The effect of inflow turbulence on wind turbine's wake replenishment has been well observed in the scientific literature. The turbulent mixing is frequently proposed to explain the faster wake replenishment in turbulent condition. In order to verify this assumption, the wake of a twin rotor vertical axis wind turbine has been studied in two conditions with different inflow turbulence levels. The 1/450 scale model was immersed in a flume tank and velocity measurements were performed with a LDV probe. The terms of the momentum budget equation were computed in order to find those responsible for the wake replenishment. The vertical advection term has been found to be the major contributor of the transport of momentum in the wake, in accordance with the literature. However, in contradiction with previous assumptions, the turbulent transport terms were not found to have a significant effect on the wake replenishment. The earlier onset of the vertical advection is identified has the main explanation for the faster wake replenishment in the turbulent condition. Finally, the cause of this earlier onset is studied in order to analyse how the vertical turbulence gradient plays a role or not on this process.