CHAPTER 11 
ADDITIONAL PROPERTIES OF A SHORT CRESTED GAUSSIAN 
SEA SURFACE IN INFINITELY DEEP WATER 
introduction 
In this chapter, the pressure, velocity fields and curvature of 
the short crested sea surface will be studied. In addition, some of 
the very important lines of future research which are possible by the 
use of these new concepts will be suggested. Once [a5(u Saye has 
been determined, all of the other desired properties of the sea sur- 
face and the fluid motions can be determined to within the accuracy 
of the linearization assumptions at the start of Chapter 2. Since 
the sea surface is Gaussian, it follows that all of the other proper- 
ties of the wave motion such as the fluid velocities, the pressure, 
and the slope and curvature of the sea surface will be Gaussian. The 
functions which describe the range of variability of these properties 
are different from those which describe the sea surface. They are 
various integrals and functional modifications involving the power 
spectrum of the free surface which lead to some very important re- 
sults about the nature of the power spectrun. 
Pressure 
In Chapter 4, equations (4.8) and (4.10) presented formulas 
for the pressure at a point below the surface produced by a finite 
wave group passing overhead. They are considered here only to show 
how complex the problem can become when an attempt to solve it by 
Fourier Integral Theory is made. Equation (4.10) shows that at x 
equal to zero the period of the waves recorded by a sub-surface 
