Measurements of some non-linear features of waves propagating over a submerged horizontal cylinder with its axis parallel with the wave crests are compared with previous analytical and numerical predictions of the potential flow. Good agreement is found in most respects with second order results for the transmitted waves and the set down in the mean surface level over the cylinder, but a non-linear contribution to the phase lag of the first harmonic wave component is attributed to the effect of circulation around thecylinder induced by viscosity. The limiting conditions at which waves first break over the cylinder are plotted over a wide range of conditions.
The flow around a horizontal cylinder beneath waves in deep water, where the wave crests are parallel with the cylinder's axis, has attracted considerable attention and revealed some unexpectedly rich physics. According to the linear potential flow problem, solved by Ogilvie (1963) following earlier work by Dean (1948) and Ursell (1950), waves propagate over the cylinder without any reflection, but they undergo a phase shift. Higher order analytical or numerical solutions of the potential flow problem have since identified the most important features of the non-linear potential flow problem. McIver & McIver (1990) showed that there is no reflection at the fundamental wave frequency also at second order, and Palm (1991) proved that there is no reflection in the leading order component at any harmonic frequency. These conclusions are supported by the numerical computations of Liu, Dommermuth & Yue (1992), which also provide predictions for the attenuation of the transmitted wave at the fundamental frequency, and, like Vada (1987), Wu (1991), and Riley & Yah (1996), for the amplitude of the second order transmitted wave at the second harmonic. Riley & Yan also computed the set-down in the mean water surface over the cylinder.
