Description:
<jats:p>The phenomenon of pattern formation is ubiquitous in the dynamics of extended nonlinear systems. Patterns arise from the interplay of external forcing, dissipation, nonlinearity, and spatial coupling. These factors are also present in many acoustic systems. However, under usual conditions where the elastic nonlinearity dominates, the development of shock fronts in nonlinear regime strongly limits the possibility of a simple analysis. Viscous media, where thermal nonlinearity dominates over the elastic one and wave distortion is inhibited at short distances, are good candidates for acoustic systems presenting patterns with similar characteristics as those found in other fields, such as hydrodynamics or optics. A model describing the evolution of pressure and temperature variations in a resonator with plane walls containing a viscous medium is presented. The large aspect ratio of the resonator allows the transverse spatial coupling, mediated by sound diffraction and temperature diffusion. The homogeneous solutions show bistability at some values of the parameters, in agreement with experimental results reported in the bibliography. We show by means of linear stability analysis that the homogeneous solutions develop spatial instabilities leading to the spontaneous generation of spatial patterns. The analytical predictions are confirmed by a numerical analysis. [Support from Spanish MEC, Project FIS2005-07931-C03-02/03, is acknowledged.]</jats:p>