Nymphs that get dislodged from their resting place in the waterway are swept down the current until they find a new resting place. Unfortunately for the nymph, most don't make it to a resting place because of the number of fish aligned in the current to intercept these tasty morsels. Terrestrials that happen to fall into the stream are going to be floating down the river until they’re either stopped by a lucky object in the river or eaten by a fish. Even during a hatch, the majority of fish are going to be facing upstream, leaving their spot for a second to grab a fly and then back to watch the action.
The best approach to sneak upon any prey is to do so from their blind side. With few exceptions, the fish in the river have a fairly wide blind side, everything that is downstream from them. Now, this is not to say that you can go lumbering up a run and because you're still behind the fish they will have no idea that you're there. No, we're still hunting these fish and we have to be hunters about it. But advancing from downstream gives us the best advantage.
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As was mentioned, there are a few exceptions to the rule. First, fish are not technically facing upstream, they’re facing the current. Remember, fish want to be in the easiest feeding lane that they can possible get, and remember, bigger fish get the best feeding lane. The best feeding lane is not always the calmest, or deepest pool, it is the lane that offers the most and/or biggest food source. In the fish world, might makes right. But, back to the point, due to the various natural features of a stream that change the current, fish can actually be facing downstream. Think about a large rock that forces the stream around it on either side, sometimes that rock creates an eddy which forces a back current. Now, unless it's a big river and a big eddy, there's not a lot of food coming through that eddy, but there might be enough for a small fish that just happens to be facing downstream.
These exceptions are just that though, exceptions to the rule. And they illustrate the need to be careful when approaching the water because you just don't know what direction the fish will actually be facing. Fish upstream and you'll scare less fish which in turn will give you more opportunities to catch those fish. As always, Good Luck and Guid Luck!