The Lagrangian view of energy transfer in turbulent flow

Hydrodynamic turbulence in 3D is characterized by a non-linear transfer of energy from large to small scales. Here, we provide a geometrical view of e nergy transfer by relating it to the deformation of fluid volumes under Lag rangian dynamics. The energy flux is parametrized in terms of the coarse-gr ained velocity difference tensor together with the tensor describing the sh ape of the volume. Our construction provides an interpretation for the non- trivial time dependence of the energy of relative motion within a cloud of Lagrangian particles observed in the direct numerical simulation turbulence .