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Five-wave interactions in inertia-gravity waves

Saranraj Gururaj* and Anirban Guha

  • *Contact author: gmsaranraj@gmail.com
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Phys. Rev. Fluids 10, 034803 – Published 28 March, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.034803

Abstract

In oceans, multiple energetic inertia-gravity waves often coexist in a region. In this paper, we study the stability of two coexisting plane inertia-gravity waves (hereafter, primary waves), with the same frequencies (ω1) and wave-vector norms, in a region of constant background stratification (denoted by N). Specifically, we explore the decay of two primary waves through triadic resonant instabilities in cases in which the primary waves do not resonantly interact with each other. Two coexisting primary waves undergoing triadic resonant instability can force two secondary waves each, and this results in two three-wave systems (3WSs). In some cases, two primary waves can have a common secondary wave, and this results in a five-wave system (5WS) composed of two different triads. We show that 5WSs are the dominant instabilities with higher growth rates than standard triads for a wide range of Coriolis frequency values (f). For two-dimensional (2D) cases, 5WSs have higher growth rates than triads for f/ω1⪆0.3 and for primary waves with the same horizontal (vertical) wave number but with the opposite vertical (horizontal) wave number. Similar results are observed for 3D cases in which the primary waves are not on the same vertical plane. Numerical simulations match the theoretical growth rates of 5WSs for a wide range of latitudes, except when f/ω1≈0.5 (critical latitude). Using theory and simulations, we show that the maximum growth rate near the critical latitude is approximately twice the maximum growth rate of all triads.

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References (36)

  1. W. Munk and C. Wunsch, Abyssal recipes II: Energetics of tidal and wind mixing, Deep Sea Res. Part I Oceanogr. Res. Pap. 45, 1977 (1998).
  2. R. Ferrari and C. Wunsch, Ocean circulation kinetic energy: Reservoirs, sources, and sinks, Annu. Rev. Fluid Mech. 41, 253 (2009).
  3. C. de Lavergne, S. Falahat, G. Madec, F. Roquet, J. Nycander, and C. Vic, Toward global maps of internal tide energy sinks, Ocean Model. 137, 52 (2019).
  4. C. R. Koudella and C. Staquet, Instability mechanisms of a two-dimensional progressive internal gravity wave, J. Fluid Mech. 548, 165 (2006).
  5. K. Hasselmann, A criterion for nonlinear wave stability, J. Fluid Mech. 30, 737 (1967).
  6. S. A. Thorpe, On wave interactions in a stratified fluid, J. Fluid Mech. 24, 737 (1966).
  7. R. E. Davis and A. Acrivos, The stability of oscillatory internal waves, J. Fluid Mech. 30, 723 (1967).
  8. J. Klostermeyer, Two- and three-dimensional parametric instabilities in finite-amplitude internal gravity waves, Geophys. Astrophys. Fluid Dyn. 61, 1 (1991).
  9. L. J. Sonmor and G. P. Klaassen, Toward a unified theory of gravity wave stability, J. Atmos. Sci. 54, 2655 (1997).
  10. B. Bourget, T. Dauxois, S. Joubaud, and P. Odier, Experimental study of parametric subharmonic instability for internal plane waves, J. Fluid Mech. 723, 1 (2013).
  11. B. Bourget, H. Scolan, T. Dauxois, M. Le Bars, P. Odier, and S. Joubaud, Finite-size effects in parametric subharmonic instability, J. Fluid Mech. 759, 739 (2014).
  12. W. R. Young, Y.-K. Tsang, and N. J. Balmforth, Near-inertial parametric subharmonic instability, J. Fluid Mech. 607, 25 (2008).
  13. P. Maurer, S. Joubaud, and P. Odier, Generation and stability of inertia–gravity waves, J. Fluid Mech. 808, 539 (2016).
  14. J. A. MacKinnon and K. B. Winters, Subtropical catastrophe: Significant loss of low-mode tidal energy at 28.9∘, Geophys. Res. Lett. 32, 2005GL023376 (2005).
  15. O. Richet, J.-M. Chomaz, and C. Muller, Internal tide dissipation at topography: Triadic resonant instability equatorward and evanescent waves poleward of the critical latitude, J. Geophys. Res Oceans 123, 6136 (2018).
  16. M. H. Alford, J. A. MacKinnon, Z. Zhao, R. Pinkel, J. Klymak, and T. Peacock, Internal waves across the pacific, Geophys. Res. Lett. 34, 2007GL031566 (2007).
  17. J. Hazewinkel and K. B. Winters, Psi of the internal tide on a β plane: Flux divergence and near-inertial wave propagation, J. Phys. Oceanogr. 41, 1673 (2011).
  18. T. Hibiya, Y. Niwa, and K. Fujiwara, Numerical experiments of nonlinear energy transfer within the oceanic internal wave spectrum, J. Geophys. Res. Oceans 103, 18715 (1998).
  19. Y. Onuki and T. Hibiya, Decay rates of internal tides estimated by an improved wave–wave interaction analysis, J. Phys. Oceanogr. 48, 2689 (2018).
  20. D. Olbers, F. Pollmann, and C. Eden, On PSI interactions in internal gravity wave fields and the decay of baroclinic tides, J. Phys. Oceanogr. 50, 751 (2020).
  21. M. Nikurashin and S. Legg, A mechanism for local dissipation of internal tides generated at rough topography, J. Phys. Oceanogr. 41, 378 (2011).
  22. A. Tabaei, T. R. Akylas, and K. Lamb, Nonlinear effects in reflecting and colliding internal wave beams, J. Fluid Mech. 526, 217 (2005).
  23. C.-H. Jiang and P. S. Marcus, Selection rules for the nonlinear interaction of internal gravity waves, Phys. Rev. Lett. 102, 124502 (2009).
  24. T. R. Akylas and H. H. Karimi, Oblique collisions of internal wave beams and associated resonances, J. Fluid Mech. 711, 337 (2012).
  25. P. Husseini, D. Varma, T. Dauxois, S. Joubaud, P. Odier, and M. Mathur, Experimental study on superharmonic wave generation by resonant interaction between internal wave modes, Phys. Rev. Fluids 5, 074804 (2020).
  26. Q. Pan, N. N. Peng, H. N. Chan, and K. W. Chow, Coupled triads in the dynamics of internal waves: Case study using a linearly stratified fluid, Phys. Rev. Fluids 6, 024802 (2021).
  27. Q. Pan, H.-M. Yin, and K. W. Chow, Triads and rogue events for internal waves in stratified fluids with a constant buoyancy frequency, J. Mar. Sci. 9, 577 (2021).
  28. A. McEwan and R. Plumb, Off-resonant amplification of finite internal wave packets, Dynam. Atmos. Ocean 2, 83 (1977).
  29. M. Mathur, G. S. Carter, and T. Peacock, Topographic scattering of the low-mode internal tide in the deep ocean, J. Geophys. Res. Oceans 119, 2165 (2014).
  30. Z. Zhao, M. H. Alford, J. B. Girton, L. Rainville, and H. L. Simmons, Global observations of open-ocean mode-1 M2 internal tides, J. Phys. Oceanogr. 46, 1657 (2016).
  31. D. O. Mora, E. Monsalve, M. Brunet, T. Dauxois, and P.-P. Cortet, Three-dimensionality of the triadic resonance instability of a plane inertial wave, Phys. Rev. Fluids 6, 074801 (2021).
  32. O. M. Phillips, The Dynamics of the Upper Ocean, 2nd ed. (Cambridge University Press, Cambridge, 1977).
  33. Y. R. Yi, S. Legg, and R. Nazarian, The impact of topographic steepness on tidal dissipation at bumpy topography, Fluids 2, 55 (2017).
  34. O. Richet, C. Muller, and J.-M. Chomaz, Impact of a mean current on the internal tide energy dissipation at the critical latitude, J. Phys. Oceanogr. 47, 1457 (2017).
  35. Z. Chen, S. Chen, Z. Liu, J. Xu, J. Xie, Y. He, and S. Cai, Can tidal forcing alone generate a gm-like internal wave spectrum?, Geophys. Res. Lett. 46, 14644 (2019).
  36. K. J. Burns, G. M. Vasil, J. S. Oishi, D. Lecoanet, and B. P. Brown, Dedalus: A flexible framework for numerical simulations with spectral methods, Phys. Rev. Res. 2, 023068 (2020).

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Phys. Rev. Fluids 10, 034803– Published 28 March, 2025
  • Received 28 June 2023
  • Accepted 23 December 2024
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