Secondary Splitting of Zero Gradient Points in Turbulent Scalar Fields

Abstract

The mechanisms related to the secondary splitting of zero gradient points of scalar fields are analyzed using the two dimensional case of a scalar extreme point lying in a region of local strain. The velocity field is assumed to resemble a stagnation point flow, cf. Gibson [1], which is approximated using a Taylor expansion up to third order. It is found that the splitting can only be explained when the third order terms of the Taylor expansion of the flow field are included. The non-dimensional splitting time turns out to depend on three parameters, namely the local Péeclet number Peδ based on the initial size of the extreme point δ and two parameters which are measures of the rate of change of the local strain. For the limiting case Peδ → 0, the splitting time is found to be finite but Péclet number independant, while for the case of Peδ → ∞ it increases logarithmically with the Péclet number.