Wave Kinematics Models For Calculation Of Wave Loads On Truss Structures
Authors: Gudmestad O.T. , Karunakaran Daniel 
Published: October 2008

ABSTRACT
Wave kinematics models for calculation of wave velocity and acceleration and subsequently the loads on truss structures are discussed in this paper with particular emphasis on the use of the Wheeler method to calculate irregular wave kinematics. Necessary changes for very steep waves will be suggested. References are also made to use of 'apparent regular waves" simulating measured waves traces in irregular seas.

INTRODUCTION
The design of safe truss structures is of particular importance for the offshore industry and the load model should be most up to date.
In accordance with the recommendations of the API RP2A's 20th edition's1,2 the recipe for calculation of environmental loads on truss structures has been changed compared to previous issues of API RP2A. This has been done to estimate the loads on such structures in the most appropriate manner. The changes consist of applying higher and more appropriate drag factors and the most appropriate wave kinematics model while including currents, to calculate the environmental load.
Results from previous investigations show that the Wheeler method can be used to calculate wave velocities in irregular seas3. For very steep waves later results, however, have shown that the Wheeler velocities must be updated4.
The use of "apparent regular waves" to calculate kinematics in irregular seas are shown to lead to misleading results for certain cases5,6 and should therefore be applied only with particular care.

THE API PROCEDURE FOR ESTIMATING WAVE KINEMATICS
The API procedure (recipe) for calculation of wave forces on slender offshore structures is described in API-RP2A1,2,7.
For static regular wave analysis, the procedure for calculation of wave plus current forces is shown in Fig. 1 (Fig. 1 C.3.2-1 of Ref (l))(Available in full paper). Relating to wave kinematics, the following applies:The two dimensional wave kinematics are determined from an appropriate wave theory for the specified wave height, storm water depth and apparent period adjusted for the Doppler effect of the current on the wave.The horizontal components of wave-induced particle velocities and accelerations are reduced by the wave kinematics factor, which accounts primarily for wave directional spreading.The local current profile (determined by multiplying the specified current profile by the current blockage factor)is combined vectorially with the wave kinematics to determine incident fluid velocities and accelerations (wave plus current kinematics) for use in Morison's equation.
The two dimensional wave kinematics can be Calculated1,2,7 using the appropriate order of Stream Function wave theory. In many cases Stokes V wave theory will produce acceptable accuracy. Extended Velocity Potential8 and Chappelear, may1,7 be used if an appropriate order of solution is selected.
Regarding selection of most appropriate regular wave theory, it should be noted that it is important to distinguish between a criterion of no mean fluid velocity (cc= O) at any point in the fluid, and a criterion of zero mass transport (cs = O)in the fluid9,10.cc is given ascc=c-û
where the mean fluid speed is ii and c is the speed at which the wave travels. c. is given ascs=c-Q/d
where Q is the volume flow rate underneath the waves in the negative x-direction.