Tom Hanks goes to war on the high seas.

Tom Hanks has always found that the military or quasi-military uniform of a much-loved authority figure appeals to him: that sensitive, slightly rheumatic look is often seen under a peaked cap or crumpled helmet. He was a container ship captain in the captain Phillips of Paul Greengrass, the heroic airline pilot of sully from Clint Eastwood, the teacher who became a soldier's soldier ryan de Spielberg. Now he's US Naval Commander Ernest Krause in this old-fashioned World War II adventure, in which Hanks also makes his screenwriting debut, adapting the 1955 novel The Good Shepherd by CS Forester.

Hanks plays a captain during the Battle of the Atlantic who has finally been promoted. He was given command of a destroyer call sign "Greyhound" and tasked with protecting vital supply convoys en route from the US to Britain, across mountainous seas and surrounded by submarines led by lethally cunning German sadists.

After formally saying goodbye to his wife, Evie (a brief cameo by Elizabeth Shue), Ernest sets sail and quickly finds himself in terrible danger. An early, quick success against the enemy leads him to miscalculate due to inexperience, and soon his convoy is attacked by a sinister pack of vengeful submarines, who begin picking off ships, one by one, with terrifying precision. Their leader (voiced by Thomas Kretschmann) shouts taunts of the sort that call Germany over the radio: “We hear the screams of your comrades as they die! You will die today!

Hanks' troubled captain is visibly tired and vulnerable, at one poignant stage, asking for his soft slippers to be brought to him to soothe his aching feet. His subordinates, including Charlie Cole ( Stephen Graham ), have affection for their boss, but you can see a small flicker of consternation on their obedient faces. Did the old man get what it takes?

Easily the most surprising moment comes with the captain making a deadly mistake when it comes to the two flight attendants, whose job it is to serve meals: Cleveland (Rob Morgan) and Pitts (Craig Tate) are the only black crew members. In his exhaustion and distraction, the captain calls each other by name. Of course, this mistake is not presented as evidence of his callousness, still less of systemic racism, just the understandable lapse of a thoroughly decent fellow under unimaginable pressure. Hanks is the only actor (and screenwriter) in Hollywood who could have gotten away with it, though I can't see him or anyone else crossing that line right now.

Greyhound is a very traditional and indeed traditionalist film, with Hanks starting and ending his first day of battle kneeling in prayer. However, the action itself largely and somewhat expressionistically clings to the tense, claustrophobic world of the bridge, with the captain barking at all sorts of opaque naval jargon. In a way, it resembles a kind of ocean theater play: the other ships in the distance and the vast gray sea are digitally rendered. But it's effective and watchable, with some genuinely tense moments as Hanks has to make split-second decisions about two Nazi torpedoes heading his way in different directions, and then desperately shouts his orders through the wind and rain. He's very much the kind of mythical figure that Walter Mitty might imagine himself to be.

I'm also a sucker for some old-fashioned cat-and-mouse strategy between Allied ships and German subs, and this doesn't disappoint. There are moments when Hanks looks urgently into the distance through his captain's binoculars, which reminded me of Jack Hawkins in the Cruel Sea.

Death is the hardest thing to portray in a war movie or any movie. Three sailors are killed in battle, and Hanks and director Aaron Schneider concoct a burial-at-sea sequence in the middle, which is notable for a slight touch of what could be called mythical insubordination. Just as a wrapped body is about to be solemnly thrown from the flag into the sea, it gets tangled up. We get an infinitesimal cut across Hanks's alarmed face: will this sad moment turn into farce? But in the next moment, the problem is solved and the ceremony moves on.

Another type of movie might have put a lot more emphasis on things like this. In addition to death and tragedy, war is full of absurdities, indignities, chaos, all sorts of bizarre and embarrassing things that are not mentioned in the official record. Greyhound is content with his lecture of somber reverence.