An investigation was carried out of the altered transverse transport of axial momentum in turbulent coolant flows during weak oscillatory instabilities of low frequency. Such instabilities can occur in two-phase flow systems, e.g., light water nuclear reactor cores. Solution of the governing momentum equation was obtained by both an integral transform method and a numerical method. Optimal modification of the steady-state eddy momentum diffusivity expression was carried out by minimizing the error between the experimentally measured and the predicted oscillatory axial velocity field.