Do commercial breweries stir in their fermenters to expose more yeast to the wort?

From what I’ve read it’s less common in beer than in wine where thick caps of fruit need to be pushed down and re-submerged.

For commercial brewers, the two reasons for stirring during fermentation are: 1) a reduction in the time it takes to complete fermentation, and 2) breaking up foam. Both are (were) done for economic reasons. Reducing the time it takes to make beer reduces the amount of fermenters a brewer needs, which not only saves money on tanks, but also on real estate, heating, cooling, etc. Foam reduction means requiring less headspace for the foam and/or reducing the amount of product lost to blowoff. Note, that since blowoff decreases hop utilization (see my article, "When fermentation rears its dirty head", Brewing Techniques; 1996; 4(3), 50-54) so savings in hops is another reason a commercial brewer would care about not having blowoff.

Most commercial brewers have abandoned stirred fermentations, however, according to my reading of professional brewing texts, due to cost, flavor differences, excessive yeast growth, and difficulty in getting the continuous stirred fermentation systems primed and in equilibrium. There's even a story about how Schlitz lost its spot at the #1 brewer in the world (to A-B) because they adopted stirred fermentaters. The story goes that switching to stirred fermenters changed the flavor of the beer enough that devoted Schlitz drinkers switched brands.

The one commercial brewer that I know of that still uses a sort of "stirring" during fermentation is Samuel Smith's The Old Brewery in Tadcaster. There, they use a yeast that is so flocculant, that they use pumps to draw beer from the bottom and spray it on top, to get the yeast back into suspension. Otherwise the beer would not fully ferment. I have pictures of the fermenters and the "fishtails" as they call them, on my website: http://www.brewinfo.org/samsmiths/samsmth5.html.

As for whether a homebrewer should swirl the fermenter to resuspend the yeast, that depends. If you have a stuck fermentation, resuspending the yeast (as you correctly point out, taking care to not introduce oxygen or bacteria) could help "unstick" the batch.

You do not need to stir or agitate the wort during fermentation. The process of diffusion does a fine job of keeping the sugars distributed. Moreover, if you have ever fermented in a glass vessel you'll see that the yeast seem to do an excellent job of stirring things up themselves.

Bottom and top fermenting is simply a concept as to where you may find the bulk of the yeast "cake" during the ferment, but there is plenty of yeast distributed throughout the entire wort. Lastly top and bottom can also be looked at from a historical concept of fermenting best at the top and bottom of the temperature range. Even though lager yeasts will ferment fine at 60>F, just not as clean.