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Particle dispersion by nonlinearly damped random waves

Published online by Cambridge University Press:  02 December 2015

Oliver Bühler  and
Yuan Guo
Oliver Bühler*
Affiliation:
Center for Atmosphere Ocean Science at the Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Yuan Guo
Affiliation:
Center for Atmosphere Ocean Science at the Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
*
†Email address for correspondence: [email protected]
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Abstract

We present a theoretical study of the dispersion of particles along quasi-horizontal stratification surfaces induced by small-amplitude internal gravity waves that are forced by white noise and dissipated by linear or nonlinear damping. This extends previous studies in which only linear damping was considered. The damping itself is a toy model for the nonlinear processes that would attenuate a wave mode in a broad spectrum of internal waves such as the Garrett–Munk spectrum for ocean internal waves. We compute the velocity covariance using an eigenfunction expansion of the Kolmogorov backward equation and investigate how the degree of nonlinearity affects the scaling of diffusivity with wave amplitude. We find a simple new expression for the diffusivity that is valid in both the linear and nonlinear cases, and we consider the likely quantitative importance of these process in the context of data from field experiments on small-scale ocean tracer dispersion.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Ocean processes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 786 , 10 January 2016 , pp. 332 - 347
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Copyright
© 2015 Cambridge University Press 

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