CHAOTIC MIXING BY INTERNAL INERTIA-GRAVITY WAVES

The Lagrangian transport of ''passive'' particles advected by inertia- gravity waves is investigated. We consider two classes of waves, namel y, vertically trapped, horizontally propagating waves, and those propa gating in three dimensions (3D). In the former case, it is shown that the superposition of at least two waves is necessary to produce chaoti c particle paths; whereas for the latter case, at least three waves ar e required to initiate chaotic mixing. Liapounov exponents are used to quantify the predictability of particle trajectories in the chaotic r egion. Whether the chaotic mixing process is temporally uniform or int ermittent is deduced from the local deviation from the Liapounov expon ent. Typical estimates of Liapounov exponents give error-doubling time s of the order of a few hours which roughly decreases as the amplitude of the perturbing wave (epsilon) increases. For waves propagating onl y in the horizontal, the chaotic mixing process tends to be more unifo rm as epsilon increases, while the reverse is the case for waves propa gating in 3D with more intermittent mixing for larger values of epsilo n. The chaos induced transport process is characterized from a relatio n of the form Delta X(2)(t) similar to t(alpha), for large t, where De lta X(2)(t) is the mean square distance traveled by a cloud of particl es. For lower values of epsilon, the horizontally propagating case giv es values of alpha greater than 2 and is nearly 2 for a larger value o f epsilon. The value of ct is nearly 2 for chaotically dispersing part icle clouds in the 3D propagating case. Also, correlation dimensions a re used to learn about the geometry of the cloud evolution. The result s show that clouds originating in the chaotic zone initially spread mo re than like a filament, subsequently become area filling, and then pr oceed toward space filling behavior. This sequence of transition has b een found to be faster for the 3D propagating waves than for the verti cally trapped case. The implications of the results to the wave-induce d mixing phenomena in geophysical flows are discussed. (C) 1997 Americ an Institute of Physics.