  The purpose of this paper is to prove that, for a large class of nonlinear
evolution equations known as scalar viscous balance laws, the spectral (linear)
instability condition of periodic traveling wave solutions implies their
orbital (nonlinear) instability in appropriate periodic Sobolev spaces. The
analysis is based on the well-posedness theory, the smoothness of the
data-solution map, and an abstract result of instability of equilibria under
nonlinear iterations. The resulting instability criterion is applied to two
families of periodic waves. The first family consists of small amplitude waves
with finite fundamental period which emerge from a local Hopf bifurcation
around a critical value of the velocity. The second family comprises
arbitrarily large period waves which arise from a homoclinic (global)
bifurcation and tend to a limiting traveling pulse when their fundamental
period tends to infinity. In the case of both families, the criterion is
applied to conclude their orbital instability under the flow of the nonlinear
viscous balance law in periodic Sobolev spaces with same period as the
fundamental period of the wave.
