Slow-fast decomposition of an inertialess flow of viscoelastic fluids

We study frequency responses of an inertialess two-dimensional channel flow of viscoelastic fluids. By rewriting the evolution equations in terms of low-pass filtered versions of the stream function, we show that strongly-elastic flows can be brought into a standard singularly perturbed form that exhibits a slow-fast decomposition. In high-Weissenberg number regime, which is notoriously difficult to study numerically, we demonstrate that the frequency responses are reliably captured by the dynamics of the fast subsystem. We use numerical computations to validate our theoretical findings and to illustrate that our formulation does not suffer from spurious numerical instabilities.