given by w*CD( p )1°/e" instead of FAC 2 17. The slopes are there- 
fore distributed according to a normal distribution with a mean of 
zero and a variance related to the integral of the function just 
given above from zero to infinity. 
The curvature of the sea surface in the x direction is given 
by equation (11.18). The curvature as a function of time at a fixed 
point is, from the same reasoning as used above, distributed ac- 
cording to a normal distribution with a zero mean and a standard 
deviation related to the integral from zero to infinity of 
2 (p(n )1°/e?. | 
Infinite values for the curvature of the sea surface mean that 
at that point on the sea surface a sharp breaking angle occurs in 
the wave profile. Equation (11.18) shows that these sharp curvature 
changes are associated with the short waves (or the higher wave fre- 
quencies). If the integral is to behave properly, the condition 
given by equation (11.19) must be imposed. 
Wave power and energy transfer 
Consider the yz plane which results from picking a fixed value 
of x. The work being done on this plane when averaged over y and t 
and integrated over depth is the wave power or the flux of energy 
in ergs/sec per centimeter of length along the y axis. The equa- 
tion given in Lamb for section 237(equation 10) can be modified to 
yield the first expression in equation (11.20). Substitution of 
equations (11.2) and (11.8), followed by the indicated integrations 
and limiting processes, then yields the average rate of transmission 
of Wave energy across the yz plane per unit length of the y axis. 
Without the cos@® term, equation (11.20) would represent the total 
10 
