TABLE OF CONTENTS Havelock (1929) applied Fourier integrals to develop the first theory for surface gravity waves forced by both planar and circular wavemakers in water of both infinite- and finite-depth. The Hudspeth and Sulisz (1991) and Sulisz and Hudspeth (1993) reviews of a second-order nonlinear WMBVP for planar wavemakers are summarized here. Even though the linear first-order eigenseries will converge for any geometry of a generic planar wavemaker (vide., Fig. 5.3 in Chapter 5.2), the weakly nonlinear second-order solutions obtained from Stokes perturbation expansions will not converge for all planar wavemaker geometries.
The two length scales applied to scale the coordinates {x, z} by the Lindstedt-Poincare perturbation method (Nayfeh, 1973, Chapter 3, Nayfeh, 1981, Chapter 4.3, or Nayfeh, 1985, Chapter 4.1) for a planar wavemaker in a 2D channel in Chapter 5.2 will now be replaced by the following single length scale for the planar wavemaker geometry illustrated in Fig. 5.3a:
where 
is a dimensional wavelength, and where all of the other scale parameters including the dimensionless perturbation parameter 
defined in Chapter 5.2 remain the same.
The dimensionless fluid motion may be computed from the negative gradient of a dimensionless scalar, time-dependent velocity potential ? (x, z, t) according to
where the two-dimensional gradient vector operator (vide., Chapter 2.2.7) is
The total dimensionless pressure field P(x, z, t) may be computed from the unsteady Bernoulli equation (4.3) in Chapter 4.1 according to
where B(t) is the dimensionless Bernoulli constant (cf.
