The Bedford Incident (1965) on Netflix

Tension is high aboard the destroyer USS Bedford as it tracks a Soviet submarine in the North Atlantic. Capt. Eric Finlander runs a taut, disciplined ship and his stern approach isn't appreciated or understood by the lone civilian on board, journalist Ben Munceford. The sub they are tracking can only stay under for a maximum of 24 hours and Finlander has every intention of being right there when it has to surface. With the ship on what is essentially a constant war footing, the officers and men are always on edge. Mistakes are inevitable.