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Turbulent oscillatory flow over rough beds

Published online by Cambridge University Press:  21 April 2006

J. F. A. Sleath
J. F. A. Sleath
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
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Abstract

Velocity measurements are presented for turbulent oscillatory flow over rough beds. Two components of velocity were measured with a laser-Doppler anemometer and the rough beds consisted of a single layer of sand, gravel or pebbles on a flat surface. Turbulence intensities showed significant variation during the course of the cycle. Maximum turbulence intensity propagated out from the bed at a more or less constant velocity for all beds. Variation of time-mean turbulence intensity with height was qualitatively similar to that observed in steady flows. Reynolds stress showed several interesting features. Near the bed, maximum Reynolds stress was in phase with one of the two peaks of turbulence intensity but further out it was in phase with the other, i.e. the phase of maximum Reynolds stress showed a 180° phase shift at a certain height above the bed. A related effect was seen in the time-mean eddy viscosity which was negative near the bed but positive further out. It is suggested that these effects are caused by the jets of fluid associated with vortex formation and ejection in oscillatory flow over rough beds. Maximum Reynolds stress was also significantly less than the horizontal force per unit area of bed obtained from the momentum integral. Eddy viscosity and mixing length were found to vary significantly during the course of the cycle. Variation with height of time-mean values of these variables showed similar trends, except in the near-bed region, to those observed in steady flow but derived values of the Kármán constant were significantly lower. Non-dimensional defect velocity appeared to show dependence on a/ks as well as on y/δ in the outer layer away from the bed, even at high Reynolds numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 182 , September 1987 , pp. 369 - 409
Copyright
© 1987 Cambridge University Press

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References

Bakker, W. T. 1974 Sand concentration in oscillatory flow. In Proc. 14th Conf. on Coastal Engng, Copenhagen, pp. 1129–1148. ASCE.
Bakker, W. T. & Van Doorn, T. 1978 Near bottom velocities in waves with a current. In Proc. 16th Conf. on Coastal Engng, Hamburg, pp. 1394–1413. ASCE.
Brevik, I. 1981 Oscillatory rough turbulent boundary layers. J. Waterway Port Coastal Ocean Div. ASCE 107 (WW3), 175–188.Google Scholar
Christoffersen, J. B. 1982 Current depth refraction of dissipative water waves. Inst. Hydrodyn. Hydraul. Engng Tech. Univ. Denmark, Series paper 30.
Corrsin, S. & Kistler, A. L. 1954 The free-stream boundaries of turbulent flows. NACA Tech. Note 3133.
Du Toit, C. G. & Sleath, J. F. A. 1981 Velocity measurements close to rippled beds in oscillatory flow. J. Fluid Mech. 112, 71–96.Google Scholar
Einstein, H. A. 1950 The bed-load function for sediment transport in open channel flows. U.S. Dept. of Agriculture. Soil Conservation Service. Tech. Bull. 1026.
Fredsoe, J. 1981a Mean current velocity distribution in combined waves and current. Inst. Hydrodyn. Hydraul. Res. Tech. Univ. Denmark Prog. Rep. 53.Google Scholar
Fredsoe, J. 1981b A simple model for the wave boundary layer. Inst. Hydrodyn. Hydraul. Res. Tech. Univ. Denmark Prog. Rep. 54.Google Scholar
Fredsoe, J. 1982 Calculation of mean current profile in combined wave—current motion by application of the momentum equation. Inst. Hydrodyn. Hydraul. Engng. Tech. Univ. Denmark Prog. Rep. 55, 56.Google Scholar
George, C. B. & Sleath, J. F. A. 1978 Oscillatory laminar flow above a rough bed. In Proc. 16th Conf. on Coastal Engng, Hamburg, pp. 898–910. ASCE.
Grant, W. D. & Madsen, O. S. 1979 Combined wave and current interaction with a rough bottom. J. Geophys. Res. 84, 1797–1808.Google Scholar
Hino, M., Kashiwayanagi, M., Nakayama, A. & Hara, T. 1983 Experiments on the turbulent statistics and the structure of a reciprocating oscillatory flow. J. Fluid Mech. 131, 363–400.Google Scholar
Horikawa, K. & Watanabe, A. 1968 Laboratory study on oscillatory boundary layer flow. Coastal Engng Japan 11, 13–28.Google Scholar
Hunt, J. C. R. & Maxey, M. R. 1978 Estimating velocities and shear stresses in turbulent flows of liquid metals driven by low frequency electromagnetic fields. In MHD-Flows and Turbulence. II (ed. H. Branover & A. Yakhot), pp. 249–269. Israel University Press.
Johns, B. 1975 The form of the velocity profile in a turbulent shear wave boundary layer. J. Geophys. Res. 80, 5109–5012.Google Scholar
Johns, B. 1977 Residual flow and boundary shear stress in the turbulent bottom layer beneath waves. J. Phys. Oceanogr. 7, 733–738.Google Scholar
Jonsson, I. G. 1963 Measurements in the turbulent wave boundary layer. In Proc. 10th Congress IAHR, London, pp. 85–92.
Jonsson, I. G. 1980 A new approach to oscillatory rough turbulent boundary layers. Ocean Engng 7, 109–152.Google Scholar
Jonsson, I. G. & Carlsen, N. A. 1976 Experimental and theoretical investigations in an oscillatory turbulent boundary layer. J. Hydraul. Res. 14, 45–60.Google Scholar
Kajiura, K. 1968 A model of the bottom boundary layer in water waves. Bull. Earthquake Res. Inst. 46, 75–123.Google Scholar
Kalkanis, G. 1957 Turbulent flow near an oscillating wall. Beach Erosion Board Tech. Memo. 97.
Kalkanis, G. 1964 Transportation of bed material due to wave action. US Army CERC Tech. Memo. 2.
Kamphuis, J. W. 1975 Friction factors under oscillatory waves. J. Waterway Harbors Coastal Eng. Div. ASCE 101 (WW2), 135–144.Google Scholar
Keiller, D. C. & Sleath, J. F. A. 1976 Velocity measurements close to a rough plate oscillating in its own plane. J. Fluid Mech. 73, 673–691.Google Scholar
Kemp, P. H. & Simons, R. R. 1982 The interaction between waves and a turbulent current: waves propagating with the current. J. Fluid Mech. 116, 227–250.Google Scholar
Kemp, P. H. & Simons, R. R. 1983 The interaction between waves and a turbulent current: waves propagating against the current. J. Fluid Mech. 130, 73–89.Google Scholar
Klebanoff, P. S. 1954 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA Tech. Note 3178.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Lundgren, H. 1972 Turbulent currents in the presence of waves. In Proc. 13th Conf. on Coastal Engng, Vancouver, pp. 623–634. ASCE.
Nielsen, P. 1985 On the structure of oscillatory boundary layers. Coastal Engng 9, 261–276.Google Scholar
Sleath, J. F. A. 1970 Measurements close to the bed in a wave tank. J. Fluid Mech. 42, 11–123.Google Scholar
Sleath, J. F. A. 1982 The effect of jet formation on the velocity distribution in oscillatory flow over flat beds of sand or gravel. Coastal Engng 6, 151–177.Google Scholar
Sleath, J. F. A. 1984 Sea Bed Mechanics. Wiley Interscience.
Smith, J. D. 1977 Modeling of sediment transport on continental shelves. In The Sea, vol. 6 (ed. E. D. Goldberg, I. N. McCave, J. J. O'Brien & J. H. Steele), pp. 539–577. Wiley Interscience.
Tanaka, H. & Shuto, N. 1981 Friction coefficient for a wave—current coexistent system. Coastal Engng Japan 24, 105–128.Google Scholar
Van Doorn, T. 1981 Experimental investigation of near-bottom velocities in water waves without and with a current. Delft Hydraulics Lab. Rep. M1423 Part 1.Google Scholar
Vincent, G. E. & Ruellan, F. 1957 Mouvements solides provoqués par la houle sur un fond horizontal. Houille Blanche. B, 693–708.