Effect of liquid depth on dynamics and collapse of large cavities generated by standing waves

Abstract

The effect of fluid depth on the collapse of large cavities generated by over-driven axisymmetric gravity waves in a 10 cm diameter cylindrical container has been studied. At a large fluid depth in a viscous glycerine–water solution, the collapse of the cavities is inertia dominant at the initial phase with the time-dependent cavity radius (rm) obeying rm ∝ τ1/2; τ = t − t0 being the time remaining for collapse, with t0 being the time at collapse. However, enhanced damping at a low liquid depth turns the late stage of the transition into the viscous regime (rm ∝ τ) at some critical depth beyond which a singular collapse (transition from non-pinch-off and pinch-off collapse) is impossible. At a shallow depth, the change in cavity radius follows a flip of the power law, i.e., rm ∝ τ at the initial stage of collapse followed by a transition to rm ∝ τ1/2, suggesting a viscous–inertial transition. For fluids with relatively lower viscosity but similar surface tension, here water, a smoother cavity with damped parasitic waves at a small liquid depth collapses at a smaller radius. The surface jet velocity due to the collapse of the cavity monotonically decreases with the decrease in the depth, whereas in the case of water, it increases with the depth reaching a maximum at a critical depth followed by a decrease again. The self-similarity, exhibited by the cavity up to the critical depth, is lost due to the axial movement restriction by the bottom wall.