Abstract
We study the horizontal dispersion of passive tracer particles on the free surface of gravity waves in deep water. For random linear waves with the JONSWAP spectrum, the Lagrangian particle trajectories are computed using an exact nonlinear model known as the John–Sclavounos equation. We show that the single-particle dispersion exhibits an unusual super-diffusive behavior. In particular, for large times t, the variance of the tracer ⟨ | X ( t ) | 2 ⟩ increases as a quadratic function of time, i.e., ⟨ | X ( t ) | 2 ⟩ ∼ t 2 . This dispersion is markedly faster than Taylor’s single-particle dispersion theory which predicts that the variance of passive tracers grows linearly with time for large t. Our results imply that the wave motion significantly enhances the dispersion of fluid particles. We show that this super-diffusive behavior is a result of the long-term correlation of the Lagrangian velocities of fluid parcels on the free surface.
Highlights
Water waves cause the material transport of fluid particles on the free surface of the fluid.The waves induce a fluid velocity on the free surface which in turn determines the horizontal motion of fluid particles on the free surface
Previous studies of particle dispersion on the free surface of a fluid can be divided into three general categories: (i) Passive tracers on a flat free surface, (ii) Linear or nonlinear waves with the induced velocity field modeled based on simplifying assumptions, and (iii) Velocity field derived from satellite altimetry data
We report our results for three wave steepness values e = 0.05, 0.075 and 0.1 which are below the threshold for breaking waves
Summary
Water waves cause the material transport of fluid particles on the free surface of the fluid. The waves induce a fluid velocity on the free surface which in turn determines the horizontal motion of fluid particles on the free surface. This phenomena has been known since Stokes [1] who studied the average velocity of fluid parcels transported by a linear monochromatic wave. Knowledge of the horizontal position x (t) of the fluid particles and the free surface elevation ζ completely determines the position of the particles. The Stokes’ theory is concerned with the first-order statistics of the fluid displacement on the free surface.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have