Energy cascade of internal gravity waves in oceans

  • Saranraj Gururaj

Student thesis: Doctoral ThesisDoctor of Philosophy


Internal gravity waves are large length scale waves that exist in the bulk of the ocean, and they play a crucial role in the ocean's energy budget. Various mechanisms cause the energy in internal gravity waves to cascade to small length scales. At small length scales, internal waves cause turbulence and mixing of waters with different densities. Mixing plays a prominent role in sustaining climate-influencing flows such as Meridional Overturning Circulation. This thesis is dedicated to understanding the mechanisms that cascade internal waves' energy to small length scales. First, using multiple scale analysis, we study triad interactions of low mode internal gravity waves that occur in the presence of slowly varying bathymetry. The waves' group speed and horizontal wavenumber vary with fluid depth, and the variation influences the energy transfer between the waves. Moreover, if the stratification is non-constant, detuning can be induced in wave-wave interactions that occur in a region of non-constant fluid depth. Detuning can affect the energy transfer between the waves. Nonlinear coupling coefficients and growth rates are observed to be sensitive to changes in fluid depth. Higher order self-interactions, where the bathymetry acts as a zero-frequency wave, are also studied.

Secondly, we study 5-wave systems that consist of two parent waves (waves with large amounts of energy) and three daughter waves (waves with infinitesimal energy). The five waves form two different triads, where each of these triads consists of one parent wave and two daughter waves, with one daughter wave shared between the two triads. The growth rate of 5-wave systems for different combinations of parent wavevectors is studied. Scenarios where the 5-wave system instability is more dominant than triads are analysed in detail. Apart from influencing wave-wave interactions, topographies can directly scatter a low mode internal wave and cause a cascade of the wave's energy. In the final chapter, internal wave topography interaction in the presence of a steady surface confined current is studied by conducting numerical simulations. The dependence of mode-1 wave scattering on the height and slope of the topography is studied. In the presence of a current, the mode-1 wave with positive phase speed has different properties compared to the mode-1 wave with negative phase speed, and we study the scattering of both mode-1 waves.
Date of Award2023
Original languageEnglish
SupervisorAnirban Guha (Supervisor), Tom Eaves (Supervisor) & Alan Cuthbertson (Supervisor)


  • Internal waves
  • Triads
  • wave-wave interaction
  • wave-topography interaction

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