Direct Numercal Simulation of two-phase turbulent boundary layer over waved water surface O. A. Druzhinin, Yu.I. Тroitskaya Institute of Applied Physics RAS, Nizhny Novgorod, Russia

Data on droplets generation by the wind by Andreas et al. (2010, JGR) Droplet number density at different wind speeds at heights from 1 to 2m.

Typical high-speed video image showing spray droplets shed by a breaking wave, captured at 200 Hz. Lab experiment by Fairall et al. (2009 JGR) Droplet volume concentration for wind speed 16m/s at different heights

OBJECTIVE In this work the detailed structure and statistical characteristics of a turbulent, droplet-laden air flow over waved water surface are studied by direct numerical simulation (DNS). Two-dimensional water wave with wave slope up to ka = 0.2 and bulk Reynolds number Re = is considered. Droplet mass concentration 0.16 is attained (up to 16 x 10 6 drops of 100μm are considered). The shape of the water wave is prescribed and does not evolve under the action of the wind and/or drops. The full, 3D Navier- Stokes equations including the impact of discrete drops and the equations of motion of individual drops are solved simultaneously in curvilinear coordinates in a frame of reference moving the phase velocity of the wave. The shear driving the flow is created by an upper plane boundary moving horizontally with a bulk velocity in the x-direction.

Schematic of numerical experiment c=0.05 – wave celerity ka = 0.2 –wave slope

GOVERNING EQUATIONS Re = Forcing of the air flow by the drops - drop coordinates - grid node coordinates - weighting factor - bulk flow Reynolds number - drop Reynolds number Equations of motion of individual drop: δ = 1000 – water/air density ratio, N d – total number of drops -drop volume - Froude number Air-flow equations: of motion

CURVILINEAR COORDINATES Mapping over η:

BOUNDARY CONDITIONS Top plane: Bottom plane: All fields are x and y periodic Drops falling on the water are re-injected in the vicinity of the wave crests in the buffer region with velocity = air flow velocity

Instantaneous vorticity modulus and drops coordinates fields: side view at y=0

Instantaneous vorticity modulus and drops coordinates fields: front view at x = 3

Instantaneous vorticity modulus and drops coordinates fields: top view at z=0.04

Trajectory of individual drop for 100< t <300 sampled at Δt=0.2

The effect of drops on the mean air-flow velocity profile Drops accelerate the air-flow

The effect of drops on the mean air-flow velocity profile Drops reduce velocity fluctuations in the air-flow

Profiles of mean drop volume concentration and x-component of the force acting on the air flow

Phase-averaged drops volume concentration

Phase-averaged x-component of the force imposed on the air-flow by drops

Phase-averaged z-component of the drops velocity

CONCLUSION The DNS results show that under the impact of drops the mean air- flow over water waves is accelerated as the turbulent air-flow velocity fluctuations and momentum flux are reduced.That means that the surface drag may be reduced under the impact of the sea spray in field conditions. Remaining problems: - we need to take into account coagulation of the drops if clastering effects are pronounced and local volume concentration of drops may become large (say of the order of ); - sea drops evaporate, this should be also taken into account in DNS; - increase the Re number