20 80 140 200 M/m 0.02 0.04 0.06 0.08 $_{Z}$/L $_{P}$=0.99 $_{P}$=0.8 $_{P}$=0.99 $_{P}$=0.8 FIG. 4: (Color online) Dimensionless relative standard deviation σ$_{Z}$/L of the position of the movable piston as a function of the mass ratio M/m . The symbols are simulation data and the lines guides for the eye. The two upper curves correspond to α = 0 . 94, and the two lower ones to α = 0 . 98. In each case, two values of α$_{P}$ have been employed: 0 . 99 (circles) and 0 . 8 (triangles). W can lead to the set up of transversal instabilities, as already mentioned. The notation stresses the constancy of the velocity of the vibrating wall. Although other compressibility coefficients could be defined, the one in (7) has the advantage of being easy to implement in experiments, at least at a conceptual level. On the other hand, it is worth to remark that by keeping v$_{W}$ constant and changing M , both the hydrodynamic profiles inside the fluid and the power injected into it through the vibrating wall are modified. In particular, the latter is given by [19] Therefore, increasing M while keeping v$_{W}$ constant produces an increase of the power Q 0 . For the two dimensional systems being considered here, the definition (7) is equivalent to k = − W Lg 0 ( ∂L ∂M )$_{v}$$_{W}$ . (9) Q 0 = W ( N$_{z}$ + M mW ) mg 0 v$_{W}$. (8) 12