Random Wave Forces on a Vertical Cylinder in the Free Surface Zone at High Reynolds Numbers

We consider the steady flow near a free surface at intermediate to high Reynolds numbers, both experimentally and theoretically. In our experiment, an axisymmetric capillary meniscus is suspended from a cylindrical tube, held slightly above a horizontal water surface. A flow of dyed water is released through the tube into the reservoir, and flow lines are thus recorded. At low Reynolds numbers, flow lines follow the free surface, and injected water spreads horizontally inside the container. Increasing the Reynolds number, the injected fluid penetrates to a certain distance into the bath, but ultimately follows the free surface. Above a critical Reynolds number of approximately 60, the flow separates from the free surface in the meniscus region and a jet projects vertically into the bath. We find no indication that the flow reattaches at higher Reynolds numbers, nor are our findings sensitive to surface contamination. We show theoretically and confirm experimentally that the separating streamline forms a right angle with the free surface.

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Wave Forces Acting on Rough Circular Cylinders at High Reynolds Numbers

10.4043/5372-ms ◽

1987 ◽

Cited By ~ 1

Author(s):

Y. Kasahara ◽

W. Koterayama ◽

K. Shimazaki

Keyword(s):

Reynolds Numbers ◽

Circular Cylinders ◽

Wave Forces ◽

High Reynolds Numbers ◽

High Reynolds

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Vortex evolution in non-axisymmetric impulsive spin-up from rest

Journal of Fluid Mechanics ◽

10.1017/s0022112096007859 ◽

1996 ◽

Vol 324 ◽

pp. 109-134 ◽

Cited By ~ 4

Author(s):

D. M. Henderson ◽

J. M. Lopez ◽

D. L. Stewart

Keyword(s):

Free Surface ◽

Boundary Layers ◽

Stokes Equations ◽

Reynolds Numbers ◽

Evolutionary Pattern ◽

Aspect Ratios ◽

High Reynolds Numbers ◽

Flow Evolution ◽

High Reynolds ◽

Vortex Merger

The flow evolution of water in a completely filled rectangular container, impulsively rotated from rest to a steady angular speed, is investigated experimentally and numerically. The pathlines of the fluid from rest to solid-body rotation primarily follow one of two possible configurations that have been described previously in the literature. The first, consisting of two cyclones that form following the separation and roll-up of the sidewall boundary layers and an anticyclone that forms subsequently, results in a pattern on the path to spin-up of cyclonic–anticyclonic–cyclonic vorticity. In the second configuration the cyclones migrate into the interior of the container and merge, resulting in a pattern on the path to spin-up of anticyclonic–cyclonic–anticyclonic vorticity. The experiments provide a parameterization of the possible evolutionary configurations as a function of horizontal and vertical aspect ratios and Reynolds numbers. Critical Reynolds numbers for vortex merger are determined experimentally. Evolutionary configurations in addition to the primary two are observed; in particular symmetry breaking occurs at high Reynolds numbers causing complicated patterns of flow evolution. For some flow conditions at high Reynolds numbers, more than one evolutionary pattern is observed for the same external parameters. The experiments are conducted with a rigid lid showing that a free surface is not required for vortex merger. Numerical integrations of the two-dimensional Navier–Stokes equations (a situation corresponding to the limiting case of a container of infinite depth, where there are no effects from the top and bottom and all flow is horizontal) reproduce qualitatively many of the features of the experimental observations, in particular the merger events. The numerical results show that neither vertical flow due to Ekman boundary layers at the top and bottom nor a free surface are necessary for the observed vortex merger.

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