EQUILIBRIUM-RANGE SPECTRUM OF WAVES PROPAGATING ON CURRENTS By Kyung Duck Suh, 1 Associate Member, ASCE, Yoo-Yin Kim, 2 and Dong Young Lee3 ABSTRACT: By extending the equation proposed in 1981 by Hedges for deep- water spectrum to a finite-depth water, an equation is developed for the equilib- rium-range spectrum of waves propagating on a following or opposing current in finite-depth water. To examine the predictability of the developed equation, lab- oratory experiments were made for the change of Texel, Marsen, and Arsloe (TMA) shallow-waterspectra due to currents in water of various depths and current velocities. Comparison with the experimental data shows that the developed equa- tion predicts reasonably well the equilibrium-range spectra of waves propagating on currents. Comparison was also made with the equation originally developed by Kitaigordskii et al. in 1975 and modified later by Gadzhiyev et al. in 1978. A statistical analysis shows that the equation developed in the present study and the equation proposed by Gadzhiyev et al. have essentially the same degree of pre- dictability, both being in reasonable agreement with observations. INTRODUCTION In coastal waters, more often than not, waves propagate on currents driven by tidal forces, earth's gravity, or wind. There have been a number of studies for dealing with the change of a wave Spectrum due to the presence of a current. Using the energy conservation and kinematic wave conservation laws and ignoring energy dissipation due to wave breaking, Huang et al. (1972) proposed an equation that describes the influence of current on the change of a wave spectrum in deep water. Based on the conservation of wave action, on the other hand, Hedges et al. (1985) proposed a similar equation that can be applied for both deep and finite-depth water. Their equation reduces to the Huang et al.'s (1972) equation in the limit of deep water. The equation proposed by Hedges et al. (1985) is useful for predicting the change of a wave spectrum due to the presence of a current if the wave spectrum does not reach an equilibrium (or saturation). When waves prop- agate onto an opposing current, their growth may be limited by the breaking of waves, especially of the waves in high frequency range. By the use of Phillips' (1958) equilibrium-range constraint, Hedges (1981) derived an equation for the equilibrium range of a deep-water wave spectrum when the waves encounter a following or opposing current [also can be found in Hedges et al. (1985) and Hedges (1987)]. On the other hand, again by 1prin. Res. Engr., Oc. Engrg. Div., Korea Ocean Res, & Development Inst., 1270, Sa-dong, Ansan, Kyonggi-do, 425-170, Korea. ZGrad. Student, Dept. of Oc. Engrg., Univ. of Rhode Island, Kingston, RI 02881; formerly, Res. Engr., Oc. Engrg. Div., Korea Ocean Res. & Development Inst., 1270, Sa-dong, Ansan, Kyonggi-do, 425-170, Korea. 3Prin. Res. Engr., Oc. Engrg. Div., Korea Ocean Res. & Development Inst., 1270, Sa-dong, Ansan, Kyonggi-do, 425-170, Korea. Note. Discussion open until March 1, 1995. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on April 14, 1993. This paper is part of the Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 120, No. 5, September/October, 1994. ISSN 0733=950X/94/0005-0434/ $2.00 + $.25 per page. Paper No. 5983. 434 J. Waterway, Port, Coastal, Ocean Eng. 1994.120:434-450. Downloaded from ascelibrary.org by SEOUL NATIONAL UNIVERSITY LIB on 08/21/14. Copyright ASCE. For personal use only; all rights reserved.