In confined bulk crystal growth techniques such as the traveling heater method, base materials in an ampoule are melted and resolidified as a single crystal. During this process, flow control is desired so that the resulting alloy semiconductors are uniform in composition and have minimal defects. Such control allows for tuned lattice parameters and bandgap energy, properties necessary to produce custom materials for specific electro-optical applications. For ternary alloys, bulk crystal growth methods suffer from slow diffusion rates between elements, severely limiting growth rates and reducing uniformity. Exposing the electrically conducting melt to an external alternating magnetic field can accelerate the mixing. A rotating magnetic field (RMF) can be used to stir the melt in the azimuthal direction, which reduces temperature variations and controls the shape at the solidification front. A traveling magnetic field (TMF) imposes large body forces in the radial and axial directions, which helps reduce the settling of denser components and return them to the growth front. In either case, mixing is desired, but turbulence is not. At large magnetic Taylor numbers the flow becomes unstable to first laminar and then turbulent transitions. It is imperative that crystal growers know when these transitions will occur and how the flow physics is affected. Here, the melt driven by electromagnetic forces is analyzed through the use of 3D numerical simulations of the flow field up to and beyond the point of laminar instability. The analysis aims to emulate laboratory conditions for generating electromagnetic forces for both types of alternating magnetic fields and highlights the differences between laboratory forces and the analytical approximations that are often assumed. Comparisons are made between the resulting forces, flow fields, and points of instability as the frequency of the alternating field varies. Critical Taylor numbers and the resulting unstable flow fields are compared to the results from linear stability theory.