This thesis documents three years of work involved in the numerical solution of atmospheric wave models. Derivation of these models is established whilst introducing the basic physical laws governing fluid motion. Numerical techniques axe investigated with particular reference to the solution of parabolic and elliptic partial differential equations. Parallel computer systems are discussed and basic concepts introduced with the emphasis placed on distributed virtual parallelism. The role of inertio-gravity waves under the influence of cyclonic Rossby waves is investigated with respect to the production of atmospheric turbulence. Results from evolving numerical systems bound by various conditions are presented. It is discovered that the wave interaction is not the sole cause of atmospheric blocking as was previously thought. The use of a loosely coupled parallel environment is discussed in relation to potential increases in speed or size of the numerical model. A solution technique is modified to enable such an implementation. The full nonlinear Barre de Saint-Venant model of fluid motion is solved using a combination of finite difference and spectral methods. Preliminary results are presented and further avenues of investigation are discussed.