I am not going to answer this question but I suggest you find the book introduction to dynamic meteorology fourth edition by James R Holton. Please read and you will understand.
waves occur in the oceans and in the atmosphere. Both water and air are fluids so the types of waves in both are the same. The Wikipedia articles describe both, e.g.
"Rossby wave
From Wikipedia, the free encyclopedia
Rossby wave, also known as planetary waves, are a natural phenomenon in the atmosphere and oceans of planets that largely owe their properties to rotation. Rossby waves are a subset of inertial waves.
Atmospheric Rossby waves on Earth are giant meanders in high-altitude winds that have a major influence on weather. These Rossby waves are associated with pressure systems and the jet stream.[1] Oceanic Rossby waves move along the thermocline: the boundary between the warm upper layer and the cold deeper part of the ocean."