I think the title, swimming softly, is a good description for how they can effortlessly move through water.
An Alligators tail is all muscle, and half the size of their entire body. A slow motion of the tail glides one along with no sounds or even ripples in the water.

Look closely at either photo and a slight water motion is visible around the nose, nothing more.

A little unfair that something so dangerous can move so quietly.
They can rise up, or go down under water with no motion at all. It’s impossible, except they can shift their lungs and other organs inside their body 😵💫. It changes their buoyancy 😳
Very stealthy – most surreal scene I have ever witnessed was watching a gator floating directly towards me and then slowly sink into the water several yards out without much of a ripple at all – this was followed by my wife high tailing it out of there for the car, thankfully she did not kneecap me first.
Just as creepy is when they surface like that 😂😂. Never a ripple, that’s the changing of the lung position internally. Very weird and perfect evolution 😁.
Nicely observed and captured.
Second nature now 😆😆