Particle dispersion by random waves in the rotating Boussinesq system
We present a theoretical and numerical study of horizontal particle dispersion due to random waves in the three-dimensional rotating and stratified Boussinesq system, which serves as a simple model to study the dispersion of tracers in the ocean by the internal wave field. Specifically, the effectiv...
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ftmit:oai:dspace.mit.edu:1721.1/73682 2023-06-11T04:14:49+02:00 Particle dispersion by random waves in the rotating Boussinesq system Ferrari, Raffaele Holmes-Cerfon, Miranda Buhler, Oliver Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Ferrari, Raffaele 2010-10 application/pdf http://hdl.handle.net/1721.1/73682 en_US eng Cambridge University Press http://dx.doi.org/10.1017/s0022112010005240 Journal of Fluid Mechanics 0022-1120 1469-7645 http://hdl.handle.net/1721.1/73682 Holmes-Cerfon, Miranda, Oliver BüHler, and Raffaele Ferrari. “Particle Dispersion by Random Waves in the Rotating Boussinesq System.” Journal of Fluid Mechanics 670 (2011): 150–175. © Cambridge University Press 2011 orcid:0000-0002-3736-1956 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. MIT web domain Article http://purl.org/eprint/type/JournalArticle 2010 ftmit https://doi.org/10.1017/s0022112010005240 2023-05-29T08:53:37Z We present a theoretical and numerical study of horizontal particle dispersion due to random waves in the three-dimensional rotating and stratified Boussinesq system, which serves as a simple model to study the dispersion of tracers in the ocean by the internal wave field. Specifically, the effective one-particle diffusivity in the sense of Taylor (Proc. Lond. Math. Soc., vol. 20, 1921, p. 196) is computed for a small-amplitude internal gravity wave field modelled as a stationary homogeneous and horizontally isotropic Gaussian random field whose frequency spectrum is bounded away from zero. Dispersion in this system does not arise simply because of a Stokes drift effect, as in the case of surface gravity waves, but in addition it is driven by the nonlinear, second-order corrections to the linear velocity field, which can be computed using the methods of wave–mean interaction theory. A formula for the one-particle diffusivity as a function of the spectrum of the random wave field is presented. It is shown that this diffusivity is much smaller than might be expected from heuristic arguments based on the magnitude of the Stokes drift or the pseudomomentum. This appears to stem from certain incompressibility constraints for the Stokes drift and the second-order velocity field. Finally, the theory is applied to oceanic conditions described by a typical model wave spectrum, the Garrett–Munk spectrum, and also by detailed field observations from the North Atlantic tracer release experiment. United States. Office of Naval Research (Grant N000140910458) Article in Journal/Newspaper North Atlantic DSpace@MIT (Massachusetts Institute of Technology) Munk ENVELOPE(-95.993,-95.993,55.979,55.979) Journal of Fluid Mechanics 670 150 175 |
institution |
Open Polar |
collection |
DSpace@MIT (Massachusetts Institute of Technology) |
op_collection_id |
ftmit |
language |
English |
description |
We present a theoretical and numerical study of horizontal particle dispersion due to random waves in the three-dimensional rotating and stratified Boussinesq system, which serves as a simple model to study the dispersion of tracers in the ocean by the internal wave field. Specifically, the effective one-particle diffusivity in the sense of Taylor (Proc. Lond. Math. Soc., vol. 20, 1921, p. 196) is computed for a small-amplitude internal gravity wave field modelled as a stationary homogeneous and horizontally isotropic Gaussian random field whose frequency spectrum is bounded away from zero. Dispersion in this system does not arise simply because of a Stokes drift effect, as in the case of surface gravity waves, but in addition it is driven by the nonlinear, second-order corrections to the linear velocity field, which can be computed using the methods of wave–mean interaction theory. A formula for the one-particle diffusivity as a function of the spectrum of the random wave field is presented. It is shown that this diffusivity is much smaller than might be expected from heuristic arguments based on the magnitude of the Stokes drift or the pseudomomentum. This appears to stem from certain incompressibility constraints for the Stokes drift and the second-order velocity field. Finally, the theory is applied to oceanic conditions described by a typical model wave spectrum, the Garrett–Munk spectrum, and also by detailed field observations from the North Atlantic tracer release experiment. United States. Office of Naval Research (Grant N000140910458) |
author2 |
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Ferrari, Raffaele |
format |
Article in Journal/Newspaper |
author |
Ferrari, Raffaele Holmes-Cerfon, Miranda Buhler, Oliver |
spellingShingle |
Ferrari, Raffaele Holmes-Cerfon, Miranda Buhler, Oliver Particle dispersion by random waves in the rotating Boussinesq system |
author_facet |
Ferrari, Raffaele Holmes-Cerfon, Miranda Buhler, Oliver |
author_sort |
Ferrari, Raffaele |
title |
Particle dispersion by random waves in the rotating Boussinesq system |
title_short |
Particle dispersion by random waves in the rotating Boussinesq system |
title_full |
Particle dispersion by random waves in the rotating Boussinesq system |
title_fullStr |
Particle dispersion by random waves in the rotating Boussinesq system |
title_full_unstemmed |
Particle dispersion by random waves in the rotating Boussinesq system |
title_sort |
particle dispersion by random waves in the rotating boussinesq system |
publisher |
Cambridge University Press |
publishDate |
2010 |
url |
http://hdl.handle.net/1721.1/73682 |
long_lat |
ENVELOPE(-95.993,-95.993,55.979,55.979) |
geographic |
Munk |
geographic_facet |
Munk |
genre |
North Atlantic |
genre_facet |
North Atlantic |
op_source |
MIT web domain |
op_relation |
http://dx.doi.org/10.1017/s0022112010005240 Journal of Fluid Mechanics 0022-1120 1469-7645 http://hdl.handle.net/1721.1/73682 Holmes-Cerfon, Miranda, Oliver BüHler, and Raffaele Ferrari. “Particle Dispersion by Random Waves in the Rotating Boussinesq System.” Journal of Fluid Mechanics 670 (2011): 150–175. © Cambridge University Press 2011 orcid:0000-0002-3736-1956 |
op_rights |
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. |
op_doi |
https://doi.org/10.1017/s0022112010005240 |
container_title |
Journal of Fluid Mechanics |
container_volume |
670 |
container_start_page |
150 |
op_container_end_page |
175 |
_version_ |
1768371125615591424 |