The definite article "the" in "under water"/"under the water"

Solution 1:

OP's cited example seems perfectly natural to me.

The first under water is a non-specific "adjectival phrase" - the writer isn't interested in any particular air or water, so in principle he could have simply joined the two words together as underwater. As this chart shows, Americans have enthusiastically adopted this one-word form in recent decades.

But in this particular instance, the next sentence is about the bubbles and their relationship with the water. I think it would be stylistically clumsy to use water as part of a "compound word", then use it (twice!) as a standalone word in the very next sentence.

Or, the writer might be an older Brit. We've been much slower to adopt the one-word form (but we're getting there).

When used as an adjective preceding a noun, the one-word form is well-established. The uncertainty only arises when it's used as a predicate adjective (as in OP's example, or my first chart showing the rise of American usage of breathe underwater).

In short - I'm quite prepared to believe the writer might ordinarily have used the one-word form, but being a competent writer, he deliberately chose not to in this particular case.

As regards "the rules" for using "the" in this situation - there aren't any, really. The writer could reasonably have dispensed with it before "bubbles" and/or the second instance of "water". He could even have added another one - "because the air is much lighter".