Linear stability of channel Poiseuille flow of viscoelastic Giesekus fluid

We numerically investigate the linear stability of plane-Poiseuille flow of viscoelastic Giesekus fluid in channel. The model under consideration is governed by the elasticity number (E), mobility number (gamma), Reynolds number (Re) and solvent viscosity to total viscosity ratio (beta), and corresponding governing temporal stability equation is numerically solved. We found that the eigenspectrum for Giesekus fluid is shown as a continuation of Newtonian spectrum, with eigenmodes displaying continuous spectrum and characteristic Newtonian Y- structure modified elastically. At large E, the Poiseuille flow of Giesekus fluid becomes unstable that belongs to center and wall modes depending on range of parameters. Qualitatively different neutral stability curves are observed in that critical Reynolds number variation is monotonically decreasing below the Newtonian instability. There exist new additional modes that emerge out above TS-mode for each gamma, revealing elasto-inertial modes, which have their Newtonian counterpart below TS mode. For some range of gamma, neutral curves start to produce two-lobed structure at higher wavenumbers with larger second critical Reynolds number. Kinetic energy budget analysis is performed to unveil physical reasons behind the occurrence of observed scenarios and it reveals that the region of negative production due to Reynolds stress is responsible for viscoelastic stability.