The laminar interactions of a pair of vortex tubes with a free surface

Abstract

A fully nonlinear numerical method is developed to study the viscous interactions of a pair of vortex tubes rising toward a free surface. The numerical theory uses Helmholtz's decomposition to treat the irrotational and vortical components of the flow as separate nonlinearly coupled equations. The laminar interactions of a pair of vortex tubes with a clean free surface at intermediate Froude and Weber numbers and a low Reynolds number show two distinct phases. During the rise phase of the vortex pairs, instabilities lead to the formation of helical vorticity. The rotation of the helical vorticity around the primary vortex tubes causes an unsteady oscillation in the free-surface elevation. During the reconnection phase, the helical vortex sheets get narrower and attach themselves to the free surface. The normal connections of cross-axis vorticity with the free surface give whirls. The free-surface elevation is well correlated with the vortical pressure. The numerical results agree qualitatively with experimental measurements.