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The dynamics and stability of a fluid-filled hollow cylindrical shell rollingon an inclined plane are analyzed. We study the motion in two dimensions byanalyzing the interaction between the fluid and the cylindrical shell. Ananalytical solution is presented to describe the unsteady fluid velocity fieldas well as the cylindrical shell motion. From this solution, we show that theterminal state is associated with a constant acceleration. We also show thatthis state is independent of the liquid viscosity and only depends on the ratioof the shell mass to the fluid mass. We then analyze the stability of thisunsteady flow field by employing a quasi-steady frozen-time framework. Thestability of the instantaneous flow field is studied and transition from astable to an unstable state is characterized by the noting the time when theeigenvalue crosses the imaginary axis. It is observed that the flow becomesunstable due to long wavelength axial waves. We find a critical Reynolds number($\approx 5.6$) based on the shell angular velocity at neutral stability withthe corresponding Taylor number being $\approx 125.4$. Remarkably, we find thatthis critical value is independent of the dimensionless groups governing theproblem. We show that this value of the critical Reynolds number can beexplained from a comparison of time scales of motion and momentum diffusion,which predicts a value near $2 \pi$.

Dynamics and stability of a fluid filled cylinder rolling on an inclined plane