Can a cruise ship at sea survive a tsunami?

At sea, the only thing that would change, Hollywood aside, is the depth of the water under the keel, and, she may pick up a few knots.

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She wouldn't pick up any knots. In deep water a tsunami passes simply as a swell, and that has no effect on a ship's speed because the water itself is not moving along the wave's track. If anything a small boat would move in a small circle about a horizontal axis as the wave lifts and lowers it.

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A tsunami becomes a destructive surge of moving water only when it reaches water shallow enough to break the true wave action.