Laboratory Study of SurfaceGravity Wave Energy Input.

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

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• 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., 1991Quasi-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.

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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.
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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.
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Data Flow Real time
Yes
No
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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.
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Pressure transducer response to an incoming
pressure wave. Time lag due to membrane
acceleration and noise filtering electronics
30ms.
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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
ltPrSlgt -0.0008 0.0734
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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.
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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.
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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.