gore 
properties of those models described above in order to design more 
definitive experiments concerning the nature of wind generated waves. 
The Lagrangian equations 
Let a, B, and 5 be the x, y, and z coordinates of a particle 
of fluid. In the Lagrangian system of equations, a solution to the equations 
consists of finding the positions x, y, and z of all of the particles in the 
fluid as a function of time and the initial positions of the particles, a, B, 
and 6. The Lagrangian equations, according to Lamb [1932] are given 
by equations (1) where subscripts denote partial differentiation. 
mati ales igs 8 CIES oe EU = © 
(1) nee Sieg (Arg 8 IA lf) = 
=n0) 
XeXs * YeeVs + (Ay, + B%5 + Pg /P = 
The equation of continuity is most conveniently expressed by 
(2) da aty.2) | — 0 
dt | 8(a, 8, 6) 
Such solutions need not be irrotational, but, if a function, 
F(a, 8, 5,t) , can be found such that 
(@)i dh = (x, x, +r Yt May 2 z,)da + Coan Ve Yat Z, aay eee (x, X¢ PMs V5 +r (z, z~)dé 
is a perfect differential, there is no vorticity. 
A zero order solution to these equations is given by 
x =a 
yaar 
(4) = 
Po=p, 7 ge 8 
in which all fluid particles are at rest in hydrostatic equilibrium under the 
force of gravity. 
We expand, following the concepts described by Stoker [1957]; 
about the zero order solution in terms of a small parameter,é, as in 
(5) in which Fe is a constant. Here we think of e as equalto ak, 
