Near-inertial parametric subharmonic instability of internal wave beams
Parametric subharmonic instability (PSI) of internal wave beams in a uniformly stratified fluid is discussed, for the case where the beam frequency is nearly twice the inertial frequency due to background rotation. Compared with generic PSI, beams of finite width are expected on physical grounds to...
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| Format: | Article |
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American Physical Society (APS)
2018
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| Online Access: | http://hdl.handle.net/1721.1/117693 https://orcid.org/0000-0002-0677-1020 https://orcid.org/0000-0002-5246-4574 |
| _version_ | 1811073826110308352 |
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| author | Karimi, Hussain H. Akylas, Triantaphyllos R |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Karimi, Hussain H. Akylas, Triantaphyllos R |
| author_sort | Karimi, Hussain H. |
| collection | MIT |
| description | Parametric subharmonic instability (PSI) of internal wave beams in a uniformly stratified fluid is discussed, for the case where the beam frequency is nearly twice the inertial frequency due to background rotation. Compared with generic PSI, beams of finite width are expected on physical grounds to be more vulnerable to subharmonic perturbations of near-inertial frequency, as these disturbances have small group velocity and stay in contact with the underlying beam longer, thus extracting more energy. A weakly nonlinear theory for such near-inertial PSI is developed in the "distinguished limit" where the effects of triad nonlinear interactions, dispersion, and viscous dissipation are equally important. This model is used to examine the linear stability of a uniform beam to infinitesimal perturbations under a "pump-wave" approximation, as well as the nonlinear development of PSI that takes into account the effect of the growing perturbations on the beam evolution. Near-inertial PSI is possible for beams of general locally confined profile, in sharp contrast to generic PSI which can arise only for quasimonochromatic beams whose profile comprises a sinusoidal carrier modulated by a locally confined envelope. The theoretical predictions are consistent with earlier numerical simulations of semidiurnal internal tide beams generated over the continental shelf break at latitudes above and below the critical value 28.8âN, at which the subharmonic semidiurnal frequency matches the local inertial frequency. |
| first_indexed | 2024-09-23T09:39:16Z |
| format | Article |
| id | mit-1721.1/117693 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T09:39:16Z |
| publishDate | 2018 |
| publisher | American Physical Society (APS) |
| record_format | dspace |
| spelling | mit-1721.1/1176932022-09-26T12:52:21Z Near-inertial parametric subharmonic instability of internal wave beams Karimi, Hussain H. Akylas, Triantaphyllos R Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Department of Mechanical Engineering Karimi, Hussain H. Akylas, Triantaphyllos R Parametric subharmonic instability (PSI) of internal wave beams in a uniformly stratified fluid is discussed, for the case where the beam frequency is nearly twice the inertial frequency due to background rotation. Compared with generic PSI, beams of finite width are expected on physical grounds to be more vulnerable to subharmonic perturbations of near-inertial frequency, as these disturbances have small group velocity and stay in contact with the underlying beam longer, thus extracting more energy. A weakly nonlinear theory for such near-inertial PSI is developed in the "distinguished limit" where the effects of triad nonlinear interactions, dispersion, and viscous dissipation are equally important. This model is used to examine the linear stability of a uniform beam to infinitesimal perturbations under a "pump-wave" approximation, as well as the nonlinear development of PSI that takes into account the effect of the growing perturbations on the beam evolution. Near-inertial PSI is possible for beams of general locally confined profile, in sharp contrast to generic PSI which can arise only for quasimonochromatic beams whose profile comprises a sinusoidal carrier modulated by a locally confined envelope. The theoretical predictions are consistent with earlier numerical simulations of semidiurnal internal tide beams generated over the continental shelf break at latitudes above and below the critical value 28.8âN, at which the subharmonic semidiurnal frequency matches the local inertial frequency. National Science Foundation (U.S.) (Grant DMS-1107335) National Science Foundation (U.S.) (Grant DMS-1512925) 2018-09-10T19:21:45Z 2018-09-10T19:21:45Z 2017-07 2017-04 2018-08-29T13:54:56Z Article http://purl.org/eprint/type/JournalArticle 2469-990X http://hdl.handle.net/1721.1/117693 Karimi, Hussain H., and T. R. Akylas. “Near-Inertial Parametric Subharmonic Instability of Internal Wave Beams.” Physical Review Fluids, vol. 2, no. 7, July 2017. © 2017 American Physical Society https://orcid.org/0000-0002-0677-1020 https://orcid.org/0000-0002-5246-4574 http://dx.doi.org/10.1103/PHYSREVFLUIDS.2.074801 Physical Review Fluids Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society (APS) APS |
| spellingShingle | Karimi, Hussain H. Akylas, Triantaphyllos R Near-inertial parametric subharmonic instability of internal wave beams |
| title | Near-inertial parametric subharmonic instability of internal wave beams |
| title_full | Near-inertial parametric subharmonic instability of internal wave beams |
| title_fullStr | Near-inertial parametric subharmonic instability of internal wave beams |
| title_full_unstemmed | Near-inertial parametric subharmonic instability of internal wave beams |
| title_short | Near-inertial parametric subharmonic instability of internal wave beams |
| title_sort | near inertial parametric subharmonic instability of internal wave beams |
| url | http://hdl.handle.net/1721.1/117693 https://orcid.org/0000-0002-0677-1020 https://orcid.org/0000-0002-5246-4574 |
| work_keys_str_mv | AT karimihussainh nearinertialparametricsubharmonicinstabilityofinternalwavebeams AT akylastriantaphyllosr nearinertialparametricsubharmonicinstabilityofinternalwavebeams |