It seems like water molecules might follow the path of a wave given what we know from the water cycle.
But, if you watch a floating object like a toy boat on a wave in the open sea it won’t travel with the wave but rather bob up and down. The water molecules are actually swirling under the waves helping to move energy to the wave. This swirling motion is known to oceanographers as the “circular orbital motion”.
When you get closer to the shore the orbital motion is non-existent because the waves touch the bottom. That phenomenon helps when you lose your boogie board in the surf zone.
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