I think I would try to solve this by having the angle point towards the gradient. (It's been a long time since I took a calculus class, so I hope I'm using the terminology correctly.) Basically, pick whatever direction points towards the steepest increase in value (or the greatest decrease would work too).
A possible downside depending on what you're doing is that you'd end up where local maxima in the perlin noise have arrows pointing in but not out. (I think this is what a sibling comment is referring to as "divergence".)
A possible downside depending on what you're doing is that you'd end up where local maxima in the perlin noise have arrows pointing in but not out. (I think this is what a sibling comment is referring to as "divergence".)