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The turbulent energy cascade in dilute polymers solution is addressed here by considering a direct numerical simulation of homogeneous isotropic turbulence of a FENE-P fluid in a triply periodic box. On the basis of the DNS data, a scale by scale analysis is provided by using the proper extension to visco-elastic fluids of the Karman-Howarth equation for the velocity. For the microstructure, an equation, analogous to the Yaglom equation for scalars, is proposed for the free-energy density associated to the elastic behavior of the material. Two mechanisms of energy removal from the scale of the forcing are identified, namely the classical non-linear transfer term of the standard Navier-Stokes equations and the coupling between macroscopic velocity and microstructure. The latter, on average, drains kinetic energy to feed the dynamics of the microstructure. The cross-over scale between the two corresponding energy fluxes is identified, with the flux associated with the microstructure dominating at small separations to become sub-leading above the cross-over scale, which is the equivalent of the elastic limit scale defined by De Gennes-Tabor on the basis of phenomenological assumptions.
Turbulent shear flows, such as those occurring in the wall region of turbulent boundary layers, manifest a substantial increase of intermittency with respect to isotropic conditions. This suggests a close link between anisotropy and intermittency. Ho
We investigate the conditional vorticity budget of fully developed three-dimensional homogeneous isotropic turbulence with respect to coherent and incoherent flow contributions. The Coherent Vorticity Extraction based on orthogonal wavelets allows to
The flow of fluids in channels, pipes or ducts, as in any other wall-bounded flow (like water along the hulls of ships or air on airplanes) is hindered by a drag, which increases many-folds when the fluid flow turns from laminar to turbulent. A major
The covariant understanding of dispersion relations as level sets of Hamilton functions on phase space enables us to derive the most general dispersion relation compatible with homogeneous and isotropic spacetimes. We use this concept to present a Pl
We consider the problem of incompressible, forced, nonhelical, homogeneous, isotropic MHD turbulence with no mean magnetic field. This problem is essentially different from the case with externally imposed uniform mean field. There is no scale-by-sca