Montreux Convention Regarding the Regime of the Straits (1936)
Article 19.
In time of war, Turkey not being belligerent, warships shall enjoy complete freedom of transit and navigation through the Straits under the same conditions as those laid down in Article 10 to 18.
Vessels of war belonging to belligerent Powers shall not however, pass through the Straits except in cases arising out of the application of Article 25 of the present Convention, and in cases of assistance rendered to a State victim of aggression in virtue of a treaty of mutual assistance binding-Turkey, concluded within the framework of the Covenant of the League of Nations, and registered and published in accordance with the provisions of Article 18 of the Covenant.
In the exceptional cases provided for in the preceding paragraph, the limitations laid down in Article 10 to 18 of the present Convention shall not be applicable.
Notwithstanding the prohibition of passage laid down in paragraph 2 above, vessels of war belonging to belligerent Powers, whether they are Black Sea Powers or not, which have become separated from their bases, may return thereto.
Vessels of war belonging to belligerent Powers shall not make any capture, exercise the right of visit and search, or carry out any hostile act in the Straits.
...Article 25.
Nothing in the present Convention shall prejudice the rights and obligations of Turkey, or of any of the other High Contracting Parties members of the League of Nations, arising out of the Covenant the League of Nations. "
Article 25 does give Russia a possible counter-argument where they could say that they were merely exercising their 'rights' as a high contracting power, (as there seems to be no actual obligation to annex Crimea, legally speaking) but that seems rather vague to me and Turkey could just as vaguely say that they were not or that they were also defending theirs.
“... then they have the power to close the Strait against them.”
Poor choice of words “the power to close”. But do they have “the power to keep them closed” after the first missiles and bombs destroy all their military facilities?