Stability threshold for the free surface flow driven by a rotating disk in a small aspect ratio cylindrical cavity

Stability threshold for the free surface flow driven by a rotating disk in a small aspect ratio cylindrical cavity. We perform a linear stability analysis of the flow inside a cylindrical tank in which the bottom rotates. The aspect ratio is such that the radius of the disk is larger than the fluid height. In. a recent experiment [S. Poncet, MR Chauve, J. Flow Vis. Image Process 14 (2007) 85-105] interesting instability patterns have been found. As the fluid rotates, the free surface is deformed, which increases the computational difficulty. As a first approach, we consider a non deformable free surface (symmetry condition). We discuss the validity of this hypothesis by comparing our results with the experiments. Finally, we discuss the necessity to take into acount the free surface deformation.