Application Regime of Wave Force Calculations

Wave force calculations have been so important in the design and analysis of the dynamic response of ocean structures. From engineer's point of view, it is desirable to have a quick justification of using an appropriate method in practical wave force calculations. In this paper, both the Morison equation and the wave diffraction theory are examined for the wave force calculations of a vertical circular cylinder. The application criteria for the methods are presented. In the Morison equation, a rather simple expression for the drag and inertia coefficients proposed by Clauss, Lehmann and Ostergaard (1992) is adopted. The flow velocity is expressed in terms of the Keulegon-Carpenter Number (K_c) as harmonic motion. The dimensionless expressions for the drag and the inertia forces are then used to determine whether the flow field is drag or inertia dominant. The results show that when the drag and inertia forces equal, the K_c is 12 for the Reynolds Number (Re) less than 10^-5, and the K_c 24 for Re greater than 10^-5. The depth function of the flow velocity is expressed as a correction coefficient to the Morison equation, and the effects to the wave force with K_c relationship can be studied. The results show that the depth effects tend to lead the flow field to be inertia dominant, and increase the Kc. Number for the division criterion of whether the flow is inertia or drag dominant. The wave diffraction theory to calculate the wave force on the vertical circular cylinder is also examined. From the linear theory, the wave force expression is recasted into the inertia term as shown in the Morison equation, and the equivalent inertia coefficient is defined. The analysis showed that for the dimensionless structure diameter (D/L) less than 0.18, the diffraction effect can be neglected. This result tends to be a correction to a criterion of 0.12 as presented by MacCamy and Fuchs (1954).