• Abramowitz, M., and I. A. Stegun, 1970: Handbook of Mathematical Functions. U.S. Natl. Bur. Stand., 1046 pp.

  • Ardhuin, F., T. H. C. Herbers, and W. C. O'Reilly, 2001: A hybrid Eulerian–Lagrangian model for spectral wave evolution with applications to bottom friction on the continental shelf. J. Phys. Oceanogr., 31 , 14981516.

    • Search Google Scholar
    • Export Citation
  • Beach, R. A., and R. W. Sternberg, 1992: Suspended sediment transport in the surf zone: Response to incident wave and longshore current interaction. Mar. Geol., 108 , 275294.

    • Search Google Scholar
    • Export Citation
  • Bendat, J. S., and A. G. Piersol, 1986: Random Data: Analysis and Measurement Procedures. Wiley-Interscience, 566 pp.

  • Bijker, E. W., J. P. T. Kalwijk, and T. Pieters, 1974: Mass transport in gravity waves on a sloping bottom. Proc. ASCE 14th Int. Coastal Engineering Conf., Copenhagen, Denmark, ASCE, 447–465.

    • Search Google Scholar
    • Export Citation
  • Bradshaw, P., D. H. Ferris, and N. P. Atwell, 1967: Calculation of boundary layer development using the turbulent kinetic energy equation. J. Fluid Mech., 30 , 241258.

    • Search Google Scholar
    • Export Citation
  • Brevik, I., 1981: Oscillatory rough turbulent boundary layers. J. Waterway, Port, Coastal Ocean Div., 107 (WW3) 175188.

  • Christoffersen, J. B., and I. G. Jonsson, 1985: Bed friction and dissipation in a combined current and wave motion. Ocean Eng., 12 , 387423.

    • Search Google Scholar
    • Export Citation
  • Chu, V. H., and C. C. Mei, 1970: On slowly varying Stokes waves. J. Fluid Mech., 41 , 873887.

  • Crawford, A. M., and A. E. Hay, 1999: A simple system for laser-illuminated video imaging of sediment suspension and bed topography. IEEE J. Oceanic Eng., 23 , 1219.

    • Search Google Scholar
    • Export Citation
  • Crawford, A. M., and A. E. Hay, 2001: Linear transitional ripple migration and wave orbital velocity skewness: Observations. J. Geophys. Res., 106 (C7) 1411314128.

    • Search Google Scholar
    • Export Citation
  • Davies, A. G., 1986: A model of oscillatory rough turbulent boundary layer flow. Estuarine Coastal Shelf Sci., 23 , 353374.

  • Dingler, J. R., and D. L. Inman, 1976: Wave-formed ripples in nearshore sands. Proc. 15th Int. Coast. Eng. Conf., Vol. 2, Honolulu, HI, ASCE, 2109–2126.

    • Search Google Scholar
    • Export Citation
  • Foster, D. L., 1996: Dynamics of the nearshore wave bottom boundary layer. Ph.D. thesis, Oregon State University, 114 pp.

  • Fredsoe, J., and R. Deigaard, 1992: Mechanics of Coastal Sediment Transport. World Scientific, 369 pp.

  • Grant, W. D., 1977: Bottom friction factor under waves in the presence of a weak current: Its relationship to coastal sediment transport. Sc.D. thesis, Massachussets Institute of Technology, Cambridge, MA, 275 pp.

    • Search Google Scholar
    • Export Citation
  • Grant, W. D., and O. S. Madsen, 1979: Combined wave and current interaction with a rough bottom. J. Geophys. Res., 84 , 17971808.

  • Grant, W. D., and O. S. Madsen, 1986: The continental shelf bottom boundary layer. Annu. Rev. Fluid Mech., 18 , 265305.

  • Guza, R. T., and E. B. Thornton, 1980: Local and shoaled comparisons of sea surface elevations, pressures, and velocities. J. Geophys. Res., 85 , 15241530.

    • Search Google Scholar
    • Export Citation
  • Hay, A. E., and D. Wilson, 1994: Rotary sidescan images of nearshore bedform evolution during a storm. Mar. Geol., 119 , 5765.

  • Herbers, T. H. C., R. L. Lowe, and R. T. Guza, 1992: Field observations of orbital velocities and pressure in weakly nonlinear surface gravity waves. J. Fluid Mech., 245 , 413435.

    • Search Google Scholar
    • Export Citation
  • Jensen, B. L., 1989: Experimental investigation of turbulent oscillatory boundary layers. IHHE Series Paper 45, Technical University of Denmark, 157 pp.

    • Search Google Scholar
    • Export Citation
  • Jensen, B. L., B. L. Sumer, and J. Fredsoe, 1989: Turbulent oscillatory boundary layers at high Reynolds numbers. J. Fluid Mech., 116 , 265298.

    • Search Google Scholar
    • Export Citation
  • Johns, B., 1969: On the mass transport induced by oscillatory flow in a turbulent boundary layer. J. Fluid. Mech., 43 , 177185.

  • Jonsson, I. G., 1966: Wave boundary layers and friction factors. Proc. 10th Int. Conf. on Coastal Engineering, Tokyo, Japan, ASCE, 127–148.

    • Search Google Scholar
    • Export Citation
  • Jonsson, I. G., and N. A. Carlsen, 1976: Experimental and theoretical investigations in an oscillatory turbulence boundary layer. J. Hydraul. Res., 14 , 4560.

    • Search Google Scholar
    • Export Citation
  • Kajiura, K., 1968: A model of the bottom boundary layer in water waves. Bulletin Earthquake Res. Inst., 46 , 75123.

  • Lavelle, J. W., and H. O. Mofjeld, 1983: Effects of time-varying viscosity on oscillatory turbulent channel flow. J. Geophys. Res., 88 (C12) 76077616.

    • Search Google Scholar
    • Export Citation
  • Madsen, O. S., 1994: Spectral wave-current bottom boundary layer flows. Proc. 24th Int. Conf. on Coastal Engineering, Vol. 1, Kobe, Japan, ASCE, 384–398.

    • Search Google Scholar
    • Export Citation
  • Madsen, O. S., and P. N. Wikramanayake, 1991: Simple model for turbulent wave-current bottom boundary layer flow. Contract Rep. DRP-91-1, U.S. Army Corps of Engineers, Coastal Engineering Research Center, Vicksburg, MS, 150 pp.

    • Search Google Scholar
    • Export Citation
  • Madsen, O. S., P. P. Mathiesen, and M. M. Rosengaus, 1990: Movable bed friction factors for spectral waves. Proc. 22d Int. Conf. on Coastal Engineering, Delft, Netherlands, ASCE, 420–429.

    • Search Google Scholar
    • Export Citation
  • Mathisen, P. P., and O. S. Madsen, 1999: Waves and currents over a fixed rippled bed. 3. Bottom and apparent roughness for spectral waves and currents. J. Geophys. Res., 104 (C8) 1844718461.

    • Search Google Scholar
    • Export Citation
  • Myrhaug, D., 1982: On a theoretical model of rough turbulent wave boundary layers. Ocean Eng., 9 , 547565.

  • Ngusaru, A. S., and A. E. Hay, 2003: Cross-shore migration of lunate megaripples during Duck94. J. Geophys. Res., in press.

  • Nielsen, P., 1984: On the structure of oscillatory boundary layers. Coastal Eng., 9 , 261276.

  • Nielsen, P., 1992: Coastal Bottom Boundary Layers and Sediment Transport. World Scientific, 324 pp.

  • Sleath, J. F. A., 1987: Turbulent oscillatory flow over rough beds. J. Fluid Mech., 182 , 369409.

  • Sleath, J. F. A., 1990: Seabed boundary layers. The Sea, B. LeMehaute and D. M. Hanes, Eds., Ocean Engineering Science, Vol. 9, John Wiley and Sons, 693–727.

    • Search Google Scholar
    • Export Citation
  • Smith, J. D., 1977: Modelling of sediment transport on continental shelves. The Sea, E. D. Goldberg et al., Eds., Marine Modeling, Vol. 6, John Wiley and Sons, 539–577.

    • Search Google Scholar
    • Export Citation
  • Smyth, C., and A. E. Hay, 2002: Wave friction factors in nearshore sands. J. Phys. Oceanogr., 32 , 34903498.

  • Smyth, C., A. E. Hay, and L. Zedel, 2002: Coherent Doppler profiler measurements of near-bed suspended sediment fluxes and the influence of bed forms. J. Geophys. Res., 107 .3105, doi:10.1029/2000JC000760.

    • Search Google Scholar
    • Export Citation
  • Tolman, H. L., 1994: Wind waves and moveable-bed bottom friction. J. Phys. Oceanogr., 24 , 9941009.

  • Townsend, A. A., 1972: Flow in a deep turbulent boundary layer over a surface distorted by water waves. J. Fluid Mech., 55 , 719735.

  • Trowbridge, J. H., and O. S. Modsen, 1984: Turbulent wave boundary layers. I. Model formulation and first-order solution. J. Geophys. Res., 89 (C5) 79877997.

    • Search Google Scholar
    • Export Citation
  • Trowbridge, J. H., and Y. C. Agrawal, 1995: Glimpses of a wave boundary layer. J. Geophys. Res., 100 (C10) 2072920743.

  • van Doorn, T., 1982: Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Delft Hydraulics Laboratory Rep. M1562-1b.

    • Search Google Scholar
    • Export Citation
  • Wilson, K. C., 1989: Friction of wave-induced sheet flow. Coastal Eng., 12 , 371379.

  • Young, I. R., and R. M. Gorman, 1995: Measurements of the evolution of ocean wave spectra due to bottom friction. J. Geophys. Res., 100 (C6) 1098711004.

    • Search Google Scholar
    • Export Citation
  • Zedel, L., and A. E. Hay, 1999: A coherent Doppler profiler for high resolution particle velocimetry in the ocean: Laboratory measurements of turbulence and particle flux. J. Atmos. Oceanic Technol., 16 , 11021117.

    • Search Google Scholar
    • Export Citation
  • Zedel, L., and A. E. Hay, 2002: A three component bistatic coherent Doppler velocity profiler: Error sensitivity and system accuracy. IEEE J. Oceanic Eng., 27 , 717725.

    • Search Google Scholar
    • Export Citation
  • Zou, Q-P., 1995: A viscoelastic model for turbulent flow over an undulating topography and progressive waves. Ph.D. thesis, Scripps Institution of Oceanography, 91 pp.

    • Search Google Scholar
    • Export Citation
  • Zou, Q-P., 1998: A viscoelastic model for turbulent flow over an undulating topography. J. Fluid Mech., 355 , 81112.

  • Zou, Q-P., 2002: An analytical model of wave bottom boundary layers incorporating turbulent relaxation and diffusion effects. J. Phys. Oceanogr., 32 , 24412456.

    • Search Google Scholar
    • Export Citation
  • Zou, Q-P., and A. E. Hay, 2001: Velocity profiles above and within the wave bottom boundary layer over a sloping bottom. Proc. 27th Int. Coastal Engineering Conf., Sydney, Australia, ASCE, 94–107.

    • Search Google Scholar
    • Export Citation
  • Zou, Q-P., A. E. Hay, and A. J. Bowen, 2003: The vertical structure of surface gravity waves propagating over a sloping sea bed: Theory and field measurements. J. Geophys. Res., in press.

    • Search Google Scholar
    • Export Citation
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The Vertical Structure of the Wave Bottom Boundary Layer over a Sloping Bed: Theory and Field Measurements

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  • 1 Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada
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Abstract

Theoretical solutions for the wave bottom boundary layer (WBL) over a sloping bed are compared with field measurements in the nearshore zone. The WBL theory is constructed using both viscoelastic–diffusion and conventional eddy viscosity turbulent closure models. The velocity solutions are then matched with those of the interior flow, given by Chu and Mei potential theory for surface gravity waves over a sloping bottom. The field measurements were obtained with a coherent Doppler profiler over a 2° bed slope. Results are presented for both flat and rippled bed conditions, the latter being characterized by low steepness, linear transition ripples. Close to the bed, the observed velocity profiles change rapidly in amplitude and phase relative to potential flow theory, indicating the presence of a wave boundary layer with a thickness of 3–6 cm. The observed velocity and shear stress profiles are in good agreement with the theory. The sloping bottom has significant effects on the vertical velocity, but not on the horizontal velocity and shear stress. Bottom roughness and friction velocity are estimated from optimizing the model–data comparisons. The friction velocities and wave friction factors are found to be consistent with values obtained from the momentum integral method and from the nearbed turbulence intensity, and with Tolman's semiempirical formulation.

Corresponding author address: Dr. Qingping Zou, Department of Oceanography, Dalhousie University, Halifax, NS B3H 4J1, Canada. Email: qingping.zou@dal.ca

Abstract

Theoretical solutions for the wave bottom boundary layer (WBL) over a sloping bed are compared with field measurements in the nearshore zone. The WBL theory is constructed using both viscoelastic–diffusion and conventional eddy viscosity turbulent closure models. The velocity solutions are then matched with those of the interior flow, given by Chu and Mei potential theory for surface gravity waves over a sloping bottom. The field measurements were obtained with a coherent Doppler profiler over a 2° bed slope. Results are presented for both flat and rippled bed conditions, the latter being characterized by low steepness, linear transition ripples. Close to the bed, the observed velocity profiles change rapidly in amplitude and phase relative to potential flow theory, indicating the presence of a wave boundary layer with a thickness of 3–6 cm. The observed velocity and shear stress profiles are in good agreement with the theory. The sloping bottom has significant effects on the vertical velocity, but not on the horizontal velocity and shear stress. Bottom roughness and friction velocity are estimated from optimizing the model–data comparisons. The friction velocities and wave friction factors are found to be consistent with values obtained from the momentum integral method and from the nearbed turbulence intensity, and with Tolman's semiempirical formulation.

Corresponding author address: Dr. Qingping Zou, Department of Oceanography, Dalhousie University, Halifax, NS B3H 4J1, Canada. Email: qingping.zou@dal.ca

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