Laminar Shear Layer
 

can anyone help me with choosing the governing equations and selecting the appropriate boundary conditions for a laminar shear layer case between the same fluid (WATER) but with different velocities (any 2 velocities)?

This is my first CFD project and i need a little push :)

Laminar Shear Layer
 

When you go through Orr Sommerfeld theory of instability, you would notice that the Reynolds number based on velocity difference between two fluid layers like in your case is zero, and the flow inherently tries to become turbulent in a shear layer.

Anyway for academic purpose you can always try laminar flow, interestingly it is laminar vs turbulent that vauses the difference between boundary layers and shear layers.

How is the Reynolds number zero? What is your definition of the Reynolds number in this case? How does laminar vs. turbulent cause the difference between boundary layers and shear layers? To my mind that statement is nonsensical.

Back to the original query; You can use either RANS or LES to solve the governing equations of motion for the flow type, with LES giving you better answers as it can capture the large-scale coherent structures that are known to exist in the plane mixing layer.

As for boundary conditions, the inflow condition is the most important to specify correctly. My advice is to use two Blasius boundary layer profiles that define the the flow of each stream - you'll need to know roughly what the momentum thickness of the boundary layer in each stream is in order to get a sensible flow development within your computational domain.

the critical Reynolds at which the flow becomes unstable and turbulent is zero, so the shear layer thus formed is always turbulent. And doing a laminar simulation for this shear layer won't be physically correct.

And yes inflow boundary can be given as Blasius profiles for both the streams.

Experimental evidence shows that the assertion that the shear layer is always turbulent is incorrect - see LS HUANG, CM HO, J. Fluid Mech, 1990, vol. 210 pp. 475-500 for details. The flow is always unstable, but there is a marked transition between unsteady laminar and fully-turbulent behaviour in the flow.