  For the clarification of the routes to elasto-inertial turbulence (EIT), it
is essential to understand how viscoelasticity modulates coherent flow
structures including the longitudinal vortices. We focused on a rotating plane
Couette flow that provides two-dimensional (2D) roll cells for the steady
laminar Newtonian-fluid case, and we investigated how the steady longitudinal
vortices are modulated by viscoelasticity at different Weissenberg numbers. The
viscoelasticity was found to induce an unsteady flow state where the 2D
roll-cell structure was periodically enhanced and damped with a constant
period, keeping the homogeneity in the streamwise direction. This pulsatile
motion of the roll cell was caused by a time lag in the response of the
viscoelastic force to the vortex development. Both the pulsation period and
time lag were found to be scaled by the turnover time of cell rotation rather
than by the relaxation time, despite the viscoelasticity-induced instability.
We also discuss the counter torque on the roll cell and the net energy balance,
considering their relevance to polymer drag reduction and EIT.
