Аннотация:

We have studied the spectral problem for plane Poiseuille-type flow of viscoelastic polymer liquid. The flow was modeled with the equations of rheological Vinogradov--Pokrovskii model. The numerical spectral procedure was used to calculate eigenvalues of the problem and to determine the critical values of parameters where the instability of the flow occurs. It was shown that the critical Reynolds number goes to well-known value of approximately 5772 (that is the critical value for the viscous fluid) while the relaxation time goes to zero. The slight increase of elastic properties of the fluid (or Weissenberg number) leads to rapid increase of critical Reynolds number, while further increase of Weissenberg number destabilizes the flow by pushing the critical Reynolds number to zero. Similar to a number of other rheological models, the Vinogradov--Porkovskii model demonstrates the elastic instability effect, that is the spectral problem has unstable modes that are not a continuation of unstable modes of the viscous newtonean flow.