Stability of viscoelastic shear flows subjected to steady or oscillatory transverse flow

摘要

The effect of superposition of a time-periodic axial Couette flow on the viscoelastic circular Couette and Dean flow instabilities is studied. Analysis is carried out for the upper-convected Maxwell and Oldroyd-B fluids. Consistent with previous results on parametrically forced systems, zero-frequency limit is found to be singular. Further, linear and nonlinear stability results for the addition of steady axial Couette and Poiseuille flows to viscoelastic instabilities in azimuthal Dean flows are also presented.