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Laboratory Study of Surface-Gravity Wave Energy Input.

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.

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Laboratory Study of Surface-Gravity Wave Energy Input.

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  1. Laboratory Study of Surface-Gravity Wave Energy Input. Ivan Savelyev. Sponsored by:

  2. 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.

  3. 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.

  4. 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.

  5. Experiment Setup Wave frequency range: f = 1 ÷ 3 Hz, Significant wave height: Hs = 0 ÷ 9 cm, Wind speed at 10m: U10 = 0 ÷ 23 m/s.

  6. Linear motor Motion Controller Pressure Transducers Water Elevation Gauges Motor Elevation Gauge Analog – Digital Converter Time lag correction Calibration Signal conditioning Elliott tube clog condition Transducer time lag correction Data Storage Smoothing algorithm Data Flow: Real time Yes No

  7. 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.

  8. Pressure transducer response to an incoming pressure wave. Time lag due to membrane acceleration and noise filtering electronics – 30ms.

  9. 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

  10. 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.

  11. 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.

  12. 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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