Transient cavities near boundaries Part 2. Free surface

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Abstract
Calculations of the growth and collapse of transient vapour cavities near a free surface when buoyancy forces may be important are made using the boundary-integral method described in Part 1. Bubble shapes, particle paths, pressure contours and centroid motion are used to illustrate the calculations. In the absence of buoyancy forces the bubble migrates away from the free surface during the collapse phase, yielding a liquid jet directed away from the free surface. When the bubble is sufficiently close to the free surface, the nonlinear response of the free surface produces a high-speed jet (‘spike’) that moves in the opposite direction to the liquid jet and, in so doing, produces a stagnation point in the fluid between the bubble and the free surface. For sufficiently large bubbles, buoyancy forces may be dominant, so that the bubble migrates towards the free surface with the resulting liquid jet in the same direction. The Kelvin impulse provides a reasonable estimate of the physical parameter space that determines the migratory behaviour of the collapsing bubbles.
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