  We investigate wind wave growth by direct numerical simulations solving for
the two phase Navier-Stokes equations. We consider ratio of the wave speed $c$
to wind friction velocity $u_*$ from $c/u_*=$ 2 to 8, i.e. in the slow to
intermediate wave regime; and initial wave steepness $ak$ from 0.1 to 0.3; the
two being varied independently. The turbulent wind and the travelling, nearly
monochromatic waves are fully coupled without any subgrid scale models. The
novel fully-coupled approach captures the simultaneous evolution of the wave
amplitude and shape, together with the underwater boundary layer (drift
current), up to wave breaking. The wave energy growth computed from the
time-dependent rms surface elevation is in quantitative agreement with that
computed from the extracted surface pressure distribution, which confirms the
leading role of the pressure forcing for finite amplitude gravity waves. The
phase shift and the amplitude of the principal mode of surface pressure
distribution are systematically reported, to provide direct evidence for
possible wind wave growth theories. For the momentum and energy fluxes, we find
that the wave form drag force is not a strong function of wave age but closely
related to wave steepness. The time evolution of the rms steepness and the wave
form drag suggests that there is an effect of the history of wind wave
coupling. The normalised wave growth rate we obtain agrees with previous
experimental and numerical studies. We make an effort to clarify various
commonly-adopted underlying assumptions, and to reconcile the scattering of the
data between different previous theoretical, numerical, and experimental
results, as we revisit this longstanding problem with new numerical evidence.
