The effect of a side wall on cavity dynamics during the water entry of a sphere at low Froude numbers

This paper comprehensively investigates the non-axisymmetric cavity dynamics of a vertically entering sphere under the influence of nearby side-walls through experimental, numerical, and theoretical analyses. Initially, we explore the characteristics of cavity evolutions with the sidewall effect. The emergence of a twin-vortex during cavity pinch-off is observed, and detailed numerical simulations provide insights into its underlying mechanisms. Both the dimensionless distance (lambda) and the Froude number Fr significantly influence the pinch-off type. A phase diagram in the lambda - F r parameter space is presented, revealing the interplay between these variables. Moreover, we investigate the sidewall effect on the pinch-off time and location at low Froude numbers. The findings indicate that as lambda decreases, both the pinch-off time and depth of the cavity increase. Generally, the wall effect is relatively weak when lambda exceeds 4. Additionally, the pinch-off time can be described by tau = k <mml:msqrt> r / g</mml:msqrt>, with the constant k determined by lambda. Utilizing 2D cavity theory, we estimate the pinch-off time of the water entry cavity with the sidewall effect, revealing a consistent collapse behavior with the mechanics of a two-dimensional cavity.