FlipGradientOrientation[grad,perm]

permutes the internal orientation of the gradients, perm can be any permutation of {"x","y","z"}.

FlipGradientOrientation[grad,flip]

flips the internal orientation of the gradients, flip can be {1,1,1}, {-1,1,1}, {1,-1,1} or {1,1,-1}.

FlipGradientOrientation[grad,flip,perm]

flips and permuter the internal orientation of the gradients.

FlipGradientOrientation[grad,perm,flip]

flips and permuter the internal orientation of the gradients.