  Studies of ocean surface transport often invoke the "Eulerian-mean
hypothesis": that wave-agnostic general circulation models neglecting explicit
surface waves effects simulate the Eulerian-mean ocean velocity time-averaged
over surface wave oscillations. Acceptance of the Eulerian-mean hypothesis
motivates reconstructing the total, Lagrangian-mean surface velocity by adding
Stokes drift to model output. Here, we show that the Eulerian-mean hypothesis
is inconsistent, because wave-agnostic models cannot accurately simulate the
Eulerian-mean velocity if Stokes drift is significant compared to the
Eulerian-mean or Lagrangian-mean velocity. We conclude that Stokes drift should
not be added to ocean general circulation model velocities. We additionally
show the viability of the alternative "Lagrangian-mean hypothesis" using a
theoretical argument and by comparing a wave-agnostic global ocean simulation
with an explicitly wave-averaged simulation. We find that our wave-agnostic
model accurately simulates the Lagrangian-mean velocity even though the Stokes
drift is significant.
