  The use of the Yang-Mills gradient flow in step-scaling studies of lattice
QCD is expected to lead to results of unprecedented precision. Step scaling is
usually based on the Schr\"odinger functional, where time ranges over an
interval [0,T] and all fields satisfy Dirichlet boundary conditions at time 0
and T. In these calculations, potentially important sources of systematic
errors are boundary lattice effects and the infamous topology-freezing problem.
The latter is here shown to be absent if Neumann instead of Dirichlet boundary
conditions are imposed on the gauge field at time 0. Moreover, the expectation
values of gauge-invariant local fields at positive flow time (and of other well
localized observables) that reside in the center of the space-time volume are
found to be largely insensitive to the boundary lattice effects.
