Spatiotemporal linear stability of viscoelastic free shear flows: Nonaffine response regime

We provide a detailed comparison of the two-dimensional, temporal and spatiotemporal linearized analyses viscoelastic free shear flows in limit low to moderate Reynolds number Elasticity obeying four different types stress-strain constitutive equations: Oldroyd-B, Upper Convected Maxwell, Johnson-Segalman (JS) linear Phan-Thien Tanner (PTT). The resulting fourth-order Orr-Sommerfeld Equation is transformed into set six auxiliary equations that are numerically integrated via Compound Matrix Method. stability analysis suggest (a) elastic stabilization at higher values elasticity number, (b) non-monotonic instability pattern intermediate for JS as well PTT model. To comprehend effect elasticity, viscosity on curves model, we consider fourth parameter, centerline rate, $\zeta_c$. `JS behaviour' recovered below critical value $\zeta_c$ above this base stresses (relative model) attenuated thereby explaining stabilizing influence elasticity. Briggs idea analytic continuation deployed classify regions stability, absolute convective instabilities, evanescent modes, results compared with previously conducted experiments Newtonian past cylinder. phase diagrams reveal two familiar inertial turbulence modified by (a recently substantiated) region elastoinertial unfamiliar temporally stable number.