Magnetohydrodynamics (MHD) is the area of physics dedicated to the study of electrically conducting fluids. These fluids can support linear waves and non-linear turbulence dynamics. This thesis presents results and analysis of the evolution of the linearised MHD equations and the full non-linear MHD equations, starting from the same initial state. A systematic parameter study is conducted, varying the mean magnetic field strength, cross helicity, and Alfvén ratio. The focus is on incompressible MHD, though compressible systems also exist, and indeed are more prevalent as incompressible MHD is largely idealised.