Laboratory Study of Surface-Gravity Wave Energy Input.
Ivan Savelyev.
Sponsored by:
Literature review.
Early theoretical works:
•Jeffreys, H., 1924: On the formation of waves by wind. Proc. Roy. Soc., 107A, 189-206.
•Jeffreys, H., 1925: On the formation of waves by wind. II. Proc. Roy. Soc., 110A, 341-347.
Experiments with wind over solid waves:
•Stanton, T. E., D. Marshall, and R. Houghton, 1932: The growth of waves on water due to the action of the wind. Proc. Roy. Soc., 137A, 283-283.
•Thijsse, J. T., 1951: Growth of wind-generated waves and energy transfer. Gravity waves, National Bureau of Standards, Washington Circular 521, 281-287.
Currently used theory:
•Miles, J. W., 1957: On the generation of surface waves by shear flows. Journal of Fluid Mechanics, 3, 185-204.
•Miles, J. W., 1959: On the generation of surface waves by shear flows, Part 2. Journal of Fluid Mechanics, 6, 568-582.
•Miles, J. W., 1960: On the generation of surface waves by turbulent shear flows. Journal of Fluid Mechanics, 7, 469-478.
•Janssen, P. A. E. M., 1991:Quasi-linear theory of wind-wave generation applied to wave forecasting. J. Phys. Oceanogr., 21, 1631-1642.
•Belcher, S. E., and J. C. R. Hunt, 1993: Turbulent shear flow over slowly moving waves. J. Fluid Mech., 251, 109-148.
Recent experimental studies:
Okuda, K., Kawai, S. & Toba, Y. 1977 Measurement of skin friction distribution along the surface of wind waves. J. Oceanogr. Soc. Japan 30,190-198.
Snyder, R. L., F. W. Dobson, J. A. Elliott, and R. B. Long, 1981: Array measurements of atmospheric pressure fluctuations above surface gravity waves. Journal of Fluid Mechanics, 102, 1-59.
Banner, M. and Peirson, W. 1998 Tangential stress beneath wind-driven air-water interfaces. J. Fluid Mech., vol. 364, pp. 115-145.
Donelan, M., Babanin, A., Young, I. & Banner, M. 2006 Wave-Follower Field Measurements of the Wind-Input Spectral Function. Part II: Parameterization of the Wind Input. J. Physical Oceanography, vol 36, pp 1672-1689.
Wave frequency range: f = 1 ÷ 3 Hz,
Significant wave height: Hs = 0 ÷ 9 cm,
Wind speed at 10m: U10 = 0 ÷ 23 m/s.
Experiment Setup
Pressure
Transducers
Water ElevationGauges
Motor ElevationGauge
Analog – Digital Converter
Calibration
Transducer time lag
correction
Data Storage
Elliott tube clog condition
Signal conditioning
Smoothing algorithm
No
Yes
Time lag correction
Linear motor
Data Flow: Real time
Motion
Controller
Wave follower position response to water elevation signal. Left: green – follower position spectrum, blue – water elevation spectrum. Right: blue - water elevation, red – Elliott probe position.
Pressure transducer response to an incoming pressure wave. Time lag due to membrane acceleration and noise filtering electronics – 30ms.
Covered Parameters:
Wave number k = 6 ÷ 40 [1/m]
Wave frequency f = 1 ÷ 3 [Hz]
Wave phase speed Cp = 0.5 ÷ 1.1 [m/s]
Wind speed at 10m height U10 = 0 ÷ 23 [m/s]
Wind speed at L/2 height U(L/2) = 0 ÷ 10 [m/s]
Inverse wave age U10/Cp = 4 ÷ 32
Pressure – slope correlation <Pr*Sl> = -0.0008 ÷ 0.0734
Static air pressure at the surface (blue line) averaged over several hundred periods at each wave phase for four various wind/wave conditions. Error bars show 95% confidence interval. Green dashed line illustrates idealized wave shape. U10 – wind speed at 10m height, U10/Cp – inverse wave age (Cp – wave phase speed), f – dominant frequency, Hs – significant wave height. Wind direction is from right to left.
Pressure – slope correlation dependence on wind speed at 10m height (left) and at L/2 height (right), where L - dominant wave length. Error bars show 95% confidence interval.
Future work:- Compare measured form drag with wave energy growth rates.- Measure the pressure - slope correlation over a range of wave frequencies and wind speeds including strongly forced breaking wave conditions.- Use Particle Image Velocimetry to deduce the viscous drag contribution to the wave growth.
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