This paper presents and analyses results of experiments in which a vertical surface-piercing cylinder was driven with a horizontal motion a cos ωt in water initially at rest. Using a novel system of 112 water surface elevation gauges that were monitored almost simultaneously at high frequency, measurements were made of the run-up on the cylinder over a wide range of conditions. According to linear theory, the run-up is of the form a cos ωt cos θ. Non-linear components at temporal and spatial frequencies up to the 3rd harmonic were identified in the measurements, and in some of these, the coefficient of the leading term in a polynomial expansion in the amplitude of motion could be computed with reasonable confidence. Very successful comparisons are made with conventional linear potential theory. Some features of the free surface motion that are normally associated with higher order solutions were also computed from the first-order potential, and in some respects they were in good agreement with the measurements.

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