Stimulated generation: extraction of energy from balanced flow by near-inertial waves

We study stimulated generation – the transfer of energy from balanced flows to existing internal waves – using an asymptotic model that couples barotropic quasi-geostrophic flow and near-inertial waves with $\text{e}^{\text{i}mz}$ vertical structure, where $m$ is the vertical wavenumber and $z$ is t...

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Bibliographic Details
Published in:Journal of fluid mechanics 2018-07, Vol.847, p.417-451
Main Authors: Rocha, Cesar B., Wagner, Gregory L., Young, William R.
Format: Article
Language:English
Subjects:
Barotropic mode
Cascading
Computational fluid dynamics
Conservation laws
Cyclones
Divergence
Energy dissipation
Geostrophic flow
Gradients
Group velocity
Inertial oscillations
Inertial waves
Internal waves
JFM Papers
Kinetic energy
Mathematical models
Ocean circulation
Phenomenology
Potential energy
Turbulence
Vertical profiles
Vorticity
Wave action
Wave dispersion
Wave energy
Wave power
Wavelengths
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Summary:We study stimulated generation – the transfer of energy from balanced flows to existing internal waves – using an asymptotic model that couples barotropic quasi-geostrophic flow and near-inertial waves with $\text{e}^{\text{i}mz}$ vertical structure, where $m$ is the vertical wavenumber and $z$ is the vertical coordinate. A detailed description of the conservation laws of this vertical-plane-wave model illuminates the mechanism of stimulated generation associated with vertical vorticity and lateral strain. There are two sources of wave potential energy, and corresponding sinks of balanced kinetic energy: the refractive convergence of wave action density into anti-cyclones (and divergence from cyclones); and the enhancement of wave-field gradients by geostrophic straining. We quantify these energy transfers and describe the phenomenology of stimulated generation using numerical solutions of an initially uniform inertial oscillation interacting with mature freely evolving two-dimensional turbulence. In all solutions, stimulated generation co-exists with a transfer of balanced kinetic energy to large scales via vortex merging. Also, geostrophic straining accounts for most of the generation of wave potential energy, representing a sink of 10 %–20 % of the initial balanced kinetic energy. However, refraction is fundamental because it creates the initial eddy-scale lateral gradients in the near-inertial field that are then enhanced by advection. In these quasi-inviscid solutions, wave dispersion is the only mechanism that upsets stimulated generation: with a barotropic balanced flow, lateral straining enhances the wave group velocity, so that waves accelerate and rapidly escape from straining regions. This wave escape prevents wave energy from cascading to dissipative scales.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2018.308