TMO escorts can be right bastards, LOL!
Key to TMO escorts is the classic mantra- run silent, run deep.
The biggest asset you have is the thermal layer.
See above for thermal layer tactics- all very sound advice.
One other thing- they like to team up. One will sit as silent as the grave while the other does a high speed run and DC drop.
If they're right over you- all ahead flank, right full rudder- get the hell away from those ash cans as soon as possible!
If they're NOT right over you, they're doing a bird dog ploy- DON'T be the quail! Sit tight, maintain course and put 'em right on your stern, and slink away.
Good hunting