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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Published in:Journal of Fluid Mechanics
Main Authors: HOLMES-CERFON, MIRANDA, BÜHLER, OLIVER, FERRARI, RAFFAELE
Format: Article in Journal/Newspaper
Language:English
Published: Cambridge University Press (CUP) 2011
Subjects:
Online Access:http://dx.doi.org/10.1017/s0022112010005240
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112010005240
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spelling crcambridgeupr:10.1017/s0022112010005240 2024-09-09T19:57:33+00:00 Particle dispersion by random waves in the rotating Boussinesq system HOLMES-CERFON, MIRANDA BÜHLER, OLIVER FERRARI, RAFFAELE 2011 http://dx.doi.org/10.1017/s0022112010005240 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112010005240 en eng Cambridge University Press (CUP) https://www.cambridge.org/core/terms Journal of Fluid Mechanics volume 670, page 150-175 ISSN 0022-1120 1469-7645 journal-article 2011 crcambridgeupr https://doi.org/10.1017/s0022112010005240 2024-06-19T04:04:11Z 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. Article in Journal/Newspaper North Atlantic Cambridge University Press Munk ENVELOPE(-95.993,-95.993,55.979,55.979) Journal of Fluid Mechanics 670 150 175
institution Open Polar
collection Cambridge University Press
op_collection_id crcambridgeupr
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.
format Article in Journal/Newspaper
author HOLMES-CERFON, MIRANDA
BÜHLER, OLIVER
FERRARI, RAFFAELE
spellingShingle HOLMES-CERFON, MIRANDA
BÜHLER, OLIVER
FERRARI, RAFFAELE
Particle dispersion by random waves in the rotating Boussinesq system
author_facet HOLMES-CERFON, MIRANDA
BÜHLER, OLIVER
FERRARI, RAFFAELE
author_sort HOLMES-CERFON, MIRANDA
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 (CUP)
publishDate 2011
url http://dx.doi.org/10.1017/s0022112010005240
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112010005240
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 Journal of Fluid Mechanics
volume 670, page 150-175
ISSN 0022-1120 1469-7645
op_rights https://www.cambridge.org/core/terms
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
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