Comparative study on response of jacket platforms under regular waves using Airy’s and Stokes’ fifth-order wave theories

Despite the random nature of ocean waves, to provide engineering solutions, regular wave theories are commonly used to estimate wave forces from the Morison equation in offshore structural analysis. These wave theories can be defined by three basic parameters, namely water depth, wave height and wave period. The applicability of a particular wave theory to a given set of wave characteristics and water depth is governed chiefly by the ratios of water depth and wave height to the wavelength. Airy’s linear wave theory, on account of its simplicity, is a popular choice, especially for preliminary calculations and for providing insight into the basic characteristics of wave-induced water motion. It is, however, applicable to small wave heights and in many conditions the linear theory is incapable of providing a satisfactory assessment of the water particle kinematics. A nonlinear theory is then required, and Stokes’ fifth order wave theory, based on the expansion of the wave solution in series form, provides a more accurate representation of the free-surface and is generally used for high waves in deep water. In this paper, a comparative study is conducted between the wave forces obtained from Morison equation utilising Airy’s wave theory and Stokes’ fifth order wave theory, acting at different levels of a jacket platform. Two sets of water depth, wave height and wave period are selected so that they satisfy the region of applicability of Airy’s wave theory and Stokes’ fifth order wave theory respectively. Two example four-legged jacket platforms are considered. It is found that for design purposes, in most cases the wave forces and structural responses from Airy’s wave theory are more conservative as compared to those from Stokes’ fifth order wave theory, though the converse is obtained in case of deep water conditions near the seabed. Overall, in deep water, high wave conditions, apart from Stokes’ fifth order wave theory, Airy’s wave theory may be used for preliminary estimations of wave forces and deck displacements, but in shallow water conditions, Stokes’ fifth order wave theory is entirely invalid.