Chaotic mixing by internal inertia-gravity waves

Abstract

The Lagrangian transport of “passive” particles advected by inertia-gravity waves is investigated. We consider two classes of waves, namely, vertically trapped, horizontally propagating waves, and those propagating in three dimensions (3D). In the former case, it is shown that the superposition of at least two waves is necessary to produce chaotic particle paths; whereas for the latter case, at least three waves are required to initiate chaotic mixing. Liapounov exponents are used to quantify the predictability of particle trajectories in the chaotic region. Whether the chaotic mixing process is temporally uniform or intermittent is deduced from the local deviation from the Liapounov exponent. Typical estimates of Liapounov exponents give error-doubling times of the order of a few hours which roughly decreases as the amplitude of the perturbing wave (ε) increases. For waves propagating only in the horizontal, the chaotic mixing process tends to be more uniform as ε increases, while the reverse is the case for waves propagating in 3D with more intermittent mixing for larger values of ε. The chaos induced transport process is characterized from a relation of the form ΔX2(t)∼tα, for large t, where ΔX2(t) is the mean square distance traveled by a cloud of particles. For lower values of ε, the horizontally propagating case gives values of α greater than 2 and is nearly 2 for a larger value of ε. The value of α is nearly 2 for chaotically dispersing particle clouds in the 3D propagating case. Also, correlation dimensions are used to learn about the geometry of the cloud evolution. The results show that clouds originating in the chaotic zone initially spread more than like a filament, subsequently become area filling, and then proceed toward space filling behavior. This sequence of transition has been found to be faster for the 3D propagating waves than for the vertically trapped case. The implications of the results to the wave-induced mixing phenomena in geophysical flows are discussed.