Nonlinear evolution of odd-viscosity-induced instability

Determine how the linear instability induced by odd viscosity in plane Poiseuille flow evolves into the nonlinear regime and whether its unstable modes influence the ensuing turbulent cascade.

Background

The paper establishes that odd viscosity can convert transient lift-up growth in the conventional Orr–Sommerfeld–Squire dynamics of plane Poiseuille flow into a self-sustaining, exponentially growing linear instability. The authors note that this instability may arise at Reynolds numbers substantially below the conventional Tollmien–Schlichting threshold.

The unresolved problem concerns the subsequent nonlinear dynamics: specifically, whether the linearly unstable modes generated by odd viscosity govern or otherwise modify the transition to nonlinear flow and the turbulent energy-transfer processes. This question is motivated by the reported ability of odd viscosity to alter turbulent cascades through odd waves, but the paper does not analyze the nonlinear evolution of the identified instability.