The flow behavior of turbulent wave boundary layers with weak currents was
described using a numerical model. Horizontal velocities, shear stresses, t
urbulent eddy viscosities, and apparent roughnesses were described. The num
erical model is based upon the fluid continuity and momentum equations in t
he vertical plane. The momentum equations retain the advection terms with v
ertical orbital velocity in contrast to previous numerical models. The hori
zontal velocities were calculated from the momentum equations, and the vert
ical orbital velocity distribution was obtained from the continuity equatio
n. The Reynolds terms were modeled by a mixing length hypothesis. The model
was compared with existing models for the wave friction factor by switchin
g off the advection terms and produced similar answers to two existing mode
ls. Next. the model was applied to a wave-only flow case with the advection
terms retained. The model reproduced the measured mass transport profile b
y van Doom and Godefroy reasonably well. The model was then applied to wave
-current flow cases with arbitrary intersection angles. The model results f
or 0 degrees, 180 degrees, and 90 degrees agreed well with measurements by
van Doom and Godefroy and van der Stel and Visser, respectively. The model
produced significant differences between the following and opposing current
cases for the same wave condition. The model results suggest that the wave
boundary layer flows for relatively strong waves and weak currents can be
accurately described by taking account of the nonlinear advection terms by
means of the vertical wave orbital velocity.