Abstract : There is a close analogy between the dynamics of primary atomization process in a two phase shear layer and the processes initiating the mixing transition in a monophase layer presenting the same shear: the primary instability and and the elongation of dense fluid "fingers" in the rapid fllow are analogous if the inlet veocity and the initial density ratio are conserved between both cases. Therefore, the primary atomization coincides with the turbulent mixing if the Reynolds number and the Weber number are sufficiently high. The study investigates these conditions using numerical simulation. Because of stiff velocity and density ratios, we use hyperbolic Roe solvers with WENO for the convective parts of Navier-Stoks equations. At small Reynolds number, for density ratio greater than one, the vorticity field resulting from the hydrodynamic instability becomes asymetric. This yeilds the time scale of first 'atomization' been governed by square root of density ratio, as a signature of baroclinic effects. The study also illustrates that at larger Reynolds numbers, the MILES approach can be used for developing ther eulerian modeling of primary atomization, dedicated to applied computations of two phase flows, as LOx H2 injection in a rocket engine.