Wave Crest Distributions: Observations and Second-Order Theory

Many empirical and heuristic distribution functions for wave crest heights have been proposed, but their predictions differ considerably. Part of the lack of agreement is due to the difficulty of making measurements that accurately record the true height of the wave crests. Surface following buoys effectively cancel out the second-order nonlinearity by making a Lagrangian measurement. Pressure transducers filter the nonlinear components of the signal in complicated ways. Wave staffs have varying degrees of sensitivity to spray. The location of the instruments also plays an important role. There is clear evidence from measurements in the North Sea that spurious crests due to spray are a problem downwind even from mounting supports that appear transparent. Much of the theoretical nonlinearity can be captured by calculations correct to second order. Explicit calculation of the interactions of each pair of components in a directional spectrum is straightforward although computationally intensive. This technique has the advantage that the effects of wave steepness, water depth, and directional spreading are included with no approximation other than the truncation of the expansion at second order. Comparisons with measurements that are believed to be of the best quality show good agreement with these second-order calculations. Simulations for a set of JONSWAP spectra then lead to parametric crest distributions, which can be used easily in applications.