The problem of co-flowing flows is a widely observed phenomenon. While this phenomenon is well studied in the field of open flows, it remains obscure in the area of semi-confined flows. The current Direct Numerical Simulation study aims to explore the flow physics when two plane Couette flow adjacent to each other in same direction but at different Reynolds numbers. The study revealed that the flow configuration exhibits a shear-layer instability when the one of the two flows has Reynolds number greater than or equal to 500 i.e., one of the two flows should be turbulent. Besides the ratio of Reynolds numbers of the two flows should be greater than 2. The flow system also exhibits a novel non-planar or a bilateral mixing-layer phenomenon i.e., the instability wave varies with the wall-normal location. The nature of the flow has shown effects on several flow statistics. The width of the mixing-layer is large close to the stationary wall and gradually decreases close to the top wall and hence the quantities vary gradually at stationary wall and sharply at the moving top wall. The development of shear-layer instability shows a similar pattern of evolution irrespective of Reynolds number combination and Reynolds number ratio (r). However, the time for development of instability is independent of Reynolds number combination but depends strongly on the Reynolds number ratio. The flow develops quickly at larger ‘r’. The diffusion of turbulence on the other side depends strongly both on Re combination and ‘r’. It was found that the diffusion is higher when the Reynolds number of the adjacent turbulent flow is high or the Reynolds number ratio is high. The plot of mean streamwise velocity exhibits the pull nature by the turbulent flow on the non-turbulent flow i.e., additional momentum is imparted to the non-turbulent flow. The plot of mean u’u’ shows the asymmetric profile of mean u’u’ and its skewness towards the top plate. Further a significant non-zero mean u’u’ values were seen on the non-turbulent side. Similar non-zero values of mean v’v’ and mean w’w’ were observed on non-turbulent side. A budget analysis of mean u’u’, mean v’v’, and mean w’w’ explained the reason for their presence on the non-turbulent side. In addition, a budget analysis of turbulent and total kinetic energy is done. A direct comparison of turbulent kinetic energy between a plane Couette flow (pCf) and the current flow showed that the tke in co-flow is higher due to increased spanwise turbulent velocity (v’). The increased v’ is associated to the instability wave, which lies in the xy-plane. The tke was also compared for several ‘r’ and it showed that a higher ‘r’ led to higher tke. In order to study the dynamics from a vorticity point of view, a comparative study of vorticity and vortex stretching between pCf and co-flow is done. The results showed that the structures are subjected to more shear in the co-flow than in pCf. The stretching of vortical structures was also quite strong in the case of co-flow. The co-flow also effected the secondary vortices, the Taylor-Gortler roll cells which were found exclusively in pCfs. The cells which are typically well-organized in pCf showed a significant distortion in the case of co-flow. Like the dynamics at global scale, it is equally important to study the dynamics at the elemental level for a comprehensive understanding of the phenomenon. To investigate this, the concept of invariant maps was used. The effect of wave and co-flow on the topology and geometry of the fluid elements were individually assessed using the invariant maps. Further the effect of bilateral nature on the elemental level was also assessed and it was found that the bilateral nature has a strong effect even at elemental level.