Lunar gravity is partly what causes oceanic currents. If we had more than one moon orbiting Earth, what [if anything], would happen to the oceans? — MS, St. Charles, Missouri
While the moon’s gravity is the major cause of tides (the sun plays a secondary role), the moon’s gravity isn’t directly responsible for any true currents. Basically, water on the earth’s surface swells up into two bulges: one on the side of the earth nearest the moon and one on the side farthest from the moon. As the earth turns, these bulges move across its surface and this movement is responsible for the tides.
If there were more than one moon, the tidal bulges would become misshapen. That is essentially what happens because of the sun. As the moon and sun adopt different arrangements around the earth, the strengths of the tides vary. The strongest tides (spring tides) occur when the moon and sun are on the same or opposite sides of the earth. The weakest tides (neap tides) occur when the moon and sun are at 90° from one another. Extra moons would probably just complicate this situation so that the strengths of the tides would vary erratically as the moons shifted their positions around the earth. Since the timing of the tides is still basically determined by the earth’s rotation, there would still be approximately 2 highs and 2 lows a day.