ABSTRACT

Deep-sea wave height, length and period each may have a Gaussian distribution. However, deep-sea wave height and length cannot be used in shoaling depths, and there is no useful algebraic equation which gives modified parameters at any desired point during shoaling. Therefore they must be calculated step-by-step.

Shoaling over real-world profiles yields complicated (polymodal) distributions of these parameters, due in part to bottom irregularities. Shoaling on many smooth-profile equations also makes polymodal wave parameter distributions, even without bottom irregularities, indicating -- among other things -- that simplistic representations of wave characteristics, at or near the surf zone, do not provide very much useful information.

Results of this work:

1. Nearshore wave parameters may have polymodal distributions, commonly with two-to-six Gaussian components.
2. Any one component of wave height, wave length or wave period may be truncated at either end.
3. Nearshore wave measurements (means and standard deviations) cannot be extrapolated seaward to get deep-water values.
4. The polymodality of the near-shore distribution of wave height, wave length and wave period cannot be explained uniquely by either deep-water conditions or shoaling processes, without additional information.
5. Initial wave period and wave height, and modal inshore wave length, fit a simple equation for algebraic profiles, but not for natural bathymetry.