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Three-dimensional perspective on a convective instability and transition to turbulence in an internal solitary wave of depression shoaling over gentle slopes

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Abstract

The shoaling of an internal solitary wave (ISW) of depression is explored in three-dimensions (3D) through high-accuracy, fully nonlinear, and nonhydrostatic simulations. Time-averaged background stratification and current profiles from field observations, along with measured bathymetry data from the South China Sea (SCS), are used. The computational approach is based on a high-resolution and high-accuracy deformed spectral multidomain penalty method incompressible flow solver. Recent field observations in the SCS indicate the presence of a convective instability followed by a subsurface recirculating core that may persist for more than tens of km and drive turbulent-induced mixing, estimated to be up to four orders of magnitude larger than that typically found in the ocean. The preceding convective instability occurs due to a sudden decrease in the wave propagation speed, below the maximum horizontal wave-induced velocity, and possible from the stretching of the near-surface vorticity layer of the baroclinic background current from the propagating ISW. Motivated by such observations, the present study examines the onset of the 3D convective instability that results in subsurface recirculating core formation, as the ISW propagates and shoals in the normal-to-isobath direction. A noise field is inserted in the wave-induced velocity and density field to force the evolution in 3D. The initial instability has a transitional structure that develops in the lateral direction. The evolution of the lateral instability and subsequent transition to turbulence in the breaking wave is compared with the wave structured observed in the field. As such, a preliminary understanding of the formation of recirculating cores in ISWs, the driver for subsequent turbulence, mixing, and particle transport in the interior is obtained.

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References

  1. Chang MH, Cheng YH, Yang YJ, Jan S, Ramp SR, Reeder DB, Hsieh WT, Ko DS, Davis KA, Shao HJ, Tseng RS (2021) Direct measurements reveal instabilities and turbulence within large amplitude internal solitary waves beneath the ocean. Commun Earth Environ 2(1):15. https://doi.org/10.1038/s43247-020-00083-6

    Article  Google Scholar 

  2. Chang MH, Lien RC, Lamb K, Diamessis P (2021) Long-term observations of shoaling internal solitary waves in the northern South China Sea. J Geophys Res Oceans. https://doi.org/10.1029/2020JC017129

    Article  Google Scholar 

  3. Lien RC, D’Asaro E, Henyey F, Chang MH, Tang TY, Yang YJ (2012) Trapped core formation within a shoaling nonlinear internal wave. J Phys Oceanogr 42:511–525

    Article  Google Scholar 

  4. Lien RC, Henyey F, Ma B, Yang YJ (2014) Large-amplitude internal solitary waves observed in the northern South China Sea: properties and energetics. J Phys Oceanogr 44(4):1095–1115. https://doi.org/10.1175/JPO-D-13-088.1

    Article  Google Scholar 

  5. Moum J, Farmer D, Smyth W, 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 33:2093–2112

    Article  Google Scholar 

  6. Moore S, Lien RC (2007) Pilot whales follow internal solitary waves in the South China Sea. Mar Mammal Sci 21(1):193–196

    Article  Google Scholar 

  7. Bogucki D, Redekopp L (1999) A mechanism for sediment resuspension by internal solitary waves. Geophys Res Lett 26(9):1317–1320

    Article  Google Scholar 

  8. Diamessis P, Redekopp L (2006) Numerical investigation of solitary internal wave-induced global instability in a shallow water benthic boundary layers. J Phys Oceanogr 36:784–812

    Article  Google Scholar 

  9. Sakai T, Diamessis PJ, Jacobs GB (2020) Self-sustained instability, transition, and turbulence induced by a long separation bubble in the footprint of an internal solitary wave. I. Flow topology. Phys Rev Fluids 5:103801. https://doi.org/10.1103/PhysRevFluids.5.103801

    Article  Google Scholar 

  10. Sakai T, Diamessis PJ, Jacobs GB (2020) Self-sustained instability, transition, and turbulence induced by a long separation bubble in the footprint of an internal solitary wave. II. Flow statistics. Phys Rev Fluids 5:103802. https://doi.org/10.1103/PhysRevFluids.5.103802

    Article  Google Scholar 

  11. Stastna M, Lamb K (2008) Sediment resuspension mechanism associated with internal waves in coastal waters. J Geophys Res. https://doi.org/10.1029/2007JC004711Citations

    Article  Google Scholar 

  12. Zulberti A, Jones NL, Ivey GN (2020) Observations of enhanced sediment transport by nonlinear internal waves. Geophys Res Lett. https://doi.org/10.1029/2020GL088499

    Article  Google Scholar 

  13. Shroyer EL, Moum JN, Nash JD (2010) Energy transformations and dissipation of nonlinear internal waves over New Jersey’s continental shelf. Nonlinear Process Geophys 17(4):345–360. https://doi.org/10.5194/npg-17-345-2010

    Article  Google Scholar 

  14. St Laurent L (2008) Turbulent dissipation on the margins of the South China Sea. Geophys Res Lett. https://doi.org/10.1029/2008GL035520

    Article  Google Scholar 

  15. St Laurent L, Simmons H, Tang TY, Wang Y (2011) Turbulent properties of internal waves in the South China Sea. Oceanography. https://doi.org/10.5670/oceanog.2011.96

    Article  Google Scholar 

  16. Shroyer EL, Moum JN, Nash JD (2010) Vertical heat flux and lateral mass transport in nonlinear internal waves. Geophys Res Lett. https://doi.org/10.1029/2010GL042715

    Article  Google Scholar 

  17. Vlasenko V, Ostrovsky L, Hutter K (2005) Adiabatic behavior of strongly nonlinear internal solitary waves in slope-shelf areas. J Geophys Res. https://doi.org/10.1029/2004JC002705

    Article  Google Scholar 

  18. Aigner A, Broutman D, Grimshaw R (1999) Numerical simulations of internal solitary waves with vortex cores. Fluid Dyn Res 25:315–333

    Article  Google Scholar 

  19. Derzho O, Grimshaw R (1997) Solitary waves with a vortex core in a shallow layer of stratified fluid. Phys Fluids 9(11):3378–3785

    Article  Google Scholar 

  20. Lamb K (2002) A numerical investigation of solitary internal waves with trapped cores formed via shoaling. J Fluid Mech 451:109–144

    Article  Google Scholar 

  21. Lamb K (2003) Shoaling solitary internal waves: on a criterion for the formation of waves with trapped cores. J Fluid Mech 478:81–100

    Article  Google Scholar 

  22. Choi W (2006) The effect of a background shear current on large amplitude internal solitary waves. Phys Fluids 18:036601

    Article  Google Scholar 

  23. He Y, Lamb K, Lien RC (2019) Internal solitary waves with subsurface cores. J Fluid Mech 873:1–17

    Article  Google Scholar 

  24. Rivera-Rosario G, Diamessis PJ, Lien RC, Lamb KG, Thomsen GN (2020) Formation of recirculating cores in convectively breaking internal solitary waves of depression shoaling over gentle slopes in the South China Sea. J Phys Oceanogr 50(5):1137–1157. https://doi.org/10.1175/JPO-D-19-0036.1

    Article  Google Scholar 

  25. Andreassen O, Easber C (1994) Gravity wave breaking in two and three dimensions: 1. Model description and comparison of two-dimensional evolutions. J Geophys Res 99(D4):8095–8108

  26. Winters K, D’Asaro E (1994) Three-dimensional wave instability near a critical layer. J Fluid Mech 272:255–284

    Article  Google Scholar 

  27. Arthur R, Fringer O (2014) The dynamics of breaking internal solitary waves on slopes. J Fluid Mech 761:360–398

    Article  Google Scholar 

  28. Dörnbrack A (1998) Turbulent mixing by breaking gravity waves. J Fluid Mech 375:113–141

    Article  Google Scholar 

  29. Fringer O, Street R (2003) The dynamics of breaking progressive interfacial waves. J Fluid Mech 494:319–353

    Article  Google Scholar 

  30. Diamessis P, Domaradzki J, Hesthaven J (2005) A spectral multidomain penalty method model for the simulation of high Reynolds number localized incompressible stratified turbulence. J Comput Phys 202:198–322

    Article  Google Scholar 

  31. Joshi S (2016) Development of fast high-order numerical methods for high-Reynolds number environmental flows. PhD thesis, Cornell University

  32. Boyd J (2001) Chebyshev and Fourier spectral methods, 2nd edn. Dover Publications Inc., Mineola

    Google Scholar 

  33. Dunphy M, Subich C, Stastna M (2011) Spectral methods for internal waves: indistinguishable density profiles and double-humped solitary waves. Nonlinear Process Geophys 18:351–358

    Article  Google Scholar 

  34. Koop G, Butler G (1981) An investigation of internal solitary waves in a two-fluid system. J Fluid Mech 112:225–251. https://doi.org/10.1017/S0022112081000372

    Article  Google Scholar 

  35. Joshi S, Thomsen G, Diamessis P (2016) Deflation-accelerated preconditioning of the Poisson—Neumann Schur problem on long domains with a high-order discontinuous element-based collocation method. J Comput Phys 313:209–232

    Article  Google Scholar 

  36. Kopriva D (2009) Implementing spectral methods for partial differential equations. Springer, Dordrecht

    Book  Google Scholar 

  37. Kundu P, Cohen I, Dowling D (2012) Fluid mechanics. Elsevier, Amsterdam

    Google Scholar 

  38. Lamb K, Warn-Varnas A (2015) Two-dimensional numerical simulations of shoaling internal solitary waves at the ASIAEX site in the South China Sea. Nonlinear Process Geophys 22:289–312

    Article  Google Scholar 

  39. Helfrich K, Melville W (2006) Long nonlinear internal waves. Annu Rev Fluid Mech 38:395–425

    Article  Google Scholar 

  40. Karniadakis G, Israeli M, Orszag S (1991) High-order splitting methods for the incompressible Navier–Stokes equations. J Comput Phys 97:411–443

    Article  Google Scholar 

  41. Abdilghanie A (2011) A numerical investigation of turbulence-driven and forced generation of internal gravity waves in stratified mid-water. PhD thesis, Cornell University

  42. Blackburn H, Schmidt S (2003) Spectral element filtering techniques for large eddy simulation with dynamic estimation. J Comput Phys 186:610–629

    Article  Google Scholar 

  43. Escobar-Vargas J, Diamessis P, Sakai T (2014) A spectral quadrilateral multidomain penalty method model for high Reynolds number incompressible stratified flows. Int J Numer Methods Fluids 75:403–425

    Article  Google Scholar 

  44. Long R (1953) Some aspects of the flow of stratified fluids: I. A theoretical investigation. Tellus 8:460–471

    Google Scholar 

  45. Turkington B, Eydeland A, Wang S (1991) A computational method for solitary internal waves in a continuously stratified fluid. Stud Appl Math 85:93–127

    Article  Google Scholar 

  46. Diamessis P, Lin Y, Domaradzki J (2008) Effective numerical viscosity in spectral multidomain penalty method-based simulations of localized turbulence. J Comput Phys 227:8145–8164

    Article  Google Scholar 

  47. Joshi S, Diamessis P, Steinmoller D, Stastna M, Thomsen G (2016) A post-processing technique for stabilizing the discontinuous pressure projection operator in marginally-resolved incompressible inviscid flow. Comput Fluids 139:120–129

    Article  Google Scholar 

  48. Canuto C, Hussaini M, Quarteroni A, Zang T (2006) Spectral methods fundamentals in single domains. Springer, Berlin

    Book  Google Scholar 

  49. Winters KB, Riley JJ (1992) Instability of internal waves near a critical level. Dyn Atmos Oceans 16:249–278

    Article  Google Scholar 

  50. Brown GL, Roshko A (1974) On the density effects and large structure in turbulent mixing layers. J Fluid Mech 64:775–816

    Article  Google Scholar 

  51. Lamb K, Nguyen V (2009) Calculating energy flux in internal solitary waves with an application to reflectance. J Phys Oceanogr 39:559–580

    Article  Google Scholar 

  52. Winters K, Lombard P, Riley J, D’Asaro E (1995) Available potential energy and mixing in density-stratified fluids. J Fluid Mech 289:115–128

    Article  Google Scholar 

  53. Diamantopoulos T (2021) A high-order hybrid flow solver for the simulation of non-linear internal waves in long complex domains: exploring the turbulent aspects of a recirculating core in a shoaling internal solitary wave of depression. PhD thesis, Cornell University

  54. Holloway P (1987) Internal hydraulic jumps and solitons at a shelf break region on the australian north west shelf. J Geophys Res 92(C2):5405–5416

    Google Scholar 

  55. Zhang S, Alford M (2015) Instabilities in nonlinear internal waves on the Washington continental shelf. J Geophys Res 120:5272–5283

    Article  Google Scholar 

  56. Klose BF, Jacobs GB, Serra M (2020) Kinematics of Lagrangian flow separation in external aerodynamics. AIAA J 58(5):1926–1938. https://doi.org/10.2514/1.J059026

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank Theodoros Diamantopoulos, Marek Stastna, Yangxin He, and Frank Henyey for their insightful comments and suggestions regarding recirculating cores and this work. Financial support is gratefully acknowledged from National Science Foundation—Division of Ocean Sciences (OCE) Grant 1634257.

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Authors and Affiliations

  1. School of Civil and Environmental Engineering, Cornell University, Ithaca, NY, USA

    Gustavo Rivera-Rosario & Peter J. Diamessis

  2. Applied Physics Laboratory, University of Washington, Seattle, WA, USA

    Ren-Chieh Lien

  3. Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada

    Kevin G. Lamb

  4. Wandering Wakhs Research, Austin, TX, USA

    Greg N. Thomsen

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  1. Gustavo Rivera-Rosario
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  2. Peter J. Diamessis
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Correspondence to Gustavo Rivera-Rosario.

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Rivera-Rosario, G., Diamessis, P.J., Lien, RC. et al. Three-dimensional perspective on a convective instability and transition to turbulence in an internal solitary wave of depression shoaling over gentle slopes. Environ Fluid Mech 23, 1015–1035 (2023). https://doi.org/10.1007/s10652-022-09844-7

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