Penetration of a spherical vortex into turbulence

The penetration of a spherical vortex into turbulence is studied theoretically and experimentally. The characteristics of the vortex are first analysed from an integral perspective that reconciles the far-field dipolar flow with the near-field source flow. The influence of entrainment on the vortex drag force is elucidated, extending the Maxworthy (J. Fluid Mech., vol. 81, 1977, pp. 465-495) model to account for turbulent entrainment into the vortex movement and vortex penetration into an evolving turbulent field. The physics are explored numerically using a spherical vortex (initial radius R0, speed Uv0), characterised by a Reynolds number Re0(= 2R0Uv0/nu, where nu is the kinematic viscosity) of 2000, moving into decaying homogeneous turbulence (root-mean-square u0, integral scale L) with turbulent intensity It = u0/Uv0. When the turbulence is absent (It = 0), a wake volume flux leads to a reduction of vortex impulse that causes the vortex to slow down. In the presence of turbulence (It > 0), the loss of vortical material is enhanced and the vortex speed decreases until it is comparable to the local turbulent intensity and quickly fragments, penetrating a distance that scales as I -1 t . In the experimental study, a vortex (Re0 similar to 1490-5660) propagating into a statistically steady, spatially varying turbulent field (Ive = 0.02 to 0.98). The penetration distance is observed to scale with the inverse of the turbulent intensity. Incorporating the spatially and temporally varying turbulent fields into the integral model gives a good agreement with the predicted trend of the vortex penetration distance with turbulent intensity and insight into its dependence on the structure of the turbulence.