  We propose a general strategy for determining the minimal finite amplitude
isturbance to trigger transition to turbulence in shear flows. This involves
constructing a variational problem that searches over all disturbances of fixed
initial amplitude, which respect the boundary conditions, incompressibility and
the Navier--Stokes equations, to maximise a chosen functional over an
asymptotically long time period. The functional must be selected such that it
identifies turbulent velocity fields by taking significantly enhanced values
compared to those for laminar fields. We illustrate this approach using the
ratio of the final to initial perturbation kinetic energies (energy growth) as
the functional and the energy norm to measure amplitudes in the context of pipe
flow. Our results indicate that the variational problem yields a smooth
converged solution providing the amplitude is below the threshold amplitude for
transition. This optimal is the nonlinear analogue of the well-studied (linear)
transient growth optimal. At and above this threshold, the optimising search
naturally seeks out disturbances that trigger turbulence by the end of the
period, and convergence is then practically impossible. The first disturbance
found to trigger turbulence as the amplitude is increased identifies the
`minimal seed' for the given geometry and forcing (Reynolds number). We
conjecture that it may be possible to select a functional such that the
converged optimal below threshold smoothly converges to the minimal seed at
threshold. This seems at least approximately true for our choice of energy
growth functional and the pipe flow geometry chosen here.
