Directional seas should be ergodic

Directional seas are often modelled as a double summation of plane sinusoidal waves from different directions at a set of discrete frequencies. Unfortunately, this model is commonly used in a way which produces unrealistic standing wave phenomena and hence is not ergodic. Consequently, time averages of variables are not necessarily the same as space averages and averages over different realisations. The resulting point spectrum is randomly distributed about the target point spectrum as required, but the time history generated is only representative of a short record of the target sea. In this note, the basis of the phenomenon and its consequences for both wave tank and computer simulation work are described. Two alternative techniques of directional wave generation are discussed.

Standing waves also occur near reflectors in the sea and test tanks; their effects on point and directional wave measurements are discussed.