Yes Reynolds number is in the numerator, the denominator is the bulk flow speed. Because the numerator includes the local flow acceleration you have to include the characteristic length and with it the Reynolds number. You are correct with vortices storing energy, when a bird takes off it creates a huge vortex sheet, and with their adjustable wings they are able to position them to take maximum effect of the laminar flow layer caused by the vortex. Trout can swim upstream because again they position their bodies so that their scales take advantage of the forward thrust caused by vortex recirculation. Also birds and fish have similar Reynolds number because of the speed and density differences put their Reynolds numbers in roughly the same range.(kind of how the moon and sun look the same size from our POV even though they're not) Fish have scales and birds have feathers which alter the characteristic length and in turn the Reynolds number. The lower the Reynolds number the lower the probability of turbulence, and since it's part of the numerator, lowering RE# also lowers Strouhal number, for a given bulk flow speed.