Revisiting wind wave growth with fully coupled direct numerical simulations

We investigate wind wave growth by direct numerical simulations solving for the two-phase Navier–Stokes equations. consider ratio of speed $c$ to friction velocity $u_*$ from $c/u_*= 2$ 8, i.e. in slow intermediate regime; and initial steepness $ak$ 0.1 0.3; two being varied independently. The turbulent travelling, nearly monochromatic waves are fully coupled without any subgrid-scale models. wall Reynolds number is 720. novel approach captures simultaneous evolution amplitude shape, together with underwater boundary layer (drift current), up breaking. energy computed time-dependent surface elevation quantitative agreement that pressure distribution, which confirms leading role forcing finite gravity waves. phase shift principal mode distribution systematically reported, provide evidence possible theories. Intermittent localised airflow separation observed steep small age, but its effect on setting phase-averaged not drastically different non-separated sheltering. find form drag force a strong function age closely related steepness. In addition, history coupling can affect drag, due crest shape other complex effects. normalised rate we obtain agrees previous studies. make an effort clarify various commonly adopted underlying assumptions, reconcile scattering data between theoretical, experimental results, as revisit this longstanding problem new evidence.