Particle motions in large-amplitude wave fields

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Abstract
We calculate the trajectories of particles in two-dimensional model flows typifying atmospheric or oceanic eddy motions. Rather than restricting the flows to be weak (but solutions to the relevant dynamics), we have considered motions where the streamfunction is only a kinematic model resembling the actual flows but the amplitude can be large so that flow speeds can greatly exceed the phase speed. For steadily propagating disturbances, there is an equivalent one-dimensional Lagrangian motion problem and we have applied results from analyses of such to periodic channel waves and isolated circular eddies. We show that the mean Lagrangian drift rate in periodic channel waves is very sensitive to the initial position and may be either prograde or retrograde. Large volumes of the fluid may be “trapped” to translate along with the wave. The wave drift depends on the phase velocity relative to the Eulerian mean flow and peaks at about 1/3 of the transient Eulerian speed at geophysically relevant amplitudes. For isolated eddies such as Gulf Stream rings, we calculate the trapped volume carried with the eddy and the displacements of the particles outside. We show that some particles may translate quite large distances along with the eddy while others move rapidly in the opposite direction and are left behind.

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