CALCULATION OF WAVE SHOALING WITH DISSIPATION 

 OVER NEARSHORE SANDS 



by 

 Robert J. Haltermeier 



I . INTRODUCTION 



As waves propagate toward breaking in shallow water, their attributes are 

 transformed by effects of water depth and bottom features. These nearshore 

 transformations are crucial in the interpretation of wave measurements and in 

 the prediction of sediment transport. Prior to wave breaking, appreciable wave 

 energy can be dissipated by friction between the oscillatory water motion and 

 the nearshore bottom, especially where waves cause strong agitation of bottom 

 sediments. This report considers such frictional dissipation. 



Ocean waves can be represented most adequately as distributions of propa- 

 gating energy with respect to frequency and direction. Near the shore, 

 extremely energetic waves are observed to constitute a somewhat regular wave 

 train approaching along a shore-normal line, with a rather well-defined wave 

 height and period. According to the Shore Protection Manual (SPM) (U.S. Army, 

 Corps of Engineers, Coastal Engineering Research Center, 1977), an idealization 

 of demonstrated value in coastal engineering is to represent real waves by a 

 characteristic height and period, the significant wave condition; this wave 

 representation is utilized here. 



This report provides a simple calculation procedure defining changes in 

 significant wave height due to water depth differences combined with bottom 

 friction at agitated sand beds. The procedure uses linear wave theory between 

 the two depths of interest and a computation of energy dissipation rate at an 

 intermediate water depth. Factors in wave transformation ignored here include: 

 wave direction and complex spectra, currents, surface wave breaking, winds, 

 water viscosity, and bottom percolation and elasticity. The technique is meant 

 for application only to energetic field wave conditions in fairly shallow water 

 with straight, parallel depth contours and relatively fine quartz bottom sands. 



Section II presents the calculation procedure for wave height changes 

 considering energy dissipation. Section III addresses the application of this 

 procedure and includes two example problems: converting nearshore wave measure- 

 ments into equivalent wave heights in shallower and in deeper water. The 

 reader is referred to Hallermeier (in preparation, 1983) for a detailed sub- 

 stantiation of elements incorporated in the calculation procedure; that refer- 

 ence reviews the empirical basis for the expression giving energy dissipation 

 coefficient and reports extensive calculated results in clear agreement with 

 multiple wave measurements at the Coastal Engineering Research Center's (CERC) 

 Field Research Facility, Duck, North Carolina, and at other sites. 



II. CALCULATION PROCEDURE 



Waves are presumed to travel perpendicular to depth contours with propaga- 

 tion described by small-amplitude (linear) wave theory. Required theoretical 

 relations are provided in Section 2.23 of the SPM. Wave and fluid character- 

 istics arising in the wave description are 



