  Linear transient growth analysis is commonly used to suggest the structure of
disturbances which are particularly efficient in triggering transition to
turbulence in shear flows. We demonstrate that the addition of nonlinearity to
the analysis can substantially change the prediction made in pipe flow from
simple 2 dimensional streamwise rolls to a spanwise and cross-stream localised
3 dimensional state. This new nonlinear optimal is demonstrably more efficient
in triggering turbulence than the linear optimal indicating that there are
better ways to design perturbations to achieve transition.
