A non-planar mixing layer observed between parallel Couette flows by Narasimhamurthy et al. (Phys Rev E 85:036,302, 2012) is considered. Direct numerical simulation is chosen, and simulations are run in order to determine the critical Reynolds number at which the interface between the co-flowing laminar and non-laminar flow becomes unstable exhibiting a meandering motion. The necessary conditions required to trigger the shear-layer instability were also discussed. Different combinations of Reynolds numbers are chosen keeping the Reynolds number ratio between the laminar and non-laminar flows as constant. Preliminary results indicate that the onset of instability occurs, and a meandering motion is observed at the interface when Reynolds number for the non-laminar flow corresponds to 650. © 2021, Springer Nature Singapore Pte Ltd.