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This work is directed towards investigating the fate of three-dimensionallong perturbation waves in a plane incompressible wake. The analysis is posedas an initial-value problem in space. More specifically, input is made at aninitial location in the downstream direction and then tracing the resultingbehavior further downstream subject to the restriction of finite kineticenergy. This presentation follows the outline given by Criminale and Drazin[Stud. in Applied Math. \textbf{83}, 123 (1990)] that describes the system interms of perturbation vorticity and velocity. The analysis is based on largescale waves and expansions using multi scales and multi times for the partialdifferential equations. The multiscaling is based on an approach where thesmall parameter is linked to the perturbation property independently from theflow control parameter. Solutions of the perturbative equations are determinednumerically after the introduction of a regular perturbation schemeanalytically deduced up to the second order. Numerically, the complete linearsystem is also integrated. Since the results relevant to the complete problemare in very good agreement with the results of the first order analysis, thenumerical solution at the second order was deemed not necessary. The use for anarbitrary initial-value problem will be shown to contain a wealth ofinformation for the different transient behaviors associated to the symmetry,angle of obliquity and spatial decay of the long waves. The amplificationfactor of transversal perturbations never presents the trend - a growthfollowed by a long damping - usually seen in waves with wavenumber of order oneor less. Asymptotical instability is always observed.

The role of long waves in the stability of the plane wake