Hydrodynamic description of granular convection.

We present a hydrodynamic model that captures the essence of granular dynamics in a vibrating bed. We carry out the linear stability analysis and uncover the instability mechanism that leads to the appearance of the convective rolls via a supercritical bifurcation of a bouncing solution. We also explicitly determine the onset of convection as a function of control parameters and confirm our picture by numerical simulations of the continuum equations. PACS numbers: 47.20.-k, 46.10+z, 81.35.+k Granular materials in a container subjected to vertical vibrations display interesting nonlinear dynamical behaviors. [1–6] Nothing really happens for Γ = Aω/g < 1, where A and ω are the frequency and the amplitude of the oscillations and g is the gravitational constant. But for 1 < Γ, the granular materials collectively move up and down, which we term the uniform bouncing [7], until Γ reaches the critical value Γc beyond which such a uniform bouncing motion becomes unstable and the permanent convective rolls develop inside the bulk. [3–5] Recent studies have revealed further complexity of this problem for values of Γ much larger than one, where reverse convection [5] and bubble formation [6] have been E-mail address: [email protected] E-mail address: [email protected]