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 output. 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.