The linearized, two-dimensional flow of an incompressible fully turbulent fluid over a sinusoidal boundary is solved using the method of matched asymptotic expansions in the limit of vanishing skin-friction.
A phenomenological turbulence model due to Saffman (1970, 1974) is utilized to incorporate the effects of the wavy boundary on the turbulence structure.
Arbitrary lowest-order wave speed is allowed in order to consider both the stationary wavy wall, and the water wave moving with arbitrary positive or negative velocity.
Good agreement is found with measured tangential velocity profiles and surface normal stress coefficients. The phase shift of the surface normal stress exhibits correct qualitative behavior with both positive and negative wave speeds, although predicted values are low.
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Benjamin, T. B.: 1959, ‘Shearing Flow Over a Wavy Boundary’,J. Fluid Mech. 6, 161–205.
Bradshaw, P.: 1973, ‘Effects of Streamline Curvature on Turbulent Flow’,Agardograph No. 169, Advisory Group for Aerospace Research and Development, North Atlantic Treaty Organization.
Bradshaw, P., Ferris, D. H., and Atwell, N. P.: 1967, ‘Calculation of Boundary-Layer Development Using the Turbulent Energy Equation’,J. Fluid Mech. 28, 593–616.
Coles, D. E. and Hirst, E. A.: 1968,Proceedings of the 1968 AFOSR-IFP-Stanford Conference on Computation of Turbulent Boundary Layers, Volume 2, Stanford University.
Davis, R. E.: 1972, ‘On Prediction of the Turbulent Flow Over a Wavy Boundary’,J. Fluid Mech. 52, 287–306.
Dobson, F. W.: 1969, ‘Observation of Normal Pressure on Wind Generated Sea Waves’, Ph.D. Thesis, University of British Columbia.
Kendall, J. M.: 1970, ‘The Turbulent Boundary Layer Over a Wall with Progressive Surface Waves’,J. Fluid Mech. 41, 259–281.
Kinsman, B.: 1965,Wind Waves, Prentice-Hall, Inc., p. 11.
Knight, D.: 1974, ‘An Analytic Investigation of Turbulent Flow Over a Wavy Boundary’, Ph.D. Thesis, California Institute of Technology.
Lamb, H.: 1945,Hydrodynamics, 6th edition, Dover, Sections 268, 348, 349.
Manton, M. J.: 1972, ‘On the Generation of Sea Waves by a Turbulent Wind’,Boundary-Layer Meterol. 2, 348–364.
Miles, J. W.:1957, ‘On the Generation of Surface Waves by Shear Flows’,J. Fluid Mech. 3, 185–204.
Miles, J. W.: 1959a, ‘On the Generation of Surface Waves by Shear Flows’, Part 2,J. Fluid Mech. 6, 568–582.
Miles, J. W.: 1959b, ‘On the Generation of Surface Waves by Shear Flows’, Part 3: Kelvin-Helmholtz Instability,J. Fluid Mech. 6, 583–598.
Miles, J. W.: 1967, ‘On the Generation of Surface Waves by Shear Flows’, Part 5,J. Fluid Mech. 30, 163–175.
Saffman, P. G.: 1970, ‘A Model for Inhomogeneous Turbulent Flow’,Proc. Roy. Soc. London A317, 417–433.
Saffman, P. G.: 1974, ‘Model Equations for Turbulent Shear Flow’,Stud. Applied Math. 53, 17–34.
Saffman, P. G.: 1976, ‘Development of a Complete Model for the Calculation of Turbulent Shear Flows’, presentation atTurbulence and Dynnmical Systems, Meeting, Duke University, April, 1976.
Saffman, P. G. and Wilcox, D. C.: 1974, ‘Turbulence-Model Predictions for Turbulent Boundary Layers’,AIAA Journal 12, 541–546.
Shemdin, O. H. and Hsu, E. Y.: 1967, ‘Direct Measurement of Aerodynamic Pressure Above a Simple Progressive Gravity Wave’,J. Fluid Mech. 30, 403–416.
Sigal, A.: 1971, ‘An Experimental Investigation of the Turbulent Boundary Layer Over a Wavy Wall’, Ph.D. Thesis, California Institute of Technology, Pasadena, California.
Townsend, A. A.: 1972, ‘Flow in a Deep Turbulent Boundary Layer Over a Surface Distorted by Water Waves’,J. Fluid Mech. 55, 719–735.
Wilcox, D. C.: 1973, ‘Calculation of Turbulent Boundary Layer Shock Interaction’,AIAA Journal 11, 1592–1594.
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Knight, D. Turbulent flow over a wavy boundary. Boundary-Layer Meteorol 11, 205–222 (1977). https://doi.org/10.1007/BF02166805
- Asymptotic Expansion
- Turbulence Model
- Wave Speed
- Water Wave
- Tangential Velocity