UPDATED: Russian Navy Cruisers Positioned to Counter U.S., French and Italian Carrier Groups in the Mediterranean, 22 Feb

< checks watch >

Turkey Closes Bosphorus, Dardanelles Straits to Warships, 28 Feb
"'It is also time for NATO, which will continue to have access of course, to send more of its ships into the Black Sea to support Turkey, Bulgaria, and Romania, the NATO members whose fleets operate routinely there,' Stavridis said."

The Russia-Ukraine Conflict, the Black Sea, and the Montreux Convention

The Montreux Convention is unique in the law of the sea in that it explicitly discriminates against nations outside the Black Sea. Instead, Montreux favors six "Black Sea Powers" (Russia, Ukraine, Turkey, Romania, Georgia, and Bulgaria) over "non-Black Sea Powers" (everyone else).
[...]
Other Considerations: the U.S. and NATO Maritime Presence and Strategic Concerns Around Escalation

The U.S. was absent from the Montreux Convention negotiations and has not joined the treaty. Nevertheless, the U.S. abides by the Convention under customary international law.

US < squint >UK do not do international law, m'k.

While there is no provision in the body of the Montreux Convention addressing aircraft carriers,  a nuclear aircraft carrier is a capital ship that exceeds Montreux's tonnage limitations.  But other U.S. and NATO vessels could still feasibly transit the Turkish Straits, provided they give Turkey ample notice under the Convention (15 days for all non-Black Sea Powers).
[...]
Vessels of war belonging to non-Black Sea Powers - which includes much of NATO's maritime force - are prohibited from remaining in the Black Sea for more than 21 days. Putin may see an increased NATO presence in the Black Sea as an escalatory measure, so it remains unclear whether this is being seriously considered

"European family that you would live next door to"