Arleigh Burke passing through the Bosphorous straits
The Truxtun is a powerful US Navy destroyer, but she clearly is not meant to confront the Russians.
She will will have no at sea support there in the Black Sea.
The USS Taylor, which was off of Sochi during the Olympics, and which is good for ASW work, is not going to be p a part of this. She's currently in port in Greece I believe, being repaired after running aground and damaging her prop...so Truxtun is alone.
Now, the Truxton is a part of the George H.W. Bush,CVN-77, carrier group and the Bush is remaining in the Med. So, with the tensions, I imagine the Bush is keeping watch and prepared to assist with aircraft f necessary...but the Russians will have them out manned and outgunned in any case way up in the Black Sea if things went awry.
I do not expect them too.
The US would have to send a couple of destroyers and be accompanied by a NATO SAG of 3-4 ships for them to pose any real surface challenge to the Russian Black Sea Fleet.
The USS Taylor is an Oliver Hazard Perry class frigate and the US still has 18 (out of an original 51 built for the US Navy) of them in service.
Their anti-air Standard missile launcher was removed because it was viewed as too expensive to upgrade them to fire the newer standard missiles. This decision also removed the capability for them to launch ASM Harpoons from the launcher. However, the Australians and the Turks upgraded their Perrys adding VLS tubes that allow the newer missiles to be launched. Those vessels now remain effective multi-role FFGs.
In US Service however, they vessels replaced the standard, single arm missile launcher and it's 40 round magazine with a single Mk-38 mod 2, 25mm auto cannon. Now, in US service the vessels are armed with the 25mm gun forward, a 76mm main gun amidships, and a 20mm Phalanx CIWS aft. They also carry two Seahawk helicopters and are therefore still very good in the ASW role.
Here's the USS Taylor, FFG-50, as she deployed. You can clearly see all three of her guns, and the two hangers for her helicopters in this photo.