On the growth of localised perturbations in isotropic turbulence

Abstract

Assessing the impact of localised perturbations is staple for the problems of data assimilation and control of turbulent flows. In the present work we exploit the public database of [1] that contains the growth and location of about 105 perturbations of approximately thirty Kolmogorov units in isotropic turbulence at moderate Reynolds numbers. All the terms in the evolution equation for the perturbation kinetic energy are analysed statistically, disregarding in the process the effect of viscosity. Of the relevant terms, only the stretching of the perturbation by the mean flow can result in production of kinetic energy, whereas every other term must only transport the perturbation across the flow field. However, it is shown that if the problem of interest is the coarse-grained propagation of the perturbation, i.e. its radius, the dynamical terms related to incompressibility are of equal importance for the growth. A simplified model based on the balance between these terms is proposed to explain the quasi-linear growth of the radius with time.