First thing to note: that page is plagiarised from a book chapter 'Internal waves generated in the straits of Gibraltar and Messina: observations from space', by Werner Alpers, Peter Brandt, and Angelo Rubino, in the book Remote sensing of the European seas (ed. V. Barale and M. Gade, Springer, 2008), pp. 319-330.

The Aristotle citation is one of those ones that takes a little while to track down because of non-standard conventions: this is a typical result of using antiquated popular editions. The Latin title given for the Aristotelean work, Problema physica, is not a standard one (it isn't even good Latin), and the chapter number isn't standard either (not specific enough).

So, the correct citation should be (pseudo-)Aristotle, Problems (23).932a, lines 5-20.

Rackham's translation is wordy but accurate:

A current is formed when after the cessation of the former wind from one direction it blows in the opposite direction over a sea which is running under the influence of the previous wind ... For the currents blowing in opposite directions thrust each other aside, just as they do in rivers, and eddies are formed.

If you read the passage, you'll see that the answer can be yes or no depending on what you want to emphasise. Yes, because what the author describes is essentially recognisable as an internal wave; no, because (a) ancient Greeks had no understanding of fluid mechanics and only a layperson's understanding of oceanography, and (b) the author thinks the currents are caused by wind, rather than a tidal gradient.

Another layer to the question is that the Problems isn't really Aristotle. It isn't a monograph, it's an accumulation of question-and-answer pieces that seems to have piled up over some time, perhaps several centuries. That said, it's feasible that Aristotle was aware of the material in this chapter. In authentic works he does have things to say about oceanography, things like how sea level in the Mediterranean and the Red Sea are the same because of the sphericity of the earth, stuff like that. But on some local phenomena he's not so well informed: for example Aristotle thought that Gibraltar was unnavigable because of muddy shallows in the Atlantic.

Let's say: the ancients were aware of the turbulent currents at Messina, and described them in a way that approximates to what modern oceanographers call an internal wave. But I wouldn't include Aristotle's name.