Higher-harmonic wave forces and ringing of vertical cylinders

Abstract

A pronounced secondary load cycle may occur in the force on a vertical circular cylinder exposed to moderately steep transient water wave events. The timing is about one quarter wave period later than the main peak of the force. The load cycle contributes locally to a pronounced higher harmonic wave force. Experimental observations of the phenomenon in small and moderate scale are characterized in terms of the local wave slope of the incoming individual waves, kη m ( k the wavenumber, η m the local maximal wave elevation), and the wavenumber relative to the cylinder radius, kR ( R the cylinder radius). The height of the secondary load cycle is typically up to about 0.1–0.15 times the peak to peak force on the cylinder during a wave event. In the small scale experiments the secondary load cycle occurs when 0.3< kη m and kR<0.33 (registrations are made for 0.1< kR). In the experiments of moderate scale the secondary load cycle occurs for a smaller wave slope than observed in the small scale experiments. This is true in the long wave regime. The secondary load cycle is then observed for a nondimensional wavenumber kR in the range 0.1–0.33 and a Froude number (Fr=ωη m / gD ; ω, the wave frequency; g, the acceleration of gravity; D=2 R) exceeding about 0.4. The important difference between the experiments in moderate and small scale is explained by the effect of flow separation. This effect is weaker in moderate than in small scale. Registrations of pronounced resonant high-frequency ‘ringing’ motions of vertical cylinders and models of offshore structures of moderate scale are compared with the force recordings. Large motion occurs for the same wave parameters as for the pronounced secondary load cycle in the moderate scale experiments. The additional load cycle contributes to a build-up of resonant body responses if the resonance frequency is close to about four times the wave frequency.