This paper presents a new approach to developing turbulence models for shear flows by supplementing the renormalization group (RNG) method with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter, \(\eta \equiv S\overline{K}/\overline{E}\), is the ratio of the turbulent to mean strain time scale. While low-order expansions provide adequate descriptions for the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of \(\eta\) suffices; terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward-facing step, showing excellent agreement with experimental data. The models satisfy important physical constraints, such as realizability and consistency with weak and strong strain limits. The von Karman constant is shown to be independent of the Reynolds number in turbulent channel flow, and the model predicts a von Karman constant of 0.4 when the constant \(\beta\) is set to 0.012. The models are particularly effective in predicting the behavior of homogeneous shear flow and turbulent flow over a backward-facing step, demonstrating their robustness and accuracy.This paper presents a new approach to developing turbulence models for shear flows by supplementing the renormalization group (RNG) method with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter, \(\eta \equiv S\overline{K}/\overline{E}\), is the ratio of the turbulent to mean strain time scale. While low-order expansions provide adequate descriptions for the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of \(\eta\) suffices; terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward-facing step, showing excellent agreement with experimental data. The models satisfy important physical constraints, such as realizability and consistency with weak and strong strain limits. The von Karman constant is shown to be independent of the Reynolds number in turbulent channel flow, and the model predicts a von Karman constant of 0.4 when the constant \(\beta\) is set to 0.012. The models are particularly effective in predicting the behavior of homogeneous shear flow and turbulent flow over a backward-facing step, demonstrating their robustness and accuracy.