A note on nonlinear stability of plane parallel shear flows (Q1763817)

The authors construct a generalized energy functional \(E\) for plane parallel shear flows to study the conditional nonlinear stability for Reynolds numbers Re below some value \(\text{Re}_E\) depending on the shear profile. To treat the incompressibility constraint, the authors use the poloidal-toroidal decomposition of the flow. Introducing further a self-adjoint positiv operator for the flow description, the authors derive a variational expression for the critical value \(\text{Re}_E\). In the case of experimentally important profiles, e.g. combinations of laminar Couette and Poiseuille flows, \(\text{Re}_E\) is shown to be at least 174.