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The bursting sequence in the turbulent boundary layer over progressive, mechanically generated water waves

Published online by Cambridge University Press:  21 April 2006

Yiannis Alex Papadimitrakis ,
Robert L. Street  and
En Yun Hsu
Yiannis Alex Papadimitrakis
Affiliation:
Goddard Space Flight Center, Code 671, Greenbelt, MD 20771, USA
Robert L. Street
Affiliation:
Environmental Fluid Mechanics Laboratory, Department of Civil Engineering, Stanford University, Stanford, CA 94305, USA
En Yun Hsu
Affiliation:
Environmental Fluid Mechanics Laboratory, Department of Civil Engineering, Stanford University, Stanford, CA 94305, USA
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Abstract

The structure of the pressure and velocity field in the air above progressive, mechanically generated water waves was investigated in order to evaluate the influence of a mobile and deformable boundary on turbulence production and the related bursting phenomena. The Reynolds stress fluctuations were measured in a transformed Eulerian wave-following frame of reference, in a wind-wave research facility at Stanford University.

The structure of the wave-coherent velocity field was found to be very sensitive to the height of the critical layer below which the waves travel faster than the wind. Because the critical-layer height changes rapidly with the ratio (c / u*) of the wave speed to the wind friction velocity, the structure of the wave-coherent velocities depends strongly on the parameter c/Uδ0, where Uδ0 is the mean free-stream wind velocity. When the critical height is large enough that most of the flow in the turbulent boundary layer is below the critical height, the structure of the wave-coherent velocities is strongly affected by the Stokes layer (in the air), which under the influence of turbulence can have thickness comparable with the wave amplitude. In contrast, when the critical height is small enough that most of the flow in the boundary layer is above the critical height, the structure of the wave-coherent velocities is strongly affected by the critical layer. The latter was found to be nonlinear and turbulently diffusive.

The dependence of the structural behaviour of the wave-coherent velocity field upon the critical and Stokes layers results in considerable modifications of the turbulence-generating mechanism during the bursting-cycle, as the dimensionless wave speed c/Uδ0 changes. Such modifications are manifested by an enhancement of the contributions to the mean Reynolds stress of the bursting events (relative to their solid-wall counterparts), and their dependence on the dimensionless wave speed. For c/Uδ0 [ges ] 0.68 (or c/u* > 20), the nonlinear critical-layer thickness is large compared to the wave amplitude (except when c/Uδ0 = 0.68), and the diffused Stokes layer stimulates the wave-associated stress production. In the water proximity, the bursting contributions remain nearly constant with dimensionless wave speed; ejections account for 90% of the mean Reynolds stress, whereas sweeps provide 77%, the excess over 100% being balanced by the outward and inward interactions. For c/Uδ0 < 0.68, the critical-layer thickness is smaller than the wave amplitude and all contributions increase gradually with c/Uao. However, the ratio of ejection to sweep contributions remains unaltered and ≈ 1.15, indicating that sweeps are nearly as energetic as ejections a t all dimensionless wave speeds. The value of c/Uδ0 ≈ 0.68 appears to separate the flow regimes of high and low critical level, respectively, where significant and weak production of the wave-associated stresses have been found. Near the water surface the height distribution of the fractional contributions of the bursting events is also sensitive to the ratio c/UJO. In the equilibrium region of the boundary layer it remains uniform and in the free stream rises sharply, independent of dimensionless wave speed.

The mean time period between ejections or sweeps depends on both the wave and wind field characteristics and does not scale with either the inner or the outer flow variables. The former can be determined from the time between the first two largest consecutive peaks of the phase-averaged Reynolds stress distribution.

In the water proximity, the height distribution of the normalized energy production is sensitive to c/Uδ0; only when c/Uδ0 [ges ] 0.68 does it show a peak of increasing magnitude with increasing dimensionless wave speed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 193 , August 1988 , pp. 303 - 345
Copyright
© 1988 Cambridge University Press

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References

Alfredsson, P. H. & Johansson, A. V. 1982 Time scales for turbulent channel flow. Royal Inst. Tech., Stockholm, Rep. TRITA-MCK-82-11.Google Scholar
Alfredsson, P. E. & Johansson, A. V. 1983 Effects of imperfect spatial resolution on measurements of wall-bounded turbulent shear flows. J. Fluid Mech. 137, 409.Google Scholar
Antonia, R. A. B. & Chambers, A. J. 1980 Wind-wave-induced disturbances in the marine surface layer. J. Phys. Oceanogr. 10, 611.Google Scholar
Benjamin, T. B. 1959 Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161.Google Scholar
Benney, D. J. & Bergeron, R. R. J. 1969 A new class of nonlinear waves in parallel flows. Stud. Appl. Maths. 48, 181.Google Scholar
Blackwelder, R. F. & Haritonidis, J. H. 1983 Scaling of the bursting frequency in turbulent boundary layers. J. Fluid Mech. 132, 87.Google Scholar
Blackwelder, R. F. & Kaplan, R. E. 1972 Intermittent structures in turbulent boundary layers. Nato-Agard CP93. London Technical Editing and Reproduction.
Bogard, D. G. & Tiederman, W. G. 1983 Investigation of flow visualization techniques for detecting turbulent bursts. Symposium on Turbulence, 1981, p. 289. University of Missouri-Rolla.
Bogard, D. G. & Tiederman, W. G. 1986 Burst detection with single-point velocity measurements. J. Fluid Mech. 162, 389.Google Scholar
Bradshaw, P. 1978 Topics in Applied Physics-Turbulence. Springer.
Brodkey, R. S., Wallace, J. M. & Eckelmann, H. 1974 Some properties of truncated turbulence signals in bounded shear flows. J. Fluid Mech. 63, 209.Google Scholar
Buckles, J., Hanratty, T. S. & Adrian, R. J. 1984 Turbulent flow over large-amplitude wavy surfaces. J. Fluid Mech. 140, 27.Google Scholar
Busch, N. E. 1973 On the mechanics of atmospheric turbulence. In Workshop on Micrometeorology (ed. D. A. Haugen), p. 1. AMS Science Press.
Cebeci, T. & Bradshaw, P. 1977 Momentum Transfer in Boundary Layers McGraw-Hill.
Chalikov, D. V. 1986 Numerical simulation of the boundary layer above waves. Boundary-Layer Met. 34, 63.Google Scholar
Chambers, A. J. & Antonia, R. A. 1981 Wave-induced effect on the Reynolds shear stress and heat flux in the marine surface layer. J. Phys. Oceanogr. 11, 116.Google Scholar
Chen, C. H. P. & Blackwelder, R. F. 1978 Large-scale motion in a turbulent boundary layer: a study using temperature contamination. J. Fluid Mech. 89, 1.Google Scholar
Cheung, T. K. 1985 A study of the turbulent boundary layer in the water at an air-water interface. Dept. Civil Engne., Stanford Univ., Tech. Rep. 287.Google Scholar
Corino, E. R. & Brodkey, R. S. 1969 A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37, 1.Google Scholar
Csanady, G. T. 1985 Air-sea momentum transfer by means of short-crested wavelets. J. phys. Oceanogr. 15, 1488.Google Scholar
Davis, R. E. 1969 On the high Reynolds number flow over a wavy boundary. J. Fluid Mech. 36, 337.Google Scholar
Dorman, C. E. & Mollo-Christensen, E. 1973 Observations on the structure of moving gust patterns over a water surface (cats paws). J. Phys. Oceanogr. 3, 120.Google Scholar
Elloitt, J. A. 1972 Microscale pressure fluctuations near waves being generated by the wind. J. Fluid Mech. 54. 427.Google Scholar
Grass, A. J. 1971 Structural features of turbulent flow over smooth and rough boundaries. J. Fluid Mech. 50, 233.Google Scholar
Hinze, J. O. 1975 Turbulence (2nd edn). p. 586. McGraw-Hill.
Hsc, C. T. & Hsu, E. Y. 1983 On the structure of turbulent flow over a progressive water wave: theory and experiment in a transformed wave-following coordinte suystem. Part 2. J. Fluid Mech. 131, 123.Google Scholar
Hsu, C. T. Hsu, E. Y. & Street, R. L. 1981 On the struture of turbulent flow over a progressive water wave: theory and experiments in a trasnts in a transformed wave-following coordinate system. Part 1. J. Fluid Mech. 105, 87.Google Scholar
Hsu, C. T., Wu, H. Y., Hsu, E. Y. & Street, R. L. 1982 Momentum and energy transfer in wind generation of waves. J. Phys. Oceanogr. 12, 929.Google Scholar
Huang, N. E., Long, S. R. & Bliven, L. F. 1981 On the importance of significant slope in empirical wind-wave studies. J. Phys. Oceanogr. 11, 569.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.Google Scholar
Jackson, R. G. 1976 Sedimentological and fluid-dynamic implications of the turbulent bursting phenomenon in geophysical flows. J. Fluid Mech. 77, 531.Google Scholar
Kawai, S. 1981 Visualization of air flow separation over wind wave crests under moderate wind. Boundar-Layer Met. 21, 93.Google Scholar
Kawai, S. 1982 Struture of flow separation over wind wave crests. Boundary-Layer Met. 23, 503.Google Scholar
Kawamura, H., Okuda, K., Kawai, S. & Toba, Y. 1981 Structure of turbulent boundary layer over wind waves in a wind tunnel. Tohoku Geophys. J. (Sci. Rep. Tohoku Univ., Ser 5) 28, 69.Google Scholar
Kawamura, H. & Toba, Y. 1985 New aspects of the turbulent boundary layer over wind waves. In The Ocean Surface. Wave Breaking, Turbulent Mixing and Radio Probing (ed. Y. Toba & H. Mitsuyasu), p. 105. Reidel.
Kendall, J. M. 1970 The turbulent boundary layer over a wall with progressive surface waves. J. Fluid Mech. 41, 259.Google Scholar
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 The prodution of turbulence near a smooth wall in a tubulent boundary layer. J. Fluid Mech. 50, 133.Google Scholar
Kinsman, B. 1965 Wind Waves: thir Generation and Propagation on The Ocean Surface. Prentice Hall.
Kline, S. J. Reynolds, W. C., Shraub, F. A. & Ruunstandler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741.Google Scholar
Kitaigorodskii, S. A. & Donelan, M. A. 1984 Wing wave effects on gas transfer. In Gas Transfer at Water Surfaces (ed. W. Brutsaert & G. H. Jirka), p. 147. Reidel.
Landahl, M. T. 1975 New trends in experimental turbulence research. Ann. Rer. Fluid Mech. 7, 307.Google Scholar
Lighthill, M. J. 1962 Physical interpretation of the mathematical theory of wave generation by wind. J. Fluid Mech. 14, 385.Google Scholar
Ligrani, P. M. & Moffat, R. J. 1986 Structure of transitionally rouogh and fully rough turbulent boundary layers, J. Fluid Mech. 162, 69.Google Scholar
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Longuet-Higgins, M. S. 1969 Action of a variable stress at the surface of water waves. Phys. Fluids. 12, 737.Google Scholar
Lu, S. S. & Willmarth, W. W. 1972 The structure of the Reynolds stress in a turbulent boundary layer. Dept. Aerospace Engn., University of Michigan, ORA Rep. 021490-2-T.Google Scholar
Lu, S. S. & Willmarth, W. W. 1973 Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60, 481.Google Scholar
McIntosh, D. A., Street, R. L. & Hsu, E. Y. 1975 Turbulent heat and momentum transfer at an air-waterinterface: the influence of surface conditions. Dept. Civil Engng. Standord Univ Tech. Rep. 197.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 genearation of surface waves by shear flows. Part 2. J. Fluid Mech. 6, 568.Google Scholar
Mollo-Christensen, E. 1973 Intermittency in large scale turbulent flows. Ann. Rev. Fluid Mech. 5, 101.Google Scholar
Morduckhovich, M. I. & Tsvang, L. R. 1966 Direct measurements of turbulent flows in two heights in the atmospheric layer, Izv. Atmos. Ocean, Phys. 2, 477.Google Scholar
Nakagawa, H. & Nesu, I. 1977 Prediction of the contributions to the Reybolds stress from bursting events in open channel flows. J. Fluid Mch. 104, 1.Google Scholar
Offen, G. R. & Kline, S. J. 1975 A comparison and analysis of detection mehods for the measuremnts of production in a boundary layer. Proc. 3rd Biennial Sympos. On Tubulence in Liquids, University of Missouri-Rolla, p. 289.Google Scholar
Okuda, K. 1983 Internal flow structure of short wind waves. Part III. Pressure distributions. J. Ocean Soc. Japan 38, 331.Google Scholar
Papadimitrakis, Y. A. 1982 Velocity and pressure measurements in the turbulent boundary layer above menchanically-generated water waves, Ph. D. dissertation, Dept. Civil Engng., Stanford University.
Papadimitrakis, Y. A. Hsu, E. Y. & Street, R. L. 1984 On the structure of the velocity field over progressive, menchanically-generated water waves. J. Phys. Oceanogr. 14, 1937.Google Scholar
Papadimitrakis, Y. A. Hsu, E. Y. & Street, R. L. 1985 On the resolution of organized spurious pressure fluctuations in wind-wave facilities. J. Acoust. Soc. Am. 77, 986.Google Scholar
Papadimitrakis, Y. A. Hsu, Y. H. L. & Wu, J. 1986 Turulent heat mass transfers across a thermally stratified air-water interface. J. Geophys. Res. 91, 10607.Google Scholar
Papadimitrakis, Y. A. Hsu, Y. H. L. & Wu, J. 1987 Thermal stability effects on the structure of the velocity field above an air-water interface. J. Geophys. Res. 92, C8. 8277.Google Scholar
Phillips, O. M. 1977 The dynamics of the Upper Ocean. Cambridge University Press.
Rao, K. N., Narasimha, R. & Badri Narayanan, M. A. 1971 The bursting phenomenonin a turbulent boundary layer. J. Fluid Mech. 48, 339.Google Scholar
Robinson, J. L. 1974 The inviscid nonlinear instability of paralleo/shear flows. J. Fluid Mech. 63, 723.Google Scholar
Schraub, F. A., Fline, S. J., Henry, J., Runstadler, P.W. J. & Litterl, A. 1965 Use of hydrogen bubbles for quantitative determination of time-dependent velocity fields in lowspeed water flows. Trans. Asme D: J. Basic Engng 87, 429.Google Scholar
Shemdin, O. H. & Lai, R. J. 1973 Investigation of the velocity field over waves using a wave follower. Tech. Rep. 18. Coasttal and Ocean Engng Lab, University of Florida.Google Scholar
Snyder, R. L., Dobson, F.W., Elliott, J. A., Ling, R. B. 1981 Array measurements of atmospheric pressure fluctuation above surface gravity waves. J. Fluid Mech. 102, 1.Google Scholar
Street, R. L. 1979 Turbulent heat and mass transfer across a rough air-water interface:a simple theory. Intl J. Heat Mass Transfer 22, 885.Google Scholar
Tiederman, W. G., Smith A. J. & Oldaker, D. K. 1977 Structure of the viscous sublayer in drug-reducing channel flows. In Proc. 4th Biennial Sympos. On Turbulence in Liquids, University of Missouri-Rolla p. 312.
Toba, Y., Kawamura, H. & Okuda, K. 1984 Ordered motions inturbulent boundary layers above and below wind waves. In Turbulence and Dhaotic Phenomena in Fluids (ed. T. Tatsumi), p. 513. Elsevier, IUTAM.
Wallace, J. M., Eckelmann, H. & Brodkey, R. S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 54, 39.Google Scholar
Warhaft, Z. & Bolgiano, R. J. 1984 Moisture and heat transport in a stably stratified boundary layer over a water surface. In Gas Transfer at Water Surfaces (ed. W. Brutsaert & G. H. Jirka). p. 133. Reidel.
Willmarth, W. W. 1975 Structure of turbulence in a boundary layer Adr. Appl. Mech. 15, 159.Google Scholar
Wu, H. Y., Hsu, E. Y. & Street, R. L. 1977 The energy transfer due to air input. non linear wave-wave interaction and white-cap dissipationassociated with wind generated waves. Dept. Civil Engng. Stanfrod Univ. Tech. Rep. 207.Google Scholar
Volkov, Y. A. 1970 Turbulent flux of momentum and heat in the atmospheric surface layer over a disturbed sea-surface. Izv. Atmos. Ocean. Phys. 6, 1295.Google Scholar