It really depends on the stage of the wine in evolution, as far as the aromas are concerned. For a younger wine, I find earth, wood, mineral and fruit. After swirling, the fruit is more obvious but some of the other components fade. With time sitting undisturbed in the glass, they reappear until the next swirl. The first wine that I used to show a consumer base was the 99 Sawyer Cab (I was in the tasting room at the time). The first pour revealed a molasses/brown sugar note along with the big red fruit and dust. After swirling, the molasses/brown sugar disappeared as well as most of the "Rutherford dust" only to come back after 5-10 minutes of sitting still. For a wine to really open up, it should sit in the glass without swirling. (IMO) It might take a longer period of time but what ever emerges is not manipulated, more powerful and a truer representation.
So in short, you should find all the aromas (if they exist) without swirling and some patience. The tertiary aromas of an older, mature wine will be more pronounced (funk) without swirling and will go away slower than if swirled. But for me, what appears after is more pleasant and accurate.
I had dinner at the French Laundry earlier this year in honor of my BdX friends 50th. We took a bottle of 55 Lafon Rochet. The wine was fabulous strait out of the bottle and improved in glass for up to 20 minutes before starting to fade. My better half swirled her wine a few times and it died much quicker (5-10 mins) in her glass than in mine. I can only attribute this to premature oxidation due to the forcing of oxygen into the glass by swirling.
These are some of my experiences and yours may be different. I suggest taking a young bottle and a mature one. Pour two glasses of each wine side by side. Swirl one and not the other and evaluate these wines for a period of 15-20 minutes. Take some notes and let us know what you think. I'm curious as to your findings.