Evaluation of an energy-propagation wave refraction model

Abstract

A simple wave refraction model, based on the conservation of wave energy entering and leaving grid squares defined by an areal array of equally spaced depth points, has been tested on a number of idealized bathymetries and against two field data sets. The model allows waves to cross by treating the directionality of the wave field in terms of discrete energy bins 10° apart. Algorithms for predicting the extent of partial breaking ( Dally, Dean and Dalrymple, 1985 ; Journal of Geophysical Research, 90, 11917–11927) and for bottom friction over a movable bed ( Grant and Madsen, 1982 ; Journal of Geophysical Research, 87, 469–481) were initially incorporated in the model but, for operational reasons, were replaced by a fixed ‘wave height to water depth’ limit of 0.5 and by a single friction factor specified by the user. For a simple linear shoreline, close correspondence was found between the model and Snell's law for offshore directions up to 45° wave height differences are <5% while for direction the differences rise to <10% in 2 m water depth. Over a linear bank differences in wave angle between opposite sides can exceed 20% when uni-directional waves are used, due to the algorithm being irreversible; when waves with a directional spread are used the differences drop to <10%. The model is able to predict well the wave heights measured at a number of locations in Haringvliet Estuary, Holland after the friction factor was tuned to 0.04, although the higher-than-predicted wave heights further into the estuary suggests that energy input from the wind is significant and so the friction factor of 0.04 is probably an underestimate. The model also shows reasonable directional predictive ability when tested against data from Pt Sapin, Canada. Wave heights at this location are also in good agreement but suggest a friction factor nearer 0.1. The model performed well when compared with field data from Holland and Canada but was found to have a number of limitations when run over simple “control’ bathymetries. These were (a) the irreversibility of the algorithm which results in different refraction rates over opposite sides of a linear bank, (b) edge influences which propagate into the middle of the domain and (c) the steady energy loss which occurs as energy leaks into directions beyond the range of the model. However, if the model is used with care, avoiding regions where diffraction and reflection may be important and selecting a friction factor appropriate to the area, it can be a useful tool for predicting wave heights and directions.