Anyone who has ever seen an ocean wave wash up on a beach has seen the effect of air on the wave. The last moments of a wave's lifespan are the moments when it contains a tremendous amount of air. Typically, as a wave approaches shallow water the top curls over its base and falls into the rest of itself. This action causes splashing and generates bubbles which are included in the weakening wave. If the theory that air bubbles can mitigate wave energy is correct, we would expect to see the very thing we do see when a wave hits the beach. My understanding is that America was blessed with the natural coast protection of "the Oceans, white with foam". At least that's how Irving Berlin put it.
Wave Goodbye! : Simple Tsunami Mitigation