A Deterministic Method To Detect Wave Directions From Surface Elevations

Abstract

This research describes a new method called SWDD (Klopman, Witteveen+Bos, 2018b), which can obtain information on wave propagation directions from the surface elevations at a set of positions. The primary intention of the method is to separate multiple incoming wave components, i.e. wave heights, phases and directions. The goal is to obtain the incoming wave conditions, that can among others be used in the design of (coastal) structures and assessment of moored ship response.

The novelty of this method is that a large number of incoming wave directions is prescribed, equally distributed around a circle. For each of these many incoming wave conditions, the wave amplitude and phase are the unknowns (while the directions are known). The main advantage is that this makes the problem linear and in that aspect easier to solve. The disadvantage is that, most often, the resulting system becomes ill-posed (having more unknowns than equations). This problem is solved by using Tikhonov regularization (Tikhonov and Arsenin, 1977) together with the L-curve method (Hansen, 1992; 2000). The main differences with other common deterministic directional wave-analysis methods are: the SWDD method is free of user-checks after each analysis, the directional resolution is higher, the computation time is faster and a wave field reconstruction after the directional wave-analysis is possible.

The applicability of the SWDD method has been tested using synthetic wave signals for (the sum of) monochromatic long-crested waves, prescribed wave patterns – containing wave-crest curvature and wave amplitude variation – and model results of a mild-slope wave model (WIHA). Multiple sensitivity analyses have been applied to check the sensitivity of the SWDD method to: various physical phenomena (e.g. diffraction and wave amplitude variation), domain variations (e.g. slopes) and input parameter variation. The study shows that the SWDD method is able to analyse irregular wave-fields using an array configuration containing a low number of gauges and a dense grid containing many gauges. Based on the findings an advisory flowchart is presented on how to determine the optimum radius of the array setup for using the SWDD method in practice, both for the analysis of data from phase-resolving numerical wave models and from measurements.

The study shows that the SWDD method is a robust and reliable method to analyse (complex) wave fields on a (near) homogeneous bathymetry. The incoming wave direction(s) and associated wave height(s) are graphically depicted in a polar plot or a directional spectrum.