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Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 1. Non-separated flows

1977; Cambridge University Press; Volume: 82; Issue: 1 Linguagem: Inglês

10.1017/s0022112077000524

1469-7645

Daniel P. Zilker, Gerald William Cook, Thomas J. Hanratty,

Wind and Air Flow Studies

Measurements of the shear-stress variation along and the velocity profiles above a solid wavy wall bounding a turbulent flow are presented for waves with height-to-length ratios of 2 a /λ = 0·0312 and 0·05. These are compared with previous measurements of the wall shear stress reported by Thorsness (1975) and by Morrisroe (1970) for 2 a /λ = 0·012. The investigation covered a range of conditions from those for which a linear behaviour is observed to those for which a separated flow is just being initiated. Pressure measurements indicate a linear response in that the spatial variation is described quite well by a single harmonic with a wavelength equal to that of the surface. However, the variation of τ w for waves with 2 a /λ = 0·0312 and 0·05 can be more rapid on the leeward side of the wave. The degree of departure from a sinusoidal variation increases with increasing wave height and fluid velocity and, from the results reported in this paper, it is suggested that nonlinear behaviour will become evident when au */ v [ges ] 27. Many aspects of the flow for all three waves are described by a solution of the linear momentum equations previously presented by Thorsness (1975) and by Thorsness & Hanratty (1977). These include the phase and amplitude of the pressure profile and the first harmonic of the shear-stress profile and the velocity field outside the viscous wall region. These results suggest that up to separation the flow is approximated quite well by linear theory. Nonlinearities affect the flow only in a region very close to the wave surface and are manifested by the appearance of higher harmonics in the variation of τ w .