Wave formation and growth during sedimentation in narrow tilted channels

A linear-stability analysis is performed to investigate in detail the conditions for wave formation and growth during sedimentation in long, narrow channels that are inclined from the vertical. The maximum amplification rates of such waves are predicted by solving the equations governing the instabilities both asymptotically for long-wavelength disturbances and also numerically for disturbances with moderate wavelengths. The general trends set forth by the linear theory are found to be consistent with experimental observations. In particular, it is shown that very tall and narrow vessels not only give the largest enhancement in the settling rate but also significantly increase the stability of inclined settling systems.