Large eddy simulation is used to study the large-scale structures in a low subsonic mixing layer and their breakdown to small scales. For 3-D simulations, different finite-difference and pseudo-spectral schemes are tested. The (2, 4) MacCormack Scheme developed by Gottlieb and Turkel (1976) shows the best overall performance. It is very fast and supplies enough but not excessive artificial dissipation. Though slower than MacCormack scheme, the pseudo-spectral method has its advantage: high resolution of the high-wavenumber range when adequate de-aliasing scheme is used. When efficient fast Fourier transform routines are available, this method can be a very good alternative to the MacCormack scheme. Most of the simulations use a modified Smagorinsky-type model (Erlabacher et al. 1992). The effect of different models and model constants is also studied. It is found that the two subgrid-scale (SGS) models, the Smagorinsky model and the linear combination model (Bardina et al. 1983), show significant difference even at the low wavenumber range of the spectra. In the study of three-dimensional subsonic temporal mixing layers, it is found that the streamwise vortex tubes play an important role in the transition process. The vortex interaction of the streamwise vortex tubes and undulated spanwise vortex structures proves to be the dominant mechanism in the development of three-dimensionality and the subsequent generation of small-scale motions. In the absence of pairing of the spanwise vortex tubes, this vortex interaction causes uneven distribution of vorticity along the span of the spanwise vortex tubes and the breaking of the large structures. Following the breaking of the spanwise vortex tubes, the secondary streamwise vortex tubes become the dominant vortex structures. In the case involving pairing, it is found that the relative motion of the spanwise vortex tubes in the pre-pairing process creates much stronger strain rate field between the pairing vortex tubes than the case without pairing. The stronger strain rate field leads to the formation of streamwise vortex tubes with very high vorticity and low induced pressure. This also leads to much stronger vortex interaction between the spanwise and streamwise vortex tubes due to the increased strength of the streamwise vortex tubes. / Ph. D.