The atmosphere is a complex, dynamic system and the weather depends on its state. There are many different phenomena that affect the state of the atmosphere - some only involve the atmosphere, others involve the interaction between the atmosphere and the ocean. These phenomena can be modelled using many equations originating from fluid dynamics and thermodynamics, and many of them are considered here. Energy travels around the atmosphere in the form of waves, such as Kelvin waves and Rossby waves. It is possible for a triad of Rossby waves to interact with each other in a way such that resonance occurs. A computer simulation investigating the sensitivity of such waves to turbulence was completed, and it was found that the energetic dominance of the resonant triad does not persist, and the greater the turbulence added to the Rossby triad, the earlier in the integration the instabilities occur.