Some websites suggest putting salmon in a bag before thawing in cold water.
Is it safe to omit the bagging, and instead thaw directly in water? (If not, why?)
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If you boil vegetables in water, some of the compounds from within the cells will leach out of the vegetables into the water. The reason is because vegetables are bags of water with goodies inside and a semi-permeable membrane holding them together (the skin). The compounds inside (vitamins and other micro-nutrients) look around and say: "Hey, it's pretty crowded in here", then look across the cell walls to the pristine water outside and say: "But that's a wide open space with nobody in it!" and make their way outside until the concentration is balanced on both sides (not really, but kinda).
This is also why salt will dry out foods. If you have a fresh chunk of meat, a significant portion of that meat will be water. If you then rub salt on the outside, the salt will dissolve into whatever moisture is on the surface, and the water molecules inside the meat will say: "Hey, there's very salty water over there, and almost no salty water in here!" And, in an attempt to form a saline equilibrium, the water will migrate out of the meat to dilute the salt concentration.
Of course, molecules don't talk the way I have indicated. That's just a high-level illustration to indicate the tendency of solutes to reach an equilibrium across a membrane. But as Johanna indicates in her answer, if you place a salmon in a pot of water, you will have the situation where the the water inside the salmon has a bunch of chemicals dissolved into it, and the water outside the salmon is mostly "pure". Therefore, the salmon must either release bits out into the water, or it must absorb water to reduce the imbalance. Fish flesh is already somewhat delicate, so creating this osmotic imbalance isn't doing you any favors, unless you are trying to boil the fish (and please, why would you waste a perfectly good salmon by boiling it???).
You may be wondering: "How do salmon stop from getting waterlogged while they are alive?" And the answer is: a combination of oily, waterproof scales, as well as active metabolic processes to balance the water inside vs. outside their bodies (i.e., they are expending energy to actively pump excess water outside, just like your body does: using kidneys). Of course, a salmon filet has already compromised their scaly first layer of protection, and I assume there are no kidneys left.
(And keep an eye on it to make sure you don't leave it in too long after thawing.)
It's interesting that Lawnmower Man brings up osmotic pressure. Though he makes some very good points, he missed the fact that you aren't bound to using plain water; you can balance the osmotic pressure by adding salt (or sugar, which is common when poaching) to the water you're putting the salmon into. The result will not be waterlogged. Just pat it dry, and cook as usual.
Brining fish is frequently a good thing to do anyway, especially salmon. Cook's Illustrated suggests a ratio of 5 tablespoons of salt dissolved in 2 quarts of water, soaking for 15 minutes. It seasons the flesh a bit, helps to keep it moist, and reduces the amount of albumin that's exuded when cooking — which salmon usually has plenty of.
Since your salmon starts frozen, the brine won't actually penetrate until the outer layer thaws, penetrating deeper as the thaw line moves deeper. So it's not ideal, but salmon is still thin enough and thaws quickly enough that this shouldn't make a huge difference. I would say: pull the salmon out about 10 minutes after it's thawed about halfway through. (I find the timing for brining is not too delicate anyway.) There may be a tiny bit still frozen in the middle with thicker pieces, but it should be close enough to cook up nicely. You should only do this very shortly before cooking anyway, so you don't need to use your very coldest water, which can speed the thaw up a bit.
This isn't my preferred method of thawing, but it has worked great for me when the kids are screaming for food.
Also note that you can even cook salmon straight from frozen: cook covered for an extra 5 minutes or so, then uncover to finish. Poaching from frozen is also relatively forgiving.
My opinion is to go ahead and do it, without the bag. The points of the other answers, about a bit of stuff leaching into the water, are generally true, but I think the effect will be quite small. People tend to overestimate how much stuff is exchanged with meat submerged in liquid, either going in (marinades) or going out (soaking). Frozen meat (or fish) will indeed have a bit more exchange, due to the cell walls being damaged, but I suspect that the stuff that will leak out when thawing in water is the same stuff that will leak out when cooking it later.
Bottom line, try it out. If it gets too watery for your taste, you can stop doing it, but I'm quite sure you won't notice the difference.
Cooking fish in water is called poaching and if done properly will give a fine flavored dish. If you have a large fillet of salmon and you need to defrost quickly, just place in a polythene bag and leave in a bowl of water. It will not harm the flesh and the salmon will still taste great when cooked.