### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 150-175 |

Number of pages | 26 |

Journal | Journal of Fluid Mechanics |

Volume | 670 |

DOIs | |

State | Published - Mar 10 2011 |

### Fingerprint

### Keywords

- internal waves
- mixing and dispersion
- rotating flows

### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*670*, 150-175. https://doi.org/10.1017/S0022112010005240

**Particle dispersion by random waves in the rotating Boussinesq system.** / Holmes-Cerfon, Miranda; Buhler, Oliver; Ferrari, Raffaele.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 670, pp. 150-175. https://doi.org/10.1017/S0022112010005240

}

TY - JOUR

T1 - Particle dispersion by random waves in the rotating Boussinesq system

AU - Holmes-Cerfon, Miranda

AU - Buhler, Oliver

AU - Ferrari, Raffaele

PY - 2011/3/10

Y1 - 2011/3/10

N2 - 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.

AB - 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.

KW - internal waves

KW - mixing and dispersion

KW - rotating flows

UR - http://www.scopus.com/inward/record.url?scp=79952758545&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952758545&partnerID=8YFLogxK

U2 - 10.1017/S0022112010005240

DO - 10.1017/S0022112010005240

M3 - Article

VL - 670

SP - 150

EP - 175

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -