That would be the gunboat diplomacy.
Both the "big stick diplomacy" and "gunboat diplomacy" are very similar but the "big stick diplomacy" is more recognizable in the US as Theodore Roosevelt's foreign affairs policy of choice. It means pursuing the international goals and diplomacy but with the show of the "big stick" that is the military power. The imperial forces used their gunboats to accomplish this effect as well so that is the reason we got the "gunboat diplomacy".
