Mixing processes in turbulent fluid motion are of fundamental interest in many situations in engineering practice. Due to its practical importance in a vast number of applications, the geometric configuration of the jet in cross-flow has been studied extensively in the past years. Recently the question has received significant attention, whether the unsteady behavior of the jet in cross flow can e influenced by either active or passive means in order to control and enhance mixing process. In the present study we use the direct numerical simulation (DNS) approach along with an adaptive mesh refinement technique to investigate the Reynolds number effect on the mixing process. The numerical computations are carried out for three different Reynolds numbers, Re = 3.17×10^3, Re = 6.34×10^3 and Re = 9.51×10^3. The study shows that the Reynolds number plays a key role in the mixing process in the way that the mixing increases with the Reynolds number.