Interaction of a deep-water wave with a vertical cylinder is characterized using techniques of high-image-density particle image velocimetry, in conjunction with measurement of the transverse and in-line loading coefficients. Phase-locked patterns of locally two-dimensional vortex formation are attainable only for sufficiently high values of the Keulegan–Carpenter number KC, e.g. $\hbox{\it KC} \,{\geq}\, 12$. Even in these cases, such patterns are interrupted by non-phase-locked patterns that, nevertheless, show basic forms, including mode inversion or switching of the initially formed vortex from the cylinder, along with patterns of symmetrical vortex formation, all represented by patterns of instantaneous vorticity.
Three-dimensionality of the flow structure along the span of the cylinder shows, at relatively low KC, patterns of transverse velocity $v$ and streamwise vorticity $\omega _{x}$ that have well-defined spanwise spacing. This spacing decreases in a continuous fashion with depth beneath the free surface, and is in accord with the decrease of local KC with depth, i.e. decrease of the diameter of the local particle trajectory. Such three-dimensional patterns are, however, not phase repetitive over a large number of wave cycles.
At sufficiently high values of KC, it is possible to identify basic classes of three-dimensional patterns. When regions of transverse velocity show like sign over a significant spanwise extent of the cylinder, the transverse loading coefficient is relatively large. As the number of zero crossings between the positive and negative regions of $v$ increases, the transverse loading coefficient decreases accordingly. Generally speaking, at these higher values of KC, patterns of streamwise vorticity are much less ordered, and of smaller scale; they are embedded within larger-scale well-defined patterns of the transverse velocity $v$ along the span.
Taken together, the patterns of locally two-dimensional (sectional) structure and the three-dimensional structure along the span indicate a criterion for locally phase-locked quasi-two-dimensional vortex formation: it occurs when the pattern of transverse velocity is of the same sign over a significant spanwise distance along the span of the cylinder.