next up previous contents
Next: Lagrangian code for polymer Up: tesi Previous: Summary   Contents


Conclusions

In this thesis I have presented a numerical and theoretical study of the effects of friction and polymer additives on two-dimensional turbulence.

The Lagrangian description of turbulent transport has been used to demonstrate the equivalence between the statistics of small-scale fluctuations of vorticity in presence of friction and that of a passive scalar field with finite lifetime transported by the same velocity field. This allowed to obtain quantitative predictions for the steepening of the energy spectrum and the scaling exponents of the structure functions of vorticity, in terms of the statistics of finite-time Lyapunov exponents. These results have been validated by means of parallel integration of Navier-Stokes equation in two dimensions, supplemented by a linear fiction term, and of the advection-reaction-diffusion equation for the passive scalar with finite lifetime.

The effects of polymers have been studied by means of the linear viscoelastic model Oldroyd-B. A Lagrangian numerical code, which preserves the symmetries of the model has been developed to obtain accurate measurements of the probability distribution function of polymer elongation, which validate the predictions obtained within the Lagrangian approach. A strong reduction of kinetic energy as a consequence of polymer addition has been observed in numerical simulations of two-dimensional Oldroyd-B model, in agreement with results of soap film experiments. I showed that this phenomenon can be explained and predicted by means of the energy balance of Oldroyd-B model.

I have then studied the effects of polymers on the statistics of finite-time Lyapunov exponents, showing that a strong reduction of Lagrangian chaos occurs. This phenomenon seems to be independent on the dimensionality of the flow.

Finally I considered the effects of polymers on the inverse energy cascade, showing that for large enough elasticity it can be completely suppressed by polymer feedback.


next up previous contents
Next: Lagrangian code for polymer Up: tesi Previous: Summary   Contents
Stefano Musacchio 2004-01-09