Gravity Driven Instability in Elastic Solid Layers

We demonstrate the instability of the free surface of a soft elastic solid facing downwards. Experiments are carried out using a gel of constant density rho, shear modulus mu, put in a rigid cylindrical dish of depth h. When turned upside down, the free surface of the gel undergoes a normal outgoing acceleration g. It remains perfectly flat for rho gh/mu < a* with a* similar or equal to 6, whereas a steady pattern spontaneously appears in the opposite case. This phenomenon results from the interplay between the gravitational energy and the elastic energy of deformation, which reduces the Rayleigh waves celerity and vanishes it at the threshold.