Journal of Fluid Mechanics

Simulation of turbulent flow over idealized water waves

a1 National Center for Atmospheric Research, Boulder, Colorado 80307, USA
a2 Department of Atmospheric Sciences and Institute of Geophysics and Planetary Physics, UCLA, Los Angeles, CA 90095, USA


Turbulent flow over idealized water waves with varying wave slope ak and wave age c/u[low asterisk] is investigated using direct numerical simulations at a bulk Reynolds number Re = 8000. In the present idealization, the shape of the water wave and the associated orbital velocities are prescribed and do not evolve dynamically under the action of the wind. The results show that the imposed waves significantly influence the mean flow, vertical momentum fluxes, velocity variances, pressure, and form stress (drag). Compared to a stationary wave, slow (fast) moving waves increase (decrease) the form stress. At small c/u[low asterisk], waves act similarly to increasing surface roughness zo resulting in mean vertical velocity profiles with shorter buffer and longer logarithmic regions. With increasing wave age, zo decreases so that the wavy lower surface is nearly as smooth as a flat lower boundary. Vertical profiles of turbulence statistics show that the wave effects depend on wave age and wave slope but are confined to a region kz < 1 (where k is the wavenumber of the surface undulation and z is the vertical coordinate). The turbulent momentum flux can be altered by as much as 40% by the waves. A region of closed streamlines (or cat's-eye pattern) centred about the critical layer height was found to be dynamically important at low to moderate values of c/u[low asterisk]. The wave-correlated velocity and flux fields are strongly dependent on the variation of the critical layer height and to a lesser extent the surface orbital velocities. Above the critical layer zcr the positions of the maximum and minimum wave-correlated vertical velocity ww occur upwind and downwind of the peak in zcr, like a stationary surface. The wave-correlated flux uwww is positive (negative) above (below) the critical layer height.

(Received April 27 1999)
(Revised September 3 1999)