Catch a butterfly, put it in a room, where there are no appreciable air currents. Sit two metres away from the butterfly, and tell me if you feel its wings batting. Do you even hear the wings batting? Now do the same experiment outside, where there is some wind. Do you feel the air pressure from the flapping wings?

There are no circumstances under which the flap will travel out into the sea or up into the atmosphere and generate a change in air flow, which would not have occurred without the flap. The statistics are as ludicrous as repealing the second law of thermodynamics. Long before any qualitative effect will be felt, other circumstances will have caused the pressure front to dissipate into noise.

Chaos does not mean every romantic notion makes sense, there are still physical and statistical constraints.

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$E(X_t|F_s) = X_s,\quad t > s$