The development of a wake flow downstream of a cylindrical rod within a curved channel under zero streamwise pressure gradient is theoretically and experimentally investigated. The measured asymmetric wake quantities such as the mean velocity and turbulent fluctuations in longitudinal and lateral directions as well as the turbulent shear stress are transformed from the probe coordinate system into the curvilinear wake eigen-coordinate system. For the transformed non-dimensionalized velocity defect and the turbulent quantities, affine profiles are observed throughout the flow regime. Based on these observations and using the transformed equations of motion and continuity, a theoretical frame work is established that generally describes the two-dimensional curvilinear wake flow. The theory also describes the straight wake as a special case, for which the curvature radius approaches infinity. The comparison of the theory with the experimental data pertaining to the curvilinear and straight wakes demonstrate the general validity of the theory.