The variation of velocity and temperature distribution in arbitrary profile along the centerline in turbulent which encounters non-linearity regular progressive gravity wave and steady uniform flow right in front are investigated analytically and verified by existing experiments. Firstly, the action of periodic waves and current are incorporated into the equation of motion as an external force and applied radiation stress for evaluating the velocity distribution over arbitrary lateral cross section. Based on the momentum exchange after the interaction between turbulent plane jet and oppositive non-linearity wave and uniform flow, the physical characteristics of jet-wave and current are able to be determined theoretically. Secondly, there are critical sections in both velocity and temperature transport processes when the turbulent plane jet influenced by wave and current motion. Fluctuating function will be close to infinity, is the order of wave sharpness; Average velocity for every wave period along the centerline approach to zero, That¡¦s thanks to the momentum of plane jet is extruded by the momentum of wave and current, Beyond the critical section, characteristics of the jet is no longer existing, such phenomena mean that only the wave and current dominating. Velocity and temperature distribution in the zone of flow developed are Gaussian curve, as has been measured in experiment. The momentum extrusion of counter flow in jet is significant in the deep water and small wave; The velocity distribution coefficient is changing with the increasing of counter flow velocity, owing to the entrainment effect, and the potential core will reducing with the increasing of counter flow velocity.