  We identify `minimal seeds' for turbulence, i.e. initial conditions of the
smallest possible total perturbation energy density $E_c$ that trigger
turbulence from the laminar state, in stably stratified plane Couette flow
using the `direct-adjoint-looping' (DAL) method for finding nonlinear optimal
perturbations that optimise the time averaged total dissipation of energy in
the flow. These minimal seeds are located adjacent to the edge manifold, the
manifold in state space that separates trajectories which transition to
turbulence from those which eventually decay to the laminar state. The edge
manifold is also the stable manifold of the system's `edge state'. The
trajectories from the minimal seed initial conditions spend a large amount of
time in the vicinity of some states: the edge state; another state contained
within the edge manifold; or even in dynamically slowly varying regions of the
edge manifold, allowing us to investigate the effects of a stable
stratification on any coherent structures associated with such states. In
unstratified plane Couette flow, these coherent structures are manifestations
of the self-sustaining process (SSP) deduced on physical grounds by Waleffe
(1997), or equivalently finite Reynolds number solutions of the vortex-wave
interaction (VWI) asymptotic equations initially derived mathematically by Hall
& Smith (1991). The stratified coherent states we identify at moderate $Re$
display an altered form from their unstratified counterparts for bulk
Richardson numbers $Ri_B=\textit{O}(Re^{-1})$, and exhibit chaotic motion for
larger $Ri_B$. We demonstrate that at high $Re$ the suppression of vertical
motions by stratification strongly disrupts input from the waves to the roll
velocity structures, thus preventing the waves from reinforcing the viscously
decaying roll structures adequately, when $Ri_B=\textit{O}(Re^{-2})$.

Fluid Dynamics