In this study it is shown that, alternatively, wave heights can be 

 calculated along streamlines, which is a natural analogy to classical 

 steady hydraulics, albeit the superposition of waves makes calculations 

 more complex. 



In steady hydraulics the concepts of a total head line and a 

 horizontal energy reference line are known to be useful tools for 

 calculating water surface heights and current velocities in rivers. 



Combining the momentum and total energy conservation equations, the 

 above-mentioned energy principle is extended to a steady, rotational, 

 large-scale current wave motion over a gently sloping seabed. 

 Dissipation due to bed friction is included. 



The discovery is made that a total head line and a horizontal 

 energy reference line also exist along streamlines in such a combined 

 flow. The horizontal energy reference line demonstrates the existence 

 of a so-called energy reference height above a datum, which is constant 

 along a streamline. It varies, however, from streamline to streamline. 



The new energy equation states that this constant height is the sum 

 of the total current wave (energy) head and the current wave dissipation 

 head. The total head is the sum of four terms: the mean water surface 

 height above datum, plus a current velocity head, plus a mean wave 

 velocity head, and minus a current wave interaction term head. The 

 current wave dissipation head is the sum of two terms: a current dissi- 

 pation head minus a wave dissipation head. This allows the calculation 

 of wave heights along streamlines. 



Since the energy reference height varies from streamline to stream- 

 line, no horizontal energy reference level exists in general for a 

 combined current wave motion. 



The findings are illustrated with four qualitative sketches, 

 corresponding to a strong/weak current, combined with a following/ 

 opposing current. A table gives the definitions of the many new 

 concepts . 



It is verified that an approach using wave-action conservation 

 leads to the same equations. Various properties of wave refraction by 

 depth changes without current are also described. 



Coastal Engineering Significance. The analysis and interpretation of 

 refraction equations given in this paper should assist engineers who 

 desire a better understanding of the subject. The energy integral along 

 streamlines and the reference levels defined here are alternatives to 

 using the conservation of wave action. This may be useful for analysis 

 or in computing simple flows, but in general it will be simpler to use 

 wave-action rather than streamline integrals since rays are computed to 

 find the frequency and wavelength. 



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