Abstract The present work provides an in‐depth analysis of the linear stability theory of viscoelastic shear‐flows, based upon a constitutive equation of the fading memory type. The particular model considered herein was introduced by Kenneth Walters through the integration of classical rate‐type fluids in a convected frame (Walters 1962). Despite their broad applicability for various materials, their utilization in shear flow stability analysis has been insufficiently explored. We close this knowledge gap by developing a generalized approach for these models and providing a concise formulation of these foundational results in terms of a displacement field, a well‐known concept in the theory of linear elasticity, inheriting several advantages. Within this framework, the analysis of Tackels and Crochet (Tackels & Crochet 1973) is extended to diverse material models, including those of rate‐type, without exact solutions in terms of convected integration. Furthermore, no assumptions on the kinematics of the base flow had to be imposed, and our approach is readily extended to the weakly non‐linear stability analysis. Thus, a framework for the analytical study of a wide class of material models emerges that hopefully leads to new insights into the stability properties of not only specific material models, but also larger classes thereof. Finally, based upon a Kelvin‐type ansatz, some strides are made to study the linear but non‐modal stability of linear shear flows.
Conrad et al. (Sat,) studied this question.