I know there's not a lot of love for the Bakshi Lord of the Rings, but check out this clip from the movie. Cut to 00:45 to see exactly. This is how I always envision the two Ringwraiths who "rode toward Frodo" in the flight to the ford.
That's not a bad bit of insight there - for the ringwraiths, Plan A every time they do anything is probably to try to panic their prey into making bad decisions. They aren't accustomed to folk who shake off their influence and continue to act more-or-less rationally, so they wouldn't necessarily form a pursuit that would be most effective against a quarry that is acting rationally.such pressure can lead to panic or at least bad decisons.
Yes, I suppose you could characterize "fall down on your face, curl up, and put your arms over your head" as a "bad decision" in a case like that. . .for the ringwraiths, Plan A every time they do anything is probably to try to panic their prey into making bad decisions.