EVALUATION OF THE COMPUTATION OF WAVE DIRECTION WITH THREE-GAGE ARRAYS 



by 

 Dinorah C. Esteva 



I . INTRODUCTION 



Wave direction is an important parameter in the solution of many 

 coastal engineering problems. A knowledge of wave direction is essen- 

 tial for (a) estimating the direction and magnitude of sediment trans- 

 port by waves, (b) using refraction calculations to infer wave conditions 

 at one site from measurements made elsewhere, and (c) verifying theories 

 of wave generation. 



Visual observations of wave directions have been collected by ship- 

 board observers for over a century. About 20 years ago the Beach Ero- 

 sion Board (BEB) , predecessor to the Coastal Engineering Research Center 

 (CERC) , engaged the assistance of U.S. Coast Guard installations in the 

 collection of visual observations of breaker direction from shore. How- 

 ever, objective determinations of wave direction are desirable without 

 being restricted to location, time of day, or visibility condition. The 

 capability to do so involves the use of wave measuring instruments. 

 Panicker (1971, 1974) presents extensive reviews of reports dealing with 

 the determination of wave direction from instrument records with partic- 

 ular euphasis on those involving sea-surface elevation or pressure records. 



In March 1970, CERC installed an array of wave gages at Pt. Mugu, 

 California. Records from the array were to be used to compare redundant 

 values of wave direction and to estimate the level of accuracy of the 

 computations. The available procedures for determining wave direction 

 from an array involved assumptions that had not been thoroughly estab- 

 lished. Thus, the records from the array would also be used in a syste- 

 matic examination of these assumptions, and of the reliability of wave 

 gages . 



This study discusses the array performance and the information gained 

 about wave direction. Redundant values of directions were obtained from 

 the 10 three-gage arrays possible with five gages. The mathematical model 

 used assumes that the sea surface is the result of the superposition of 

 a small number of narrow-banded wave trains consisting of long-crested 

 waves traveling in well-defined directions. It was also assumed that 

 only one wave train is present with a particular period. The first 

 assumption is supported by the energy spectra computed at CERC (Thompson, 

 1974), by aerial photos of the sea surface (Fig. 1), and by radar images 

 of the wave field (Fig. 2) . Many published reports include photos similar 

 to that in Figure 1; e.g., McClenan and Harris (1975). Fujinawa (1974, 

 1975) conjectured that narrow directional spread might be responsible 

 for the incomplete recovery of the true directional spectrum from field 

 records in his computations using high directional resolution. 



Average values of wave direction for bands of constant frequency 

 width were computed from cross-spectra between gage pairs. Direction 



