Some characteristics of entrainment at a cylindrical turbulence boundary

Over the last 30 years, turbulent entrainment has come to be viewed as a large-scale process, directed by coherent structures, and described as engulfing. With turbulence simulations, we examined the process of entrainment directly, as growth of vorticity and concentration along fluid particle pathlines which were computed simultaneously. Our results indicate that the process is more often small scale. Growth occurs close to the turbulence boundary, within small radial displacements, and in times which are smaller than local large-scale times. These observations can be cast into a model to show that overall rates can be predicted by large-scale quantities even though the process occurs at small scales; the only requirement is a fixed relationship across scales as in fully developed turbulent flows. So it is not inconsistent that engulfment can be a successful, and accepted, model for fully developed flows even if it is not the more frequent process.