Linear model of turbulent cascades and fractional fields

Speaker: Ricardo Grande Izquierdo

Abstract: In this talk, we will propose a linear SPDE that serves as a toy model for the
transfer of energy in fully developed fluid turbulence. In order to dissipate the energy
that is constantly injected into the system, our “fluid” will transfer the energy from large
scales towards small scales, leading to a loss of regularity at infinite time.
We will illustrate these results with numerical simulations. First, we will present some
shortcomings of pseudo-spectral methods based on the FFT. Next, we will propose a
finite volume method that is well-adapted to the roughness of the forcing and solution.
This is joint work with G.B. Apolinário, G. Beck, C.-E. Bréhier, L. Chevillard, I. Gallagher,
and W. Ruffenach.