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Calculations of laminar viscous flow over a moving wavy surface

  • E. A. Caponi (a1), B. Fornberg (a1) (a2), D. D. Knight (a1) (a3), J. W. McLean (a1), P. G. Saffman (a1) (a2) and H. C. Yuen (a1)...
Abstract

The steady, laminar, incompressible flow over a periodic wavy surface with a prescribed surface-velocity distribution is found from the solution (via Newton's method) of the two-dimensional Navier–Stokes equations. Validation runs have shown excellent agreement with known analytical (Benjamin 1959) and analytico-numerical (Bordner 1978) solutions for small-amplitude wavy surfaces: For steeper waves, significant changes are observed in the computed surface-pressure distribution (and consequently in the nature of the momentum flux across the interface) when a surface orbital velocity distribution, of the type found in water waves, is included,

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References
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Banner, M. L. & Phillips, O. M. 1974 On the incipient breaking of small scale waves. J. Fluid Mech. 65, 647656.
Benjamin, T. B. 1959 Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161205.
Benney, D. J. & Bergeron, R. F. 1968 A new class of nonlinear waves in parallel flows. Stud. Appl. Math 48, 181204.
Bordner, G. L. 1978 Nonlinear analysis of laminar boundary layer flow over a periodic wavy surface. Phys. Fluids 21, 14711474.
Caponi, E. A. 1979 Laminar air flow over prescribed water waves. TRW Tech. Rep. no. 9994–6447-RU-00.
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185204.
Wu, J. 1975 Wind-induced drift currents. J. Fluid Mech. 68, 4970.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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