  The way in which kinetic energy is distributed over the multiplicity of
inertial (intermediate) scales is a fundamental feature of turbulence.
According to Kolmogorov's 1941 theory, on the basis of a dimensional analysis,
the form of the energy spectrum function in this range is the -5/3 spectrum.
Experimental evidence has accumulated to support this law. Until now, this law
has been considered a distinctive part of the nonlinear interaction specific to
the turbulence dynamics. We show here that this picture is also present in the
linear dynamics of three-dimensional stable perturbation waves in the
intermediate wavenumber range. Through extensive computation of the transient
life of these waves, in typical shear flows, we can observe that the residual
energy they have when they leave the transient phase and enter into the final
exponential decay shows a spectrum that is very close to the -5/3 spectrum. The
observation times also show a similar scaling. The scaling depends on the
wavenumber only, i.e. it is not sensitive to the inclination of the waves to
the basic flow, the shape-symmetry of the initial condition and the Reynolds
number.
