  An efficient method to describe the nonlinear evolution of Stimulated
Brillouin Scattering in long scale-length plasmas is presented. The method is
based on a decomposition of the hydrodynamics variables in long- and
short-wavelength components. It makes it possible to describe the
self-consistent coupling between the plasma hydrodynamics, Stimulated Brillouin
Scattering, and the generation of harmonics of the excited ion acoustic wave
(IAW). This description is benchmarked numerically and proves to be reliable
even in the case of an undamped ion acoustic wave. The momentum transferred
from the electromagnetic waves to the plasma ions is found to induce a plasma
flow which modifies the resonant three wave coupling between the IAW and the
light waves. A novel picture of SBS arises, in which both IAW harmonics and
flow modification reduce the coherence of SBS by inducing local defects in the
density and velocity profiles. The spatial domains of Stimulated Brillouin
activity are separated by these defects and are consequently uncorrelated,
resulting in a broad and structured spectrum of the scattered light and in a
temporally chaotic reflectivity.
