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 energy transfer by relating it to the deformation of fluid volumes under Lagrangian dynamics. The energy flux is parametrized in terms of the coarse-grained velocity difference tensor together with the tensor describing the shape of the volume. Our construction provides an intepretation 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.