Double structures of steady streaming in the oscillatory viscous flow over a wavy wall

Abstract

The steady streaming induced by oscillatory viscous flow of small amplitudes over a wavy wall has been analysed, and the computed flow patterns have been found to agree well with the flow patterns visualized experimentally in a tube. When the first parameter, α/δ (the ratio of the wavelength of the wavy wall to the thickness of Stokes layer), becomes larger than about 26, the streaming has a double structure consisting of regions of upper and lower pairs of recirculations. As the second parameter, L/δ (the ratio of the amplitude of the wavy wall to the thickness of Stokes layer), is increased, the upper pair of recirculations squeezes in a gap between the lower recirculations above the troughs of the wall. A similar double structure of steady streamings was also observed above ripple marks formed under oscillatory viscous flow. A bearing is suggested of this phenomenon on the determination of stationary profiles of ripple marks.

Numerical simulation of oscillatory flows over a rippled bed by immersed boundary method

“…The numerical results are found to be in qualitative agreement with the experimental observations. It should be noted, however, that the experimental results shown in Kaneko and Honji [ 2 ] were based on Lagrangian average while the numerical results in this work are for the Eulerian average. Fig.…”

“…2 ( b ) and 3 ( b ) of the paper by Kaneko and Honji [ 2 ] are considered for a test. In their experiments, a sinusoidal wave bed was used.…”

“…In contrast, two regions of recirculation were observed if the wavelength is much greater than the Stokes layer thickness. Lyne's theory was extended by Kaneko and Honji [ 2 ] and the steady streaming structures were obtained in their both experimental and numerical studies. They found that the double structure streaming appeared when the ratio of the ripple wavelength to the Stokes layer thickness reaches the value of 26.…”

“…In this work, a systematic study is carried out on the oscillatory flows over a steeply rippled bed, with the aim of better understanding the flow hydrodynamics near the natural ripples under the sea waves. An accurate simulation of vortices generation as a result of flow separation at the ripple bed is obtained, and the criterion for separating the single and double structure streaming proposed by Kaneko and Honji [ 2 ] is discussed. The numerical results, including the steady streaming in particular, may be useful to improve the understanding of the sediment transport and the evolution of seabed.…”

Modeling of Developed Meanders of an Alluvial Channel

“…The non-linear viscous oscillatory flow over a wavy wall of small amplitudes is determined. The solution holds for arbitrary values of a*/L* (a* is the amplitude of fluid oscillations near the wall and L* is the wavelength of wall perturbation); previous work by Lyne (1971) and Kaneko and Honji (1979) are thus extended. An independent analysis for small values of a*/L* is performed by Vittori (1989), and the relevance of the results to the study of ripples formation at the bottom of sea waves is discussed.…”