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Internal wave boluses as coherent structures in a continuously stratified fluid

Published online by Cambridge University Press:  06 January 2020

Guilherme S. Vieira Open the ORCID record for Guilherme S. Vieira [Opens in a new window]  and
Michael R. Allshouse Open the ORCID record for Michael R. Allshouse [Opens in a new window]
Guilherme S. Vieira
Affiliation:
Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA02115, USA
Michael R. Allshouse*
Affiliation:
Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA02115, USA
*
†Email address for correspondence: [email protected]
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Abstract

Internal waves shoaling on the continental slope can break and form materially coherent vortices called boluses. These boluses are able to trap and transport material up the continental slope, yet the global extent of bolus transport is unknown. Previous studies of bolus formation primarily focused on systems consisting of two layers of uniform density, which do not account for the presence of ocean pycnoclines of finite thickness. We use hyperbolic tangent profiles to model the density stratification in our simulations and demonstrate the impact of the pycnocline on the bolus. A spectral clustering method is used to objectively identify the bolus as a Lagrangian coherent structure that contains the material advected upslope. The bolus size and displacement upslope are examined as a function of the pycnocline thickness, incoming wave energy, density change across the pycnocline and topographic slope. The dependence of bolus transport on the pycnocline thickness demonstrates that boluses in continuous stratifications tend to be larger and transport material further than in corresponding two-layer stratifications.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , A35
Copyright
© 2020 Cambridge University Press

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References

Abernathey, R. & Haller, G. 2018 Transport by Lagrangian vortices in the eastern pacific. J. Phys. Oceanogr. 48, 667–685.CrossRefGoogle Scholar
Aghsaee, P., Boegman, L. & Lamb, K. G. 2010 Breaking of shoaling internal solitary waves. J. Fluid Mech. 659, 289–317.CrossRefGoogle Scholar
Aikman, F. III 1984 Pycnocline development and its consequences in the Middle Atlantic Bight. J. Geophys. Res. 89 (C1), 685–694.CrossRefGoogle Scholar
Alford, M. H. 2003 Redistribution of energy available for ocean mixing by long-range propagation of internal waves. Nature 423, 159–162.CrossRefGoogle ScholarPubMed
Alford, M. H., Peacock, T., MacKinnon, J. A., Nash, J. D., Buijsman, M. C., Centurioni, L. R., Chao, S.-Y., Chang, M.-H., Farmer, D. M., Fringer, O. B. et al. 2015 The formation and fate of internal waves in the South China Sea. Nature 521 (7550), 65.CrossRefGoogle ScholarPubMed
Allshouse, M. R., Lee, F. M., Morrison, P. J. & Swinney, H. L. 2016 Internal wave pressure, velocity, and energy flux from density perturbations. Phys. Rev. Fluids 1, 014301.CrossRefGoogle Scholar
Allshouse, M. R. & Peacock, T. 2015 Lagrangian based methods for coherent structure detection. Chaos: An interdiscip. J. Nonlinear Sci. 25 (9), 097617.CrossRefGoogle ScholarPubMed
Allshouse, M. R. & Thiffeault, J.-L. 2012 Detecting coherent structures using braids. Physica D 241 (2), 95–105.Google Scholar
Arthur, R. S. & Fringer, O. B. 2014 The dynamics of breaking internal solitary waves on slopes. J. Fluid Mech. 761, 360–398.CrossRefGoogle Scholar
Arthur, R. S. & Fringer, O. B. 2016 Transport by breaking internal gravity waves on slopes. J. Fluid Mech. 789, 93–126.CrossRefGoogle Scholar
Arthur, R. S., Koseff, J. R. & Fringer, O. B. 2017 Local versus volume-integrated turbulence and mixing in breaking internal waves on slopes. J. Fluid Mech. 815, 169–198.CrossRefGoogle Scholar
Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31 (2), 209–248.CrossRefGoogle Scholar
Boegman, L., Ivey, G. N. & Imberger, J. 2005 The degeneration of internal waves in lakes with sloping topography. Limnol. Oceanogr. 50 (5), 1620–1637.CrossRefGoogle Scholar
Boegman, L. & Stastna, M. 2019 Sediment resuspension and transport by internal solitary waves. Annu. Rev. Fluid Mech. 51, 129–154.CrossRefGoogle Scholar
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, 21–33.CrossRefGoogle Scholar
Cacchione, D. & Wunsch, C. 1974 Experimental study of internal waves over a slope. J. Fluid Mech. 66 (2), 223–239.CrossRefGoogle Scholar
Carter, G. S., Gregg, M. C. & Lien, R.-C. 2005 Internal waves, solitary-like waves, and mixing on the Monterey Bay shelf. Cont. Shelf Res. 25 (12-13), 1499–1520.CrossRefGoogle Scholar
Dauxois, T., Didier, A. & Falcon, E. 2004 Observation of near-critical reflection of internal waves in a stably stratified fluid. Phys. Fluids 16 (6), 1936–1941.CrossRefGoogle Scholar
Dettner, A., Paoletti, M. S. & Swinney, H. L. 2013 Internal tide and boundary current generation by tidal flow over topography. Phys. Fluids 25, 1–13.CrossRefGoogle Scholar
Duda, T. F., Lynch, J. F., Irish, J. D., Beardsley, R. C., Ramp, S. R., Chiu, C.-S., Tang, T. Y. & Yang, Y.-J. 2004 Internal tide and nonlinear internal wave behavior at the continental slope in the northern south China Sea. IEEE J. Ocean. Engng 29 (4), 1105–1130.CrossRefGoogle Scholar
Fringer, O. B. & Street, R. L. 2003 The dynamics of breaking progressive interfacial waves. J. Fluid Mech. 494, 319–353.CrossRefGoogle Scholar
Froyland, G. & Junge, O. 2018 Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories. SIAM J. Appl. Dyn. Syst. 17 (2), 1891–1924.CrossRefGoogle Scholar
Froyland, G. & Padberg-Gehle, K. 2015 A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos: An interdiscip. J. Nonlinear Sci. 25 (8), 087406.CrossRefGoogle ScholarPubMed
Froyland, G., Santitissadeekorn, N. & Monahan, A. 2010 Transport in time-dependent dynamical systems: finite-time coherent sets. Chaos: An interdiscip. J. Nonlinear Sci. 20, 043116.CrossRefGoogle ScholarPubMed
Fructus, D., Carr, M., Grue, J., Jensen, A. & Davies, P. A. 2009 Shear-induced breaking of large internal solitary waves. J. Fluid Mech. 620, 1–29.CrossRefGoogle Scholar
Gerkema, T. & Zimmerman, J. T. F. 2008 An Introduction to Internal Waves, vol. 207. Royal NIOZ.Google Scholar
Hadjighasem, A., Karrasch, D., Teramoto, H. & Haller, G. 2016 Spectral-clustering approach to Lagrangian vortex detection. Phys. Rev. E 93 (6), 063107.Google ScholarPubMed
Haller, G. 2002 Lagrangian coherent structures from approximate velocity data. Phys. Fluids A 14, 1851–1861.CrossRefGoogle Scholar
Haller, G. & Beron-Vera, F. J. 2013 Coherent Lagrangian vortices: The black holes of turbulence. J. Fluid Mech. 731, R4.CrossRefGoogle Scholar
Haller, G., Hadjighasem, A., Farazmand, M. & Huhn, F. 2016 Defining coherent vortices objectively from the vorticity. J. Fluid Mech. 795, 136–173.CrossRefGoogle Scholar
Ham, F. & Iaccarino, G. 2004 Energy conservation in collocated discretization schemes on unstructured meshes. In Annual Research Briefs, pp. 3–14. Stanford University.Google Scholar
Helfrich, K. R. 1992 Internal solitary wave breaking and run-up on a uniform slope. J. Fluid Mech. 243, 133–154.CrossRefGoogle Scholar
Helfrich, K. R. & Melville, W. K. 1986 On long nonlinear internal waves over slope-shelf topography. J. Fluid Mech. 167, 285–308.CrossRefGoogle Scholar
Helfrich, K. R. & Melville, W. K. 2006 Long nonlinear internal waves. Annu. Rev. Fluid Mech. 38, 395–425.CrossRefGoogle Scholar
Hosegood, P., Bonnin, J. & van Haren, H. 2004 Solibore-induced sediment resuspension in the Faeroe-Shetland channel. Geophys. Res. Lett. 31 (9), L09301.CrossRefGoogle Scholar
Inall, M. E., Rippeth, T. P. & Sherwin, T. J. 2000 Impact of nonlinear waves on the dissipation of internal tidal energy at a shelf break. J. Geophys. Res. 105 (C4), 8687–8705.CrossRefGoogle Scholar
King, B., Zhang, H. P. & Swinney, H. L. 2009 Tidal flow over three-dimensional topography in a stratified fluid. Phys. Fluids 21, 116601.CrossRefGoogle Scholar
Klymak, J. M. & Moum, J. N. 2003 Internal solitary waves of elevation advancing on a shoaling shelf. Geophys. Res. Lett. 30, 2045.CrossRefGoogle Scholar
Kunze, E. 2003 A review of oceanic salt-fingering theory. Prog. Oceanogr. 56 (3–4), 399–417.CrossRefGoogle Scholar
Lamb, K. G. 2003 Shoaling solitary internal waves: on a criterion for the formation of waves with trapped cores. J. Fluid Mech. 478, 81–100.CrossRefGoogle Scholar
Lamb, K. G. 2014 Internal wave breaking and dissipation mechanisms on the continental slope/shelf. Annu. Rev. Fluid Mech. 46, 231–254.CrossRefGoogle Scholar
Lee, F. M., Allshouse, M. R., Swinney, H. L. & Morrison, P. J. 2018 Internal wave energy flux from density perturbations in nonlinear stratifications. J. Fluid Mech. 856, 898–920.CrossRefGoogle Scholar
Lee, F. M., Paoletti, M. S., Swinney, H. L. & Morrison, P. J. 2014 Experimental determination of radiated internal wave power without pressure field data. Phys. Fluids 26, 046606.CrossRefGoogle Scholar
Legg, S. & Adcroft, A. 2003 Internal wave breaking at concave and convex continental slopes. J. Phys. Oceanogr. 33 (11), 2224–2246.2.0.CO;2>CrossRefGoogle Scholar
Liu, Q., Jia, Y., Liu, P., Wang, Q. & Chu, P. C. 2001 Seasonal and intraseasonal thermocline variability in the central south China Sea. Geophys. Res. Lett. 28 (23), 4467–4470.CrossRefGoogle Scholar
Long, R. R. 1956 Solitary waves in the one- and two-fluid system. Tellus 8 (4), 460–471.CrossRefGoogle Scholar
Long, R. R. 1965 On the Boussinesq approximation and its role in the theory of internal waves. Tellus 17 (1), 46–52.CrossRefGoogle Scholar
von Luxburg, U. 2007 A tutorial on spectral clustering. Stat. Comput. 17 (4), 395–416.CrossRefGoogle Scholar
Maderich, V. S., Van Heijst, G. J. F. & Brandt, A. 2001 Laboratory experiments on intrusive flows and internal waves in a pycnocline. J. Fluid Mech. 432, 285–311.CrossRefGoogle Scholar
Mahesh, K., Constantinescu, G. & Moin, P. 2004 A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys. 197, 215–240.CrossRefGoogle Scholar
Masunaga, E., Arthur, R. S., Fringer, O. B. & Yamazaki, H. 2017 Sediment resuspension and the generation of intermediate nepheloid layers by shoaling internal bores. J. Mar. Syst. 170, 31–41.CrossRefGoogle Scholar
Masunaga, E., Homma, H., Yamazaki, H., Fringer, O. B., Nagai, T., Kitade, Y. & Okayasu, A. 2015 Mixing and sediment resuspension associated with internal bores in a shallow bay. Cont. Shelf Res. 110, 85–99.CrossRefGoogle Scholar
Maxworthy, T., Leilich, J. S. J. E., Simpson, J. E. & Meiburg, E. H. 2002 The propagation of a gravity current into a linearly stratified fluid. J. Fluid Mech. 453, 371–394.CrossRefGoogle Scholar
Mercier, M. J., Martinand, D., Mathur, M., Gostiaux, L., Peacock, T. & Dauxois, T. 2010 New wave generation. J. Fluid Mech. 657, 308–334.CrossRefGoogle Scholar
Michallet, H. & Ivey, G. N. 1999 Experiments on mixing due to internal solitary waves breaking on uniform slopes. J. Geophys. Res. 104 (C6), 13467–13477.CrossRefGoogle Scholar
Moore, C. D., Koseff, J. R. & Hult, E. L. 2016 Characteristics of bolus formation and propagation from breaking internal waves on shelf slopes. J. Fluid Mech. 791, 260–283.CrossRefGoogle Scholar
Moum, J. N., Farmer, D. M., Smyth, W. D., Armi, L. & Vagle, S. 2003 Structure and generation of turbulence at interfaces strained by internal solitary waves propagating shoreward over the continental shelf. J. Phys. Oceanogr. 33 (10), 2093–2112.2.0.CO;2>CrossRefGoogle Scholar
Moum, J. N., Klymak, J. M., Nash, J. D., Perlin, A. & Smyth, W. D. 2007 Energy transport by nonlinear internal waves. J. Phys. Oceanogr. 37 (7), 1968–1988.CrossRefGoogle Scholar
Munk, W. & Wunsch, C. 1998 Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res. I 45, 1977–2010.CrossRefGoogle Scholar
Osborne, A. R. & Burch, T. L. 1980 Internal solitons in the Andaman sea. Science 208 (4443), 451–460.CrossRefGoogle ScholarPubMed
Paoletti, M. S., Drake, M. & Swinney, H. L. 2014 Internal tide generation in nonuniformly stratified deep oceans. J. Geophys. Res. 119, 1943–1956.CrossRefGoogle Scholar
Pedlosky, J. 2013 Geophysical Fluid Dynamics. Springer Science & Business Media.Google Scholar
Pineda, J. 1991 Predictable upwelling and the shoreward transport of planktonic larvae by internal tidal bores. Science 253 (5019), 548–549.CrossRefGoogle ScholarPubMed
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), 427–458.CrossRefGoogle Scholar
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 (2–4), 123–143.CrossRefGoogle Scholar
Ray, R. D. & Mitchum, G. T. 1996 Surface manifestation of internal tides generated near Hawaii. Geophys. Res. Lett. 23 (16), 2101–2104.CrossRefGoogle Scholar
Reid, E. C., DeCarlo, T. M., Cohen, A. L., Wong, G. T. F., Lentz, S. J., Safaie, A. et al. 2019 Internal waves influence the thermal and nutrient environment on a shallow coral reef. Limnol. Oceanogr. 64 (5), 1949–1965.CrossRefGoogle Scholar
Sandstrom, H. & Elliott, J. A. 1984 Internal tide and solitons on the Scotian shelf: a nutrient pump at work. J. Geophys. Res. 89 (C4), 6415–6426.CrossRefGoogle Scholar
Sandstrom, H. & Oakey, N. S. 1995 Dissipation in internal tides and solitary waves. J. Phys. Oceanogr. 25 (4), 604–614.2.0.CO;2>CrossRefGoogle Scholar
Schlitzer, R. 2000 Electronic atlas of WOCE hydrographic and tracer data now available. EOS Trans. AGU 81 (5), 45–45.CrossRefGoogle Scholar
Serra, M., Sathe, P., Beron-Vera, F. & Haller, G. 2017 Uncovering the edge of the polar vortex. J. Atmos. Sci. 74 (11), 3871–3885.CrossRefGoogle Scholar
Sigman, D. M., Jaccard, S. L. & Haug, G. H. 2004 Polar ocean stratification in a cold climate. Nature 428 (6978), 59.CrossRefGoogle Scholar
Simpson, J. E. 1972 Effects of the lower boundary on the head of a gravity current. J. Fluid Mech. 53 (4), 759–768.CrossRefGoogle Scholar
Stastna, M. & Lamb, K. G. 2008 Sediment resuspension mechanisms associated with internal waves in coastal waters. J. Geophys. Res. 113, C10016.CrossRefGoogle Scholar
Susanto, R., Mitnik, L. & Zheng, Q. 2005 Ocean internal waves observed. Oceanography 18 (4), 80.CrossRefGoogle Scholar
Sutherland, B. R., Barrett, K. J. & Ivey, G. N. 2013 Shoaling internal solitary waves. J. Geophys. Res. 118 (9), 4111–4124.CrossRefGoogle Scholar
Thorpe, S. A. 1968 On the shape of progressive internal waves. Phil. Trans. R. Soc. Lond. A 263 (1145), 563–614.CrossRefGoogle Scholar
Thorpe, S. A. 1971 Experiments on the instability of stratified shear flows: miscible fluids. J. Fluid Mech. 46 (2), 299–319.CrossRefGoogle Scholar
Troy, C. D. & Koseff, J. R. 2005 The instability and breaking of long internal waves. J. Fluid Mech. 543, 107–136.CrossRefGoogle Scholar
Venayagamoorthy, S. K. & Fringer, O. B. 2006 Numerical simulations of the interaction of internal waves with a shelf break. Phys. Fluids 18 (7), 076603.CrossRefGoogle Scholar
Venayagamoorthy, S. K. & Fringer, O. B. 2007 On the formation and propagation of nonlinear internal boluses across a shelf break. J. Fluid Mech. 577, 137–159.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Wang, Y.-H., Dai, C.-F. & Chen, Y.-Y. 2007 Physical and ecological processes of internal waves on an isolated reef ecosystem in the South China Sea. Geophys. Res. Lett. 34, L18609.CrossRefGoogle Scholar
White, B. L. & Helfrich, K. R. 2008 Gravity currents and internal waves in a stratified fluid. J. Fluid Mech. 616, 327–356.CrossRefGoogle Scholar
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36, 281–314.CrossRefGoogle Scholar
Zhang, L. & Swinney, H. L. 2014 Virtual seafloor reduces internal wave generation by tidal flow. Phys. Rev. Lett. 112, 104502.CrossRefGoogle ScholarPubMed

Viera et al. supplementary movie 1

Density perturbation field ρ' of the sample simulation presented in section 2.2 for the (top) full domain and (bottom) breaking region. Positive values (red) represent fluid displaced upward and negative values (blue) represent fluid displaced downward. The solid gray lines represent isopycnals. The isopycnal ρ=1015 kg/m3 is drawn in black and used to highlight the bolust front boundary. The breaking region (bottom) corresponds to the region surrounded by the thick black box in the full domain (top).

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Viera et al. supplementary movie 2

Density perturbation field ρ' of the sample simulation presented in section 2.2 for the (top) full domain and (bottom) breaking region with passive tracers distributed outside and inside the breaking zone. The tracers in the constant depth region temporarily oscillate vertically as the wave passes. Tracers in the breaking region are entrained in the resulting vortex demonstrating how the breaking mechanism results in effective transport.

Download Viera et al. supplementary movie 2(Video)
Video 37 MB

Viera et al. supplementary movie 3

(top) Evolution of the sample simulation tracers with the tracer color determined by cluster membership. Seven clusters have been identified, with the Lagrangian bolus cluster represented in green. (bottom) The time evolution for the bolus cluster from t0 = 19.25s to tf = 65s. Instantaneous positions of the bolus presented in figure 5(b) are presented here as well. The trajectory of the bolus center of volume is illustrated in gray.

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Video 30.8 MB

Viera et al. supplementary movie 4

Time evolution of the boluses, from t0 to tf indicated by the time values on the left and right, for stratifications with pycnocline thicknesses δ = 0.025, 0.1, 0.2, 0.25 and 0.3m. This movie corresponds to a dynamic view of the data presented in figure 8.

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Video 45.5 MB
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Supplementary material A.

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Supplementary material B.

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Supplementary material C.

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Supplementary material D.

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Additional movie descriptions

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