  A formulation is developed to assimilate ocean-wave data into the Numerical
Flow Analysis (NFA) code. NFA is a Cartesian-based implicit Large-Eddy
Simulation (LES) code with Volume of Fluid (VOF) interface capturing. The
sequential assimilation of data into NFA permits detailed analysis of
ocean-wave physics with higher bandwidths than is possible using either other
formulations, such as High-Order Spectral (HOS) methods, or field measurements.
A framework is provided for assimilating the wavy and vortical portions of the
flow. Nudging is used to assimilate wave data at low wavenumbers, and the wave
data at high wavenumbers form naturally through nonlinear interactions, wave
breaking, and wind forcing. Similarly, the vertical profiles of the mean
vortical flow in the wind and the wind drift are nudged, and the turbulent
fluctuations are allowed to form naturally. As a demonstration, the results of
a HOS of a JONSWAP wave spectrum are assimilated to study short-crested seas in
equilibrium with the wind. Log profiles are assimilated for the mean wind and
the mean wind drift. The results of the data assimilations are (1) Windrows
form under the action of breaking waves and the formation of swirling jets; (2)
The crosswind and cross drift meander; (3) Swirling jets are organized into
Langmuir cells in the upper oceanic boundary layer; (4) Swirling jets are
organized into wind streaks in the lower atmospheric boundary layer; (5) The
length and time scales of the Langmuir cells and the wind streaks increase away
from the free surface; (6) Wave growth is very dynamic especially for breaking
waves; (7) The effects of the turbulent fluctuations in the upper ocean on wave
growth need to be considered together with the turbulent fluctuations in the
lower atmosphere; and (8) Extreme events are most likely when waves are not in
equilibrium.
