Non-continuous Froude number scaling for the closure depth of a cylindrical cavity

TL;DR

This study investigates the collapse of a cylindrical cavity created by dragging a cylinder through water, revealing non-universal scaling behavior due to capillary wave effects, challenging traditional Froude number scaling assumptions.

Contribution

It demonstrates that the cavity's pinch-off depth does not follow the expected Froude$^{1/3}$ law and introduces capillary waves as the cause for the observed non-continuous scaling regimes.

Findings

Pinch-off depth exhibits two distinct scaling regimes.

Capillary waves created by the cylinder's passage influence collapse.

Experimental and numerical results are consistent.

Abstract

A long, smooth cylinder is dragged through a water surface to create a cavity with an initially cylindrical shape. This surface void then collapses due to the hydrostatic pressure, leading to a rapid and axisymmetric pinch-off in a single point. Surprisingly, the depth at which this pinch-off takes place does not follow the expected Froude$^{1/3}$ power-law. Instead, it displays two distinct scaling regimes separated by discrete jumps, both in experiment and in numerical simulations (employing a boundary integral code). We quantitatively explain the above behavior as a capillary waves effect. These waves are created when the top of the cylinder passes the water surface. Our work thus gives further evidence for the non-universality of the void collapse.