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Nonlinear Evolution of Localized Internal Gravity Wave Packets: Theory and Simulations with Rotation, Background Flow, and Anelastic Effects

  • Author / Creator
    Gervais, Alain D

  • A series of three studies investigates theoretically and numerically the evolution, stability, and pseudomomentum transport of fully localized three-dimensional internal gravity wave packets, as they self-interact nonlinearly with their induced mean flow.

    The first study considers a rotating, uniformly stratified Boussinesq fluid that is stationary in the absence of waves. We derive through perturbation theory an integral expression for the mean ``Bretherton flow'' induced by fully localized wave packets influenced by the Coriolis force. We perform numerical simulations of fully localized wave packets with the predicted Bretherton flow superimposed, for a range of initial amplitudes, wave packet aspect ratios, and relative vertical wavenumbers spanning the hydrostatic and nonhydrostatic regimes. Results are compared with predictions based on linear theory of wave breaking due to overturning, convection, self-acceleration, and shear instability. We find that nonhydrostatic wavepackets tend to destabilize due to self-acceleration, eventually overturning although the initial amplitude is well below the overturning amplitude predicted by linear theory. Strongly hydrostatic waves are found not to attain amplitudes sufficient to become shear unstable, overturning instead due to localized steepening of isopycnals. Results are discussed in the broader context of previous studies of one- and two-dimensional wave packet overturning, and recent observations of oceanic internal waves.

    The second study considers the transmission and reflection of finite amplitude internal gravity wave packets across a reflection level in a nonrotating Boussinesq fluid with a nonuniform retrograde shear flow. We derive the critical amplitude for wave packets to transmit partially above the reflection level predicted by linear theory. We find that transmitted and reflected wave packets corresponding to strongly nonhydrostatic primary waves can interact resonantly to generate quadratically nonlinear secondary wave packets. We propose a novel weakly nonlinear mechanism to explain the generation of secondary wave packets by nonbreaking moderately nonhydrostatic primary waves, and predict the critical amplitude for its onset. Simulations are performed for a range of nonhydrostatic wave packets with small to moderately large initial amplitudes with their predicted Bretherton flow superimposed. Transmission is quantified using the pseudomomentum corresponding to upward-propagating waves above the reflection level. In most cases transmission transiently grows and decays as wave packets first cross and then reflect from the reflection level. For all but the most strongly nonhydrostatic wave packets, larger-amplitude waves exhibit smaller peak transmission, relative to the total pseudomomentum. Strongly nonhydrostatic wave packets exhibit continuous transmission well above the reflection level. When we consider the time interval for transmission to decrease to half its peak value, we find this becomes longer with larger initial amplitude. These behaviours result from the combined effects of modulational instability, and the generation and evolution of secondary wave packets. Results are discussed in the context of previous studies of one- and two-dimensional wave packet transmission and reflection.

    The third study considers the transmission and reflection of three-dimensional internal gravity wave packets in an anelastic gas in which the background flow models the Quasi-Biennial Oscillation (QBO). We derive an integral expression for the anelastic Bretherton flow, and the conditions for wave packets to tunnel partially through the QBO winds. Simulations are performed for a range of moderately nonhydrostatic wave packets with their predicted Bretherton flow superimposed, incident upon two model QBO profiles. Transmission is quantified using the pseudomomentum of waves above the QBO. Transmission decreases as wave packets are initialized to be progressively more nonhydrostatic. Varying initial wave amplitude is found to have no quantitative effect on transmission (relative to the initial pseudomomentum) for physically relevant initial amplitudes because nonlinear interactions with the Bretherton flow occur on a significantly slower time scale than that of transmission. Transmitted wave packets tend to grow exponentially in amplitude due to the exponentially decreasing atmospheric background mass density, ultimately inducing a local mean flow that acts to drive the waves to overturn and break turbulently. Results are discussed in the context of previous studies of one- and two-dimensional wave packet transmission and reflection, and of the theorized role of internal gravity waves in driving QBO dynamics.

  • Subjects / Keywords
  • Graduation date
    Fall 2023
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/r3-t0gh-s911
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.