mixing enhances lateral dispersal near continental margins. Deep-Sea Res. 53 (1), 4259.
McPhee-Shaw, E. E. & Kunze, E. 2002 Boundary layer intrusions from a sloping bottom: a mechanism for generating intermediate nepheloid layers. J. Geophys. Res. 107 (C6), 116.
McPhee-Shaw, E. E., Sternberg, R. W., Mullenbach, B. & Ogston, A. S. 2004 Observations of intermediate nepheloid layers on the northern California continental margin. Cont. Shelf Res. 24 (6), 693720.
Michallet, H. & Ivey, G. N. 1999 Experiments on mixing due to internal solitary waves breaking on uniform slopes. J. Geophys. Res. 104 (C6), 1346713477.
Nakayama, K. & Imberger, J. 2010 Residual circulation due to internal waves shoaling on a slope. Limnol. Oceanogr. 55 (3), 10091023.
Nakayama, K., Shintani, T., Kokubo, K., Kakinuma, T., Maruya, Y., Komai, K. & Okada, T. 2012 Residual currents over a uniform slope due to breaking of internal waves in a two-layer system. J. Geophys. Res. 117, C10002.
Omand, M. M., Leichter, J. J., Franks, P. J., Guza, R. T., Lucas, A. J. & Feddersen, F. 2011 Physical and biological processes underlying the sudden appearance of a red-tide surface patch in the nearshore. Limnol. Oceanogr. 56 (3), 787801.
Pineda, J. 1994 Internal tidal bores in the nearshore: warm-water fronts, seaward gravity currents and the onshore transport of neustonic larvae. J. Mar. Res. 52 (3), 427458.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Quaresma, L. S., Vitorino, J., Oliveira, A. & da Silva, J. 2007 Evidence of sediment resuspension by nonlinear internal waves on the western Portuguese mid-shelf. Mar. Geol. 246 (2), 123143.
Scotti, A. & Pineda, J. 2004 Observation of very large and steep internal waves of elevation near the Massachusetts coast. Geophys. Res. Lett. 31 (22), L22307.
Shanks, A. L. 1983 Surface slicks associated with tidally forced internal waves may transport pelagic larvae of benthic invertebrates and fishes shoreward. Mar. Ecol. Prog. Ser. 13 (2), 311315.
Venayagamoorthy, S. K. & Fringer, O. B. 2006 Numerical simulations of the interaction of internal waves with a shelf break. Phys. Fluids 18 (7), 076603.
Venayagamoorthy, S. K. & Fringer, O. B. 2007 On the formation and propagation of nonlinear internal boluses across a shelf break. J. Fluid Mech. 577, 137159.
Vlasenko, V. & Hutter, K. 2002 Numerical experiments on the breaking of solitary internal waves over a slope-shelf topography. J. Phys. Oceanogr. 32 (6), 17791793.
Wallace, B. C. & Wilkinson, D. L. 1988 Run-up of internal waves on a gentle slope in a two-layered system. J. Fluid Mech. 191, 419442.
Walter, R. K., Woodson, C. B., Arthur, R. S., Fringer, O. B. & Monismith, S. G. 2012 Nearshore internal bores and turbulent mixing in southern Monterey Bay. J. Geophys. Res. 117, C07017.
Walter, R. K., Woodson, C. B., Leary, P. R. & Monismith, S. G. 2014 Connecting wind-driven upwelling and offshore stratification to nearshore internal bores and oxygen variability. J. Geophys. Res. 116 (6), 35173534.
Warner, J. C., Sherwood, C. R., Arango, H. G. & Signell, R. P. 2005 Performance of four turbulence closure models implemented using a generic length scale method. Ocean Model. 8 (1), 81113.
Zang, Y., Street, R. L. & Koseff, J. R. 1994 A non-staggered grid, fractional step method for time-dependent incompressible Navier–Stokes equations in curvilinear coordinates. J. Comput. Phys. 114, 1833.
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