  This work is directed towards investigating the fate of three-dimensional
long perturbation waves in a plane incompressible wake. The analysis is posed
as an initial-value problem in space. More specifically, input is made at an
initial location in the downstream direction and then tracing the resulting
behavior further downstream subject to the restriction of finite kinetic
energy. This presentation follows the outline given by Criminale and Drazin
[Stud. in Applied Math. \textbf{83}, 123 (1990)] that describes the system in
terms of perturbation vorticity and velocity. The analysis is based on large
scale waves and expansions using multi scales and multi times for the partial
differential equations. The multiscaling is based on an approach where the
small parameter is linked to the perturbation property independently from the
flow control parameter. Solutions of the perturbative equations are determined
numerically after the introduction of a regular perturbation scheme
analytically deduced up to the second order. Numerically, the complete linear
system is also integrated. Since the results relevant to the complete problem
are in very good agreement with the results of the first order analysis, the
numerical solution at the second order was deemed not necessary. The use for an
arbitrary initial-value problem will be shown to contain a wealth of
information for the different transient behaviors associated to the symmetry,
angle of obliquity and spatial decay of the long waves. The amplification
factor of transversal perturbations never presents the trend - a growth
followed by a long damping - usually seen in waves with wavenumber of order one
or less. Asymptotical instability is always observed.
