Penetration of a spherical vortex into turbulence

Abstract

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 $R_0$ , speed $U_{v0}$ ), characterised by a Reynolds number $Re_0(=2R_0U_{v0}/\nu$ , where $\nu$ is the kinematic viscosity) of 2000, moving into decaying homogeneous turbulence (root-mean-square $u_0$ , integral scale $L$ ) with turbulent intensity $I_t=u_0/U_{v0}$ . When the turbulence is absent ( $I_t=0$ ), a wake volume flux leads to a reduction of vortex impulse that causes the vortex to slow down. In the presence of turbulence ( $I_t> 0$ ), 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 $I_t^{-1}$ . In the experimental study, a vortex ( $Re_0\sim 1490\unicode{x2013}5660$ ) propagating into a statistically steady, spatially varying turbulent field ( $I_{ve}=0.02$ 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.