I love the flavor of a Wave Elemental, but I didn't like how the original had its effect happen only once which also can't happen during the first turn it is in play. It's a living embodiment of waves! How could it not be doing wave-y things the whole time it's alive?
I decided that waves should be associated with attacking, since standing still would be like calm waters. But to make sure it still did its thing the first turn it was in play, I had the trigger for its "wave" ability to trigger off of entering the battlefield OR attacking. Besides, the Wave Elemental could have crashed into play. Go, go crashing of waves.
I wanted the player to FEEL like they were sending a wave toward another creature by requiring the tap of an untapped Island. Usually, this will be the basic land Island being tapped, which is the desired experience.