The premixed flame growth period of about 1% of the cylinder mass burned has been theoretically investigated under typical homogeneous charge engine conditions. For this purpose various flame kernel development models have been tested against measured values of flame radius vs. time after ignition in a research engine. The flame kernel growth has been computed on the basis of a zero-dimensional model incorporating spark-induced energy, heat loss to the electrodes and flame curvature effects. Subsequently the transition phase from laminar to fully turbulent flame propagation is shown to depend strongly on the relationship between the turbulent kinetic energy spectrum and characteristic scales of the flame. We thereby make use of recently reported results of fundamental experiments on vortex-flamelet interaction, that yield typical vortex sizes for flame wrinkling and quenching. Predictions based on this model are in good agreement with measured flame radii over a wide range of engine speeds and equivalence ratios. Moreover, in comparison to simpler flame speed models for steady flame propagation, the spectral approach contributes to a better understanding of the involved processes during flame growth in SI engine combustion.