Effect of background mean flow on PSI of internal wave beams

An asymptotic model is developed for the parametric subharmonic instability (PSI) of finite-width nearly monochromatic internal gravity wave beams in the presence of a background constant horizontal mean flow. The subharmonic perturbations are taken to be short-scale wavepackets that may extract ene...

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Bibliographic Details
Published in:Journal of fluid mechanics 2019-06, Vol.869, Article R1
Main Authors: Fan, Boyu, Akylas, T. R.
Format: Article
Language:English
Subjects:
Dynamics
Energy
Fluid mechanics
Gravitational waves
Gravity
Gravity waves
Group velocity
Instability
Interactions
Internal waves
JFM Rapids
Nonlinear systems
Nonlinearity
Perturbations
Photosystem I
Reynolds number
Stability
Velocity
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Summary:An asymptotic model is developed for the parametric subharmonic instability (PSI) of finite-width nearly monochromatic internal gravity wave beams in the presence of a background constant horizontal mean flow. The subharmonic perturbations are taken to be short-scale wavepackets that may extract energy via resonant triad interactions while in contact with the underlying beam, and the mean flow is assumed to be small so that its advection effect on the perturbations is as important as dispersion, triad nonlinearity and viscous dissipation. In this ‘distinguished limit’, the perturbation dynamics are governed by the same evolution equations as those derived in Karimi & Akylas (J. Fluid Mech., vol. 757, 2014, pp. 381–402), except for a mean flow term that affects the group velocity of the perturbations and imposes an additional necessary condition for PSI, which stabilizes very short-scale perturbations. As a result, it is possible for a small amount of mean flow to weaken PSI dramatically.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2019.247