Hybrid Method Of Computing Wave Loading
Authors: Dean Robert G. 
Published: October 2008

ABSTRACT
This paper presents the development of a "hybrid" method for computing design wave force and moment loading on offshore structures; the method is illustrated by several-examples.
The "hybrid" character of the method is due to the combination of linear and nonlinear wave theories to determine wave loading which incorporates the most significant features of a realistic sea system in nature, 1.e., the non1inearities and the directional spectrum. Wave loading due to nonlinear waves with energy present over a continuum of frequencies and directions is represented as the product of a nonlinear wave force and a linearized force transfer coefficient, the latter representing the effect of the directional spectrum. Loading on a single or multiple-pile platform is first calculated from one of a number of nonlinear theories which are valid-for a wave of single fundamental frequency propagating in a single direction. The force transfer function is based on linear wave theory and, in principle, can represent any distribution of the wave energy over frequency and direction.
Examples presented include loading on single and multiple pile structures for idealized directional spectra. For the case of a platform supported by four piling on a square array of 60 ft dimensions in plan and spectra for which the princip1e directions associated with each frequency differ substantially, it is found that the linearized force transfer function can result in significantly lower forces (77% of the forces due to unidirectional waves). This case of highly directional waves may be realistic near the center of hurricanes where considerable variability in wind direction occurs over fairly small areas.

INTRODUCTION
The problem of computing design wave forces on single or multiple piling 11:1 complicated due to the nonlinearity of the waves and the complexity of the random and directional sea surface. Two essentially different approaches have developed in an attempt to establish realistic design wave loading. One approach is to attempt to represent the nonlinearities of the motion for a single fundamental wave characterized by a period and its higher harmonics. A number of such theories have been developed for waves without currents and Dalrymple has extended the stream function theory to include linear and bilinear shear currents. Although more data for wave theory evaluation are always welcome, it has been demonstrated that nonlinear theories are now available which satisfy fairly accurately the mathematical formulation. This approach accounts for the nonlinearities but avoids the random and directional character of the sea surface. The second approach is to exploit the utility of superposition of linear systems by considering the wave system to be composed of an infinite number of random linear waves which, in the general case, can be characterized by a directional spectrum; that is the energy is distributed over a continuum of frequencies and also at each frequency, spread over a range of directions. It is recognized that in design, elements of randomness, directionality and nonlinearity can all be significant.