  In this work, we study the Bloch wave homogenization for the Stokes system
with periodic viscosity coefficient. In particular, we obtain the spectral
interpretation of the homogenized tensor. The presence of the incompressibility
constraint in the model raises new issues linking the homogenized tensor and
the Bloch spectral data. The main difficulty is a lack of smoothness for the
bottom of the Bloch spectrum, a phenomenon which is not present in the case of
the elasticity system. This issue is solved in the present work, completing the
homogenization process of the Stokes system via the Bloch wave method.
