Fast wandering of slow birds

I study a single slow bird moving with a flock of birds of a different and faster (or slower) species. I find that every species of flocker has a characteristic speed γ ≠ v(0), where v(0) is the mean speed of the flock such that if the speed v(s) of the slow bird equals γ, it will randomly wander transverse to the mean direction of flock motion far faster than the other birds will: Its mean-squared transverse displacement will grow in d = 2 with time t like t(5/3), in contrast to t(4/3) for the other birds. In d = 3, the slow bird's mean-squared transverse displacement grows like t(5/4), in contrast to t for the other birds. If v(s) ≠ γ, the mean-squared displacement of the slow bird crosses over from t(5/3) to t(4/3) scaling in d = 2 and from t(5/4) to t scaling in d = 3 at a time t(c) that scales according to t(c) proportionally |v(s) - γ|(-2).