Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T14:29:53.700Z Has data issue: false hasContentIssue false
  • English
  • Français

On the structure of turbulent flow over a progressive water wave: theory and experiment in a transformed, wave-following co-ordinate system

Published online by Cambridge University Press:  20 April 2006

Chin-Tsau Hsu ,
En Yun Hsu  and
Robert L. Street
Chin-Tsau Hsu
Affiliation:
Department of Civil Engineering, Stanford University, California 94305 Now at Fluid Mechanics Department, TRW/DSSG, One Space Park, Redondo Beach, California.
En Yun Hsu
Affiliation:
Department of Civil Engineering, Stanford University, California 94305
Robert L. Street
Affiliation:
Department of Civil Engineering, Stanford University, California 94305
Get access Rights & Permissions [Opens in a new window]

Abstract

An investigation of the turbulent flow structure over a progressive water wave, as well as the structure of the wave-induced flow field in a transformed wave-following frame, is reported. Experimental results are given for a free-stream velocity of 2·4 m s−1 over a 1 Hz mechanically generated deep-water wave. The velocity components were measured with a cross hot-film probe oscillating in a transformed wave-following frame. The amplitude and phase of the wave-induced velocity components are deduced by correlation to the generated water wave. The mean flow tends to follow the wave form so that the water wave should not be regarded as surface roughness. The mean velocity profile is basically log-linear and is similar to that over a smooth plate, because ripples riding on the waves do not produce sufficient roughness to interfere with the wind field. The wave-induced motion in the free stream is irrotational; but, in the boundary layer, it has strong shear behaviour related to the wave-associated Reynolds stress. The shear stress production as well as the energy production from the mean flow is concentrated near the interface. A phase jump of 180° in the wave-induced turbulent Reynolds stresses in the middle of the boundary layer was observed. The relationships between the induced turbulent Reynolds stresses and the induced velocities are of an eddy-viscosity type.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 105 , April 1981 , pp. 87 - 117
Copyright
© 1981 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acharya, M. & Reynolds, W. C. 1975 Measurements and predictions of a fully developed turbulent channel flow with imposed controlled oscillations. Stanford Univ., Dept Mech. Engng, Tech. Rep. no. TF-8.Google Scholar
Banner, M. L. & Melville, W. K. 1976 On the separation of air flow over water waves. J. Fluid Mech. 77, 825–842.Google Scholar
Barnett, T. P. & Wilkerson, J. C. 1967 On the generation of ocean wind waves as inferred from airborne radar measurements of fetch-limited spectra. J. Mar. Res. 25, 292–321.Google Scholar
Bendat, J. S. & Piersol, A. G. 1971 Random Data: Analysis and Measurement Procedures. Wiley-Interscience.
Benjamin, T. B. 1959 Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161–205.Google Scholar
Bole, J. B. & Hsu, E. Y. 1969 Response of gravity water waves to wind excitation. J. Fluid Mech. 35, 657–675.Google Scholar
Coles, D. E. 1954 The problem of the turbulent boundary layer. Z. angew. Math. Phys. 5, 181–203.Google Scholar
Coles, D. W. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.Google Scholar
Colonell, J. M. 1966 Laboratory simulation of sea waves. Stanford Univ., Dept Civil Engng, Tech. Rep. no. 65.Google Scholar
Davis, R. E. 1970 On the turbulent flow over a wavy boundary. J. Fluid Mech. 42, 721–731.Google Scholar
Davis, R. E. 1972 On prediction of the turbulent flow over a wavy boundary. J. Fluid Mech. 52, 287–306.Google Scholar
Dobson, F. W. 1971 Measurements of atmospheric pressure on wind-generated sea waves. J. Fluid Mech. 48, 91–127.Google Scholar
Dobson, F. W. & Elliott, J. A. 1978 Wave-pressure correlation measurements over growing sea waves with a wave follower and fixed height pressure sensors. In Turbulent Fluxes Through the Sea Surface, Wave Dynamics and Prediction (ed. A. Favre & K. Hasselmann), pp. 421–432. Plenum.
Elliott, J. 1972 Microscale pressure fluctuations near waves being generated by the wind. J. Fluid Mech. 54, 427–448.Google Scholar
Gent, P. R. 1977 A numerical model of the air flow above water waves. Part 2. J. Fluid Mech. 82, 349–369.Google Scholar
Gent, P. R. & Taylor, P. A. 1976 A numerical model of the air flow above water waves. J. Fluid Mech. 77, 105–128.Google Scholar
Gent, P. R. & Taylor, P. A. 1977 A note on ‘separation’ over short wind waves. Boundary-Layer Met. 11, 65–87.Google Scholar
Hasselmann, K., Barnett, T. P., Bouws, E., Carlson, H., Cartwright, D. E., Enke, K., Ewing, J. A., Gienapp, H., Hasselmann, D. E., Kruseman, P., Meerburg, A., Müller, P., Olbers, D. J., Richter, K., Sell, W., & Walden, H. 1973 Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project. Deutsches Hydrographisches Institut. Hamburg.
Hinze, J. O. 1975 Turbulence - An Introduction to Its Mechanism and Theory. McGraw-Hill.
Hsu, E. Y. 1965 A wind, water-wave research facility. Stanford Univ., Dept Civil Engng, Tech. Rep. no. 57.Google Scholar
Hsu, C. T., Hsu, E. Y. & Street, R. L. 1977 The structure of modulated turbulent flow over progressive water waves. Stanford Univ., Dept Civil Engng, Tech. Rep. no. 221.Google Scholar
Hussain, A. K. M. F. & Reynolds, W. C. 1970 The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41, 241–258.Google Scholar
Kendall, J. M. 1970 The turbulent boundary layer over a wall with progressive surface waves. J. Fluid Mech. 41, 259–281.Google Scholar
Klebanoff, P. S. 1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. N.A.C.A. Rep. no. 1247.Google Scholar
Lighthill, M. J. 1962 Physical interpretation of the mathematical theory of wave generation by wind. J. Fluid Mech. 14, 385–398.Google Scholar
Liu, J. T. C. & Merkine, L. 1976 On the interactions between large-scale structure and finegrained turbulence in a free shear flow. I. The development of temporal interactions in the mean. Proc. Roy. Soc. A 352, 213–247.Google Scholar
Long, R. B. 1971 On generation of ocean waves by a turbulent wind. Ph.D. dissertation, University of Miami.
Longuet-Higgins, M. S. 1969 Action of a variable stress at the surface of water waves. Phys. Fluids 12, 737–740.Google Scholar
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185.Google Scholar
Miles, J. W. 1959 On the generation of surface waves by shear flows. Part 2. J. Fluid Mech. 6, 568–582.Google Scholar
Miles, J. W. 1967 On the generation of surface waves by shear flows. Part 5. J. Fluid Mech. 30, 163–175.Google Scholar
Norris, H. L. & Reynolds, W. C. 1975 Turbulent channel flow with a moving wavy boundary. Stanford Univ., Dept Mech. Engng, Tech. Rep. no. TF-7.Google Scholar
Phillips, O. M. 1957 On the generation of surface waves by turbulent wind. J. Fluid Mech. 2, 417–445.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean, 2nd ed. Cambridge University Press.
Saeger, J. C. & Reynolds, W. C. 1971 Perturbation pressures over traveling sinusoidal waves with fully developed turbulent shear flow. Stanford Univ., Dept Mech. Engng, Rep. no. FM-9.Google Scholar
Schlichting, H. 1968 Boundary Layer Theory. McGraw-Hill.
Snyder, R. L. 1974 A field study of wave-induced pressure fluctuations above surface gravity waves. J. Mar. Res. 32, 497–531.Google Scholar
Snyder, R. L. & Cox, C. S. 1966 A field study of the wind generation of ocean waves. J. Mar. Res. 24, 141–178.Google Scholar
Stewart, R. H. 1970 Laboratory studies of the velocity field over deep-water waves. J. Fluid Mech. 42, 733–754.Google Scholar
Stewart, R. W. 1967 Mechanics of air-sea interface. Phys. Fluids Suppl. 10, S47–55.Google Scholar
Stewart, R. W. 1974 The air-sea momentum exchange. Boundary-Layer Met. 6, 151–167.Google Scholar
Takeuchi, K. & Mogel, T. R. 1975 A performance evaluation of a mini-computer. Rev. Sci. Instrum. 46, 686–691.Google Scholar
Townsend, A. A. 1972 Flow in a deep turbulent boundary layer over a surface distorted by water waves. J. Fluid Mech. 55, 719–753.Google Scholar
Wu, J. 1968 Laboratory studies of wind-wave interactions. J. Fluid Mech. 34, 91–111.Google Scholar
Yu, H. Y., Hsu, E. Y. & Street, R. L. 1971 A refined measurement of aerodynamic pressure over progressive water waves. Stanford Univ., Dept Civil Engng, Rep. no. 146.Google Scholar