### Abstract

For an idealized inertia-gravity wave, the Stokes drift, defined as the difference in end positions of a fluid parcel as derived in the Lagrangian and Eulerian coordinates, is exactly zero after one wave cycle in a deterministic flow. When stochastic effects are incorporated into the model, nonlinearity in the velocity field changes the statistical properties. Better understanding of the statistics of a passive tracer, such as the mean drift and higher order moments, leads to more accurate predictions of the pattern of Lagrangian mixing in a realistic environment. In this paper, we consider the inertia-gravity wave equation perturbed by white noise and solve the Fokker-Planck equation to study the evolution in time of the probability density function of passive tracers in such a flow. We find that at initial times the tracer distribution closely follows the nonlinear background flow and that nontrivial Stokes drift ensues as a result. Over finite times, we measure chaotic mixing based on the stochastic mean flow and identify nontrivial mixing structures of passive tracers, as compared to their absence in the deterministic flow. At later times, the probability density field spreads out to sample larger regions and the mean Stokes drift approaches an asymptotic value, indicating suppression of Lagrangian mixing at long time scales.

Original language | English (US) |
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Article number | 126601 |

Journal | Physics of Fluids |

Volume | 22 |

Issue number | 12 |

DOIs | |

State | Published - Dec 14 2010 |

### ASJC Scopus subject areas

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes