Wavelength of Ocean Waves and Surf Beat at Duck from Array Measurements

Wavelength of ocean waves and surf beat (infra gravity waves) has for the first time been computed as a function of frequency from different combinations of non-collinear 3-gauge arrays. Data at the 15-gauge polygonal array at 8m depth at Duck, North Carolina, USA, has been used. The method used is an extension of the 3-gauge method of Esteva 1976 & 1977 for computing wave direction. Wavelength was also computed using the Singular Value Decomposition (SVD) method of Herbers et al. 1995 from (i) κ_rms and (ii) κ_x, κ_y. The wavelength computed from the array measurements, using both the 3-gauge as well as the SVD(κ_x, κ_y) method, is nearly identical to the wavelength predicted by the well known dispersion relation for ocean waves (DROW), viz., (2πf)² = κg tanh κd, in the ocean wave regime (T ⩽ 11.64s spectral period); and is approximately thrice the predicted value in the surf beat regime (T ⩾ 32.00s). The implication of wavelength of surf beat at Duck being much larger than mat predicted by DROW, is that methods for determining the directional spectrum which use DROW can erroneously indicate a surf beat direction much closer (≅; 30° closer) to the shore normal than it actually is in the field. For example the variational method of Herbers et al. 1995 and the 2-gauge array method of Borgman 1974 are unfortunately both tainted with this error due to use of DROW.