Abstract This paper, dedicated to Norbert Peters, follows his lead in developing theoretical understanding of the complex flow-turbulence interactions occurring in the propagation of premixed flames. The work is based on the asymptotic hydrodynamic model of premixed flames, where the flame is modeled by a surface that separates unburned and burned gases and propagates relative to the incoming flow at a speed that depends locally on the flame stretch rate. As such the work may be categorized as corresponding to the “flamelet regime”, based on the turbulent combustion regimes diagram. The results at the present are limited to mixtures corresponding to positive Markstein lengths, and to “two-dimensional turbulent flows”. In this parametric study, the different factors affecting the turbulent flame speed have been examined and scaling laws for the turbulent flame speed are proposed for low-to-moderate turbulence intensities that highlight the dependence on physically measurable quantities. Comparison to various empirical correlations suggested in the literature is presented. The results, devoid of turbulence-modeling assumptions and/or ad-hoc coefficients, can help explaining the influence of varying the system parameters individually and collectively, and formulating physically-based small-scale models for large-scale numerical simulations of turbulent flames.