Energy spectra in viscoelastic turbulence

A set of new equations addressing the spectral balance of turbulent fluctuations in dilute polymer solutions has been recently derived and discussed (Casciola and De Angelis, 2007 [13]). An appropriate choice for the polymer descriptor with respect to the traditional one led, at least for mild stretching of the chains, to an L2L2 structure for the total free energy density of the system, thus allowing for the extension of the classical tools for addressing energy fluctuation dynamics to the case of polymeric fluids. Here the resulting spectral decomposition of the energy of the system is discussed by means of numerical simulations for both homogeneous and wall bounded viscoelastic turbulent flows. Some preliminary considerations on the results in the context of the classical theories of viscoelastic turbulence are offered.

► The spectral balance of turbulent fluctuations in polymer solutions is addressed.
► An appropriate choice for the polymer descriptor allows this.
► Numerical results for both homogeneous and wall turbulent flows are reported.
► A discussion in the context of the theories of viscoelastic turbulence is offered.