Paolo Cifani

Paolo Cifani, Klas Modin, Cecilia Pagliantini et al.

We compare three approaches for structure preserving numerical integration of isospectral flows on quadratic Lie algebras. Such flows originate from Hamiltonian dynamics on the cotangent bundle of the Lie group. It is known, via discrete reduction theory, that symplectic Runge--Kutta methods applied to the cotangent bundle formulation induce isospectral symplectic Runge--Kutta (ISOSYRK) schemes on the Lie algebra. Here, we show that the same symplectic Runge--Kutta method, but applied to the transport formulation of the flow on the Lie group, is equivalent to the corresponding ISOSYRK scheme. We also give numerical results suggesting that the formulation on the Lie group is more efficient for schemes with two or more intermediate stages.

Paolo Cifani, Franco Flandoli, Andrea Zanoni

Modeling turbulent flows by a random Fourier decomposition is a classical procedure in order to use simplified models of turbulence in heat transport and other applications. We carefully investigate the Fourier time series of two-dimensional turbulent flows forced at intermediate scales and identify significant statistical structures. In particular, we find the existence of a typical time correlation length, and propose a stochastic model for the Fourier components. Finally, we compute the transport of a passive tracer under purely convective dynamics by means of direct numerical simulation of the turbulent flow and compare it with the effective diffusion produced by the stochastic model.