On Reynolds Stresses over Wind Waves Tel-Aviv University School of Mechanical Engineering Supported by Israel Science Foundation Lev Shemer and Andrey Zavadsky

TAU Wind-Wave Flume Test Section Dimensions: 5 m Long, 0.4 m Wide, m High Water Depth 0.2 m Max Wind Speed: > 15 m/s

View of the sensors Pitot tube X-hot film Static pressure sensor Capacitance wave gauges Max. crest height detector

View within the test section in operating conditions

Experimental conditions Each 40 cm; 100 cm ≤ x ≤ 340 cm7 Fetches (x) U 10 = 16.5 m/s; 18.6 m/s; 21.0 m/s; 25.4 m/s 4 Wind Velocities 5 mm ≤ z< ≈ 150 mm above the highest crest At each fetch, 40 vertical locations Surface Elevation η, Static pressure p, instantaneous horizontal u and vertical w air velocities Simultaneously Recorded Parameters Temperature is maintained constant for thermo- anemometry Duration: 5 – 10 sampling rate of 120 Hz or 1200 Hz Continuous Sampling Measurement session for 4 wind speeds and all elevations lasts overnight (about 16 hours) Automatic sensor calibration and data recording at each fetch

Vertical Air Velocity Profiles

Vertical Distribution of –u’w’

Friction Velocity u * (m/s) The values of the friction velocity u * determined from fitting the log velocity profile (κ=0.4) and from the Reynolds stress measurements agree within 10-20% Full symbols – from log velocity profile; Empty symbols – from Reynolds stresses

Air velocity fluctuations u’w’ U 10 =16.5 m/s U 10 =25.4 m/s

Records of velocity components u and w and pressure fluctuations p in air compared to the surface elevation η; U 10 =25.4 m/s Simultaneous measurements at x=300cm, 5 mm above the highest crest

Cross-Spectral Analysis Measured records of 2 signals: f(t) = f(t i ) and g(t) = g(t i ); t i = (i-1) Δt; i=1,…N Cross-correlation function and cross-spectrum Magnitude Squared Coherence (MSC)

Coherence between turbulent velocity components u’, w’ and surface elevation η U 10 =16.5 m/s U 10 =25.4 m/s η - u η - w

Phase relations between surface elevation and air velocity fluctuations “Coherent” wave-induced velocity fluctuations do not contribute to Reynolds shear stress

Conclusions  Detailed experimental results on the structure of turbulent air flow over waves are presented, including spatial distributions of normal and shear Reynolds stresses and phase relations between waves and air flow  To enable those measurements, a fully automated procedure was developed to control the experimental conditions and to record data simultaneously from numerous sensors  These results can serve a basis for validation of theoretical models dealing with wind-wave interactions  Extensive further experiments, also involving mechanically generated waves are now in progress

Thank you !