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Abstract High-frequency wave propagation in near-inertial wave shear has, for four decades, been considered fundamental in setting the spectral character of the oceanic internal wave continuum and for transporting energy to wave breaking. We compare idealized ray-tracing numerical results with metrics derived using a wave turbulence derivation for the kinetic equation and a path integral to study this specific process. Statistical metrics include the time-dependent ensemble mean vertical wavenumber, referred to as a mean drift; dispersion about the mean drift; time-lagged correlation estimates of wavenumber; and phase locking of the wave packets with the background. The path integral permits us to identify the mean drift as a resonant process and dispersion about that mean drift as nonresonant. At small inertial wave amplitudes, ray tracing, wave turbulence, and the path integral provide consistent descriptions for the mean drift of wave packets in the spectral domain and dispersion about the mean drift. Extrapolating these results to the background internal wavefield overpredicts downscale energy transports by an order of magnitude. At oceanic amplitudes, however, the numerics support diminished transport and dispersion that coincide with the mean drift time scale becoming similar to the lagged correlation time scale. We parse this as the transition to a non-Markovian process. Despite this decrease, numerical estimates of downscale energy transfer are still too large. We argue that residual differences result from an unwarranted discard of Bragg scattering resonances. Our results support replacing the long-standing interpretive paradigm of extreme scale-separated interactions with a more nuanced slate of “local” interactions in the kinetic equation.
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An Oceanic Ultra-Violet Catastrophe, Wave-Particle Duality and a Strongly Nonlinear Concept for Geophysical Turbulence
Abstract: There is no theoretical underpinning that successfully explains how turbulent mixing is fed by wave breaking associated with nonlinear wave-wave interactions in the background oceanic internal wavefield. We address this conundrum using one-dimensional ray tracing simulations to investigate interactions between high frequency internal waves and inertial oscillations in the extreme scale separated limit known as “Induced Diffusion”. Here, estimates of phase locking are used to define a resonant process (a resonant well) and a non-resonant process that results in stochastic jumps. The small amplitude limit consists of jumps that are small compared to the scale of the resonant well. The ray tracing simulations are used to estimate the first and second moments of a wave packet’s vertical wavenumber as it evolves from an initial condition. These moments are compared with predictions obtained from the diffusive approximation to a self-consistent kinetic equation derived in the ‘Direct Interaction Approximation’. Results indicate that the first and second moments of the two systems evolve in a nearly identical manner when the inertial field has amplitudes an order of magnitude smaller than oceanic values. At realistic (oceanic) amplitudes, though, the second moment estimated from the ray tracing simulations is inhibited. The transition is explained by the stochastic jumps obtaining the characteristic size of the resonant well. We interpret this transition as an adiabatic ‘saturation’ process which changes the nominal background wavefield from supporting no mixing to the point where that background wavefield defines the normalization for oceanic mixing models.
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- Award ID(s):
- 1634644
- PAR ID:
- 10044578
- Date Published:
- Journal Name:
- Fluids
- Volume:
- 2
- Issue:
- 36
- ISSN:
- 2353-4516
- Page Range / eLocation ID:
- 1-26
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/doi:10.3390/fluids2030036
