Particle dispersion by stochastic waves

When dropped in the ocean, a patch of dye will diffuse much faster that if released in an absolutely still body of water, even in the quietest parts of the ocean. This indicates that even there, fluid motions are at work to mix tracers, but which types of motions? We tested the hypothesis that the advection of particles by a background white noise of internal waves could be sufficient to explain the value for the horizontal diffusivity, measured in the ocean. We combined simple stochastic models and direct nonlinear numerical simulations of three-dimensional internal waves that weakly dissipate. In contrast with the results for perfectly non-dissipative internal waves, in which such dispersion arises only at fourth-order in wave amplitude, our dissipative model induces a diffusivity at second-order. This finding reinforces the possibility that internal waves are much more efficient horizontal mixers than previously thought.

NoisePhysical        What the internal wave field looks like,...

Trajectories

... the trajectories of a set of Lagrangian particles,
dropped in the wave field above,...

Trajectory
... and a close-up of one trajectory in particular. On top of the
oscillations due to the internal waves (the hundreds of circular
oscillations), the particle slowly drifts, describing a random walk.

 

Reference: O. Bühler, N. Grisouard and M. Holmes-Cerfon. Strong particle dispersion induced by weakly dissipative random internal waves. Journal of Fluid Mechanics, 719:R4, 2013. (pdf, copyright Cambridge University Press | doi)