Susan Friedlander
University of Illinois, Chicago, USA

Nonlinear instability for stratified shear flow

We present an example of a stratified shear flow in which an explict construction is given for unstable eigenvalues with smooth eigenfunctions for the Taylor-Goldstein equations. We show that for any plane parallel shear flow the unstable spectrum is purely discrete. This result allows us to apply a rather general theorem to the our specific example to prove that such stratified shear flows are nonlinearly unstable.