forward with the speed, (gn) V2, i.e. the group velocity of shallow 
water waves. 
The various terms involved in the computation of the top part 
of figure 43 are shown below the graph of the integrand of (12.50) 
for the case under study. The term in the square bracket, namely, 
_ 2H KTH H) 
g sinn[2H—L(H aH) By 
is graphed first. It ranges from the value of two to the value of 
one and is equal to two at # equal to zero and asymptotically equal 
to one as # approaches infinity. For practical purposes, it is 
equal to one at # equal to 27/4. With a one half from out in front 
of the integral the graph is simply the classical expression, Gie52)., 
graphed as a function of » , i.e., (2r/T), over the range of interest. 
The other term, namely g/u I(p,H), is the wave crest speed (a 
g is needed from out in front of the integral). At# equal to zero, 
it equals “gH and tor large # it approaches zero values (since capil- 
larity is neglected). The value at # equal to zero is 985 cm/sec 
since the depth is 991 cm.* 
The bottom graph is the group velocity of the various spectral 
components. It equals 985 cm/sec for low values of # and falls to 
half this value at 27/5.4. This graph times the energy in the wave 
record per band of the » axis given by (pe/2)[ Ay (py eA then gives 
the flux of energy toward shore. 
Finally, a numerical integration of the top of figure 43 yields 
the result that the energy flux toward the shore is equal to 
4.58 x 107 ergs/sec per centimeter of length along the wave crest. 
* The mean low water value was corrected to mean sea level, and a 
possible two foot tidal amplitude was neglected. 
107 
