A Tensor Formulation of the Lumley Decomposition Applied to the Jet Far-field*

A tensor formulation of the Lumley Decomposition (LD) is applied to the jet far-field which is analyzed in curvilinear coordinates. Fourier-based eigenfunctions along the streamwise direction are deduced directly from the LD, but only if a specific weighted inner-product space is chosen for the decomposition. A Galerkin projection of the turbulence kinetic energy (TKE) production term is then analyzed in order to quantify the TKE production capabilities of the eigenfunctions. It is shown that a wide range of mode- and wavenumbers exhibit similar rates of energy extraction directly from the mean flow, as hypothesized by [Wänström 2009]. Data obtained from PIV measurements of the jet far-field then suggest that the energy transport between eigenfunctions is not strictly governed by the classical Richardson cascade model, but that a wide range of modes are – at least partially - able to circumvent this cascade. \\ \\ \noindent [W{\"a}nstr{\"o}m 2009] Spatial decompositions of a fully-developed turbulent round jet sampled with particle image velocimetry. Ph.d. thesis, Chalmers University of Technology.