Wind Waves

This is the second paper in a group of three that
reports the systematic measurements of wind-generated
water waves in a wind tunnel experiment. Here, the
structure of the boundary layer on the air side of the water–
air interface was analysed and compared with the boundary
layer over a smooth plane rigid wall. The contribution of
the wave-induced Reynolds stress was detected through
filtering the spectrum of velocity fluctuations. Wave induced
Reynolds stresses became negligible for z[5
Hrms. The intermittency factor in the boundary layer over
water waves was similar to that in a boundary layer over a
rigid plane wall, with several differences near the interface.
Here, the presence/absence of water damps out the turbulence.
The quadrant analyses revealed that ejection and
sweep events were dominant and more concentrated. At
small fetches, the large-amplitude negative streamwise
perturbations were preferentially lifted. Turbulence energy
production peaked at z/d = 0.2 and had a distribution
similar to that observed for a self-preserving boundary
layer with a strong adverse gradient pressure. The quadrant
analysis contribution to the energy production revealed that
ejections still dominated the balance and that the production
was spatially modulated in the wind direction with a
couple of cells and with a minimum in the area of the free
surface wave height reduction.

This paper is the  third part of a report on  systematic measurements and analyses of wind-generated water waves in  a laboratory environment. The  results of the  measurements of the  turbulent flow on  the  water side  are  presented here, the  details of  which include the  turbulence structure, the  correlation functions, and the  length and velocity scales. It shows that the  mean turbulent velocity profiles are  logarithmic, and the  flows are  hydraulically rough. The friction velocity in the  water boundary layer is an order of magnitude smaller than that in the  wind boundary layer.  The level  of turbulence is enhanced immediately beneath the water surface due to micro-breaking, which reflects that the  Reynolds shear stress is of the  order u*w. The vertical  velocities of the  turbulence are  related to the  relevant velocity scale  at the  still-water level.  The autocor- relation function in the  vertical direction shows features of typical anisotropic turbulence comprising a large range of wavelengths. The  ratio between the  microscale and macroscale can  be  expressed as λ / Λ = a Ren,
with the  exponent n slightly different from − 1/2,  which is the  value when turbulence production and dissipation are in balance. On the  basis  of the  wavelength and turbulent velocity, the  free-surface flows in the  pre- sent experiments fall into  the  wavy free-surface flow regime. The integral turbulent scale  on  the  water side alone underestimates the  degree of disturbance at the  free  surface.

This study  detailed  the structure  of turbulence  in the air-side and  water-side  boundary layers in wind­ induced surface waves. lnside the air boundary layer, the kurtosis is always greater than 3 (the value for nor­mal distribution) for both horizontal and vertical velocity fluctuations.The skewness for the horizontal veloc­ity is negative, but the skewness for the vertical velocity is always positive. On the water side, the kurtosis is always greater than 3, and the skewness is slightly negative for the horizontal velocity and slightly positive for the vertical velocity.The statistics of the angle between the instantaneous vertical fluctuation and the in­stantaneous horizontal velocity in the air is similar to those obtained over solid walls.Measurements in water show a large variance, and the peak is biased towards negative angles.In the quadrant analysis, the contribu­tion of quadrants Q2 and Q4 is dominant on both the air side and the water side.The non-dimensional relative contributions  and  the  concentration  match  fairly well  near  the  interface. Sweeps  in  the  air side (belonging to quadrant Q4) act directly on the interface and exert pressure fluctuations, which, in addition to the tangential stress and form drag, lead to the growth of the waves. The water  drops detached  from the crest and accelerated  by the wind can play a major role in transferring momentum and in enhancing the turbulence level in the water side.
On the air side, the Reynolds stress tensor's principal axes are not collinear with the strain rate tensor, and show an angle aa =-20° to-25°. On the water side, the angle is  aa = -40° to-45°. The ratio be­tween  the  maximum  and  the  minimum  principal  stresses  is aolab =3 to 4  on  the  air  side,  and  arJ ab=1.5 to 3 on the water side. In this respect,  the air-side flow behaves like a classical boundary layer on a solid wall, while the water-side flow resembles a wake. The frequency  of bursting on the water  side in­ creases significantly along the flow, which can be attributed  to micro-breaking  effects - expected  to be more frequent at larger fetches.