46
(ECt), = the stable energy flux.
H = the local wave height
The stable energy flux is obtained by assuming it to be a function of the height of a wave
propagating over a flat bottom after breaking ceases, and that this height is a constant
times the water depth, = 7. The constants K and 7 were determined by analysis of
experimental data obtained from Horikawa and Kuo (1966).
Kirby related Dailys work to the dissipation term w by deriving a conservation equation
for the wave action j. Garrett (1967) and Bretherton and Garrett (1968) showed that for
waves propagating in a moving and variable medium, the quantity that is conserved is the
wave action (7) > which is the wave energy divided by the intrinsic frequency. Kirby derived
a wave action conservation equation from the linear hyperbolic wave Eq. (3.34) using the
definition of W as given by Eq. (3.35):
^ + (v* U)^ Vfc(CC,Vfcft + ( = 0 (3.91)