Internal flow behaviour and melt-pool surface oscillations during arc welding are complex and not yet fully understood. In the present work, high-fidelity numerical simulations are employed to describe the effects of welding position, sulphur concentration (60-300 ppm) and travel speed (1.25-5 mm s-1) on molten metal flow dynamics in fully-penetrated melt-pools. A wavelet transform is implemented to obtain time-resolved frequency spectra of the oscillation signals, which overcomes the shortcomings of the Fourier transform in rendering time resolution of the frequency spectra. Comparing the results of the present numerical calculations with available analytical and experimental datasets, the robustness of the proposed approach in predicting melt-pool oscillations is demonstrated. The results reveal that changes in the surface morphology of the pool resulting from a change in welding position alter the spatial distribution of arc forces and power-density applied to the molten material, and in turn affect flow patterns in the pool. Under similar welding conditions, changing the sulphur concentration affects the Marangoni flow pattern, and increasing the travel speed decreases the size of the pool and increases the offset between top and bottom melt-pool surfaces, affecting the flow structures (vortex formation) on the surface. Variations in the internal flow pattern affect the evolution of melt-pool shape and its surface oscillations.