On the stretching of material lines and surfaces in isotropic turbulence with zero fourth cumulants

Abstract
The convective effects of isotropic turbulence on arbitrary vector and scalar fields satisfying certain conservation conditions are studied under the assumption that all fourth-order cumulant tensors are zero. In the absence of molecular conduction, the behaviours of such vector and scalar fields are related to those of material lines and surfaces respectively, and the diffusive action of the turbulence results in a stretching of these lines and surfaces. The present analysis leads to a definite prediction for the corresponding strain rates which suggests that an initially spherical material volume element is drawn out into a long thin ribbon of constant width.

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