Sir Brennen
Legend
By using the grapple rules as the stand? The alligator would use the "Moving a Grappled Creature" rule to drag the creature in the water. For the drowning part, I don't have my books with me, but aren't there rules for water hazards somewhere? DMG? Those would likely apply.And an alligator is more likely to try and drag you into the water too, biting and drowning you simultaneously. How would that be replicated in the rules?
Also, there's obviously a difference between taking a lungful of air, going underwater when you're ready and causally swimming around vs. being violently pulled under and fighting for your life. (Alligators also vigorously twist around with their prey once it's pulled under, helping with the drowning/tenderizing). Again, no books on hand, but I know previous editions differentiated the two, usually based on your Con score.