The effects of viscoelasticity on the stability of the two-dimensional mixing layer are examined through linear stability analysis and direct numerical simulations using four rheological models to describe the polymer.; The linear stability analysis of the inviscid flow described by the Oldroyd-B model shows that in the special limit of a fluid with a relaxation time comparable in magnitude to viscous diffusion time, the effect of increasing viscoelasticity is to reduce the instability of the flow resulting in smaller growth rates and a narrower spectrum of unstable wavenumbers. On the other hand, the effects of viscoelasticity on the viscous modes are model dependent and in general remain weak for moderate Reynolds number, Re, and Weissenberg number, We.; Direct numerical simulations of the temporally evolving mixing layer have been performed using a spectral method based on the Hartley transform. The code has been validated by reproducing the main structures of roll-up and pairing of the Newtonian fluid. Using the FENE-P model, simulations of the roll-up and pairing of the viscoelastic fluid have been conducted for various values of the Reynolds number, and sufficiently high Weissenberg numbers. These simulations did not show important changes in the roll-up and pairing times or in the global structure of the vortex. They have however, revealed that viscoelasticity tends to produce an intensification of vorticity in some regions of the flow namely the braids and that this intensification is spatially correlated with regions of build-up of the first normal stress difference. In agreement with previous experimental studies of the viscoelastic mixing layer, we observed a trend for smaller values of the minimal (negative) vorticity as well as the tendency for the vortex structures to be more compact and to have longer life times than in the Newtonian case.; The examination of the evolution of the first normal stresses revealed that the stresses are initially entrained by the roll-up of the flow and then reach a steady state characterized by the absence of any extensional forces and a balance between shearing forces and the polymer relaxation stresses.
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