Optimal transient growth in thin-interface internal solitary waves
Date
2018-01-10Author
Passaggia, Pierre-Yves
Concept link
Helfrich, Karl R.
Concept link
White, Brian L.
Concept link
Metadata
Show full item recordCitable URI
https://hdl.handle.net/1912/9567As published
https://doi.org/10.1017/jfm.2018.19Keyword
Solitary waves; Internal waves; InstabilityAbstract
The dynamics of perturbations to large-amplitude Internal Solitary Waves (ISW) in
two-layered
ows with thin interfaces is analyzed by means of linear optimal transient
growth methods. Optimal perturbations are computed through direct-adjoint iterations
of the Navier-Stokes equations linearized around inviscid, steady ISWs obtained from
the Dubreil-Jacotin-Long (DJL) equation. Optimal perturbations are found as a function
of the ISW phase velocity c (alternatively amplitude) for one representative stratification. These disturbances are found to be localized wave-like packets that originate
just upstream of the ISW self-induced zone (for large enough c) of potentially unstable
Richardson number, Ri < 0:25. They propagate through the base wave as coherent
packets whose total energy gain increases rapidly with c. The optimal disturbances are
also shown to be relevant to DJL solitary waves that have been modi ed by viscosity
representative of laboratory experiments. The optimal disturbances are compared to the
local WKB approximation for spatially growing Kelvin-Helmholtz (K-H) waves through
the Ri < 0:25 zone. The WKB approach is able to capture properties (e.g., carrier frequency,
wavenumber and energy gain) of the optimal disturbances except for an initial
phase of non-normal growth due to the Orr mechanism. The non-normal growth can
be a substantial portion of the total gain, especially for ISWs that are weakly unstable
to K-H waves. The linear evolution of Gaussian packets of linear free waves with the
same carrier frequency as the optimal disturbances is shown to result in less energy gain
than found for either the optimal perturbations or the WKB approximation due to nonnormal
effects that cause absorption of disturbance energy into the leading face of the
wave. Two-dimensional numerical calculations of the nonlinear evolution of optimal disturbance
packets leads to the generation of large-amplitude K-H billows that can emerge
on the leading face of the wave and that break down into turbulence in the lee of the wave.
The nonlinear calculations are used to derive a slowly varying model of ISW decay due
to repeated encounters with optimal or free wave packets. Field observations of unstable
ISW by Moum et al. (2003) are consistent with excitation by optimal disturbances.
Description
Author Posting. © The Author(s), 2018. This is the author's version of the work. It is posted here under a nonexclusive, irrevocable, paid-up, worldwide license granted to WHOI. It is made available for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 840 (2018): 342-378, doi:10.1017/jfm.2018.19.
Collections
Suggested Citation
Preprint: Passaggia, Pierre-Yves, Helfrich, Karl R., White, Brian L., "Optimal transient growth in thin-interface internal solitary waves", 2018-01-10, https://doi.org/10.1017/jfm.2018.19, https://hdl.handle.net/1912/9567Related items
Showing items related by title, author, creator and subject.
-
The 1998 WHOI/IOS/ONR internal solitary wave workshop : contributed papers
Duda, Timothy F.; Farmer, David M. (Woods Hole Oceanographic Institution, 1999-07)A workshop entitled "Internal Solitary Waves in the Ocean: Their Physics and Implications for Acoustics, Biology, and Geology" was held during October, 1998 in Sydney, British Columbia, Canada. It was jointly organized by ... -
Temporal sound field fluctuations in the presence of internal solitary waves in shallow water
Katsnelson, Boris G.; Grigorev, Valery A.; Badiey, Mohsen; Lynch, James F. (Acoustical Society of America, 2009-06-19)Temporal variations of intensity fluctuations are presented from the SWARM95 experiment. It is hypothesized that specific features of these fluctuations can be explained by mode coupling due to the presence of an internal ... -
LOCOMOOR : a LOw-COst MOORing for the measurement of internal solitary waves
Lord, Jeffrey; Irish, James D.; Duda, Timothy F.; Kemp, John N. (2000-05-09)In order to supplement the ASIAEX field effort to measure the temporal and spatial structure of the internal solitary wave field in relationship to acoustic propagation and scattering studies, an array of low-cost ...