Directional spectrum of ocean waves from array measurements using phase/time/path difference methods

Wave direction has for the first time been consistently, accurately and unambiguously evaluated from array measurements using the phase/time/path difference (PTPD) methods of Esteva in case of polygonal arrays and Borgman in case of linear arrays. We have used time series measurements of water surface elevation at a 15-gauge polygonal array, in 8 m water depth, operational at the CERC's Field Research Facility at Duck, North Carolina, USA. Two modifications have been made in the methodology. One modification is that we use the true phase instead of the apparent phase, the other modification being that estimates of wave direction are registered only if the relevant gauges in the array are coherent at 0.01 significance level. PTPD methods assume that in a spectral frequency band the waves approach from a single direction, and are simple, expedient and provide redundant estimates of wave direction. Using Esteva's method with the above modifications, we found that at Duck: (i) the directions of swell and surf beat, when energetic swell is present, conform to the schematic diagram of surf beat generation given by Herbers et al., (ii) surf beat of remote origin occurs when the significant wave height, H_mo, falls below 0.41 m, (iii) the surf beat of remote origin is not normally incident at the shore contrary to Herbers et al. In fact we found that the surf beat of remote origin is incident at angles in excess of 45° with respect to the shore normal, and (iv) the surf beat of remote origin is largely trans-oceanic in origin.