Wave interaction with a vertical cylinder: spanwise flow patterns and loading

Abstract

A vertical cylinder is located in a free-surface wave, and a two-camera version of high-image-density particle image velocimetry is employed to characterize the spanwise modes of the flow structure in terms of instantaneous velocity and vorticity. These modes are classified according to organized patterns of velocity in the near wake, and are further interpreted in terms of distinctive arrangements of streamwise vorticity concentrations.At low Keulegan–Carpenter number, which corresponds to small wave height, locally two-dimensional vortices having small scale and circulation tend to form as a symmetrical pair and remain attached, or in close proximity, to the surface of the cylinder. Along the span of the cylinder, the near wake shows either a sinuous S or a unidirectional U mode. The spanwise wavelength λ of the S modes, relative to the cylinder diameter D, lies in the range 1 [lsim ] λ/D [lsim ] 4:5. These values of λ/D represent the spacing between extrema of patterns of cross flow velocity, as well as between clusters of streamwise vorticity of like sign. As the free surface is approached, the value of λ/D scales with the ratio of the minor to major axes of the elliptical particle trajectory of the wave.At moderate values of the Keulegan–Carpenter number, locally two-dimensional vortices having large scale and circulation are shed from the cylinder in an asymmetric arrangement. The corresponding spanwise mode represents the phase variation of this shedding along the span of the cylinder. These sinuous S modes involve large-scale distortions of patterns of both cross flow velocity and streamwise vorticity, which have wavelengths in the range 10 [lsim ] λ/D [lsim ] 110, in contrast to the spacing between individual concentrations of vorticity, which is 1:5D to 4D. Remarkably, it is possible to attain a unidirectional U mode, whereby the phase of the locally two-dimensional vortex shedding is preserved along the entire extent of the cylinder. Signatures of the moments due to the transverse and in-line forces on the cylinder were acquired simultaneously with the patterns of instantaneous velocity and vorticity. Severe modulations of the moment due to the transverse force are associated with spontaneous transformations between basic forms of the sinuous S and unidirectional U modes. The overall form of the signature of the moment due to the in-line force is, however, not generally affected by the spontaneous transformation between modes, but distortion of its peaks is evident.