Comparison of Wave Forces Computed by Linear and stream Function Methods
Authors: Hudspeth R.T. , Dalrymple R.A. , Dean R.G. 
Published: October 2008

ABSTRACT
Two previously-published deterministic methods which have been employed to compute the water particle kinematics required to predict hurricane-generated water wave forces on piles by the Morison equation are (1) the linear filter technique and (2) the stream function representation. -Exact comparisons between these previous studies have not been possible because the linear filter technique utilized continuous time data records of no periodic water waves while the stream function representation utilized only single waves from the continuous data records with water surface profiles which were assumed to be permanent, periodic forms traveling with a speed equal to the wave celerity. In order to compare these two methods, forty two single waves with we?ll defined (but asymmetric) crests and troughs were selected from the four continuous data files recorded during Hurricane Carla byway Force Project II. In addition, thirteen single waves recorded by Wave Force Project I were utilized in a phase averaged form for comparison by the two methods. Based on the same data sets, comparisons of the normalized mean square differences between measured and predicted forces computed using the previously published force coefficients indicate generally better results from the stream function method using Dean-Aagaard coefficients. Under certain conditions, results obtained using the linear filter technique may be improved when used with the Dean-Aagaard coefficients.

INTRODUCTION
The general problem of offshore design requires a capability for reasonably accurate prediction of expected maximum wave forces for the geographic area and storm duration of concern. The most appropriate method of wave force prediction may depend on the wave environment and compliance characteristics of the structure. For example, if the structure is relatively rigid and? the largest waves are swell, then a high-order nonlinear wave theory characterized by a single fundamental period combined with a static analysis of the structure may be the most appropriate analysis. However, if the site is located in an active generation area and/or if the structure is sufficiently compliant that the natural period lies within the range of wave excitation, then a linear random sea representation combined with spectral analysis methods may be more appropriate. Present capabilities do not include the realistic representation of nonlinear irregular seas; however, methods are available for the representation of hi8hly nonlinear waves of a single fundamental period (10), (11), (l2) and of linear seas characterized by a directional spectrum(7).
The initial research specifically related at wave forces on offshore structures was conducted by Morison, O'Brien, Johnson, and Schaaf(15). They represented the total wave force as the sum of a drag and an inertia component and provided some supporting laboratory data. The equation employed in calculating wave forces is frequently referred to as the "Morison" equation. Later efforts centered about the development of improved wave theories(9),(17), (21), (22) and the experimental determination of drag and inertia coefficients, CD and CM.
Extensions of the Stokes' wave theory to fifth order have been developed and tabulated by Skjelbreia and Hendrickson(16).