Backwards mixing

Grimaud Pillet (1) , Stephan Fauve (2) , Florence Raynal (1)

1 LMFA - Laboratoire de Mecanique des Fluides et d'Acoustique
2 Physique Non-Linéaire

In three-dimensional time-periodic advection of a passive scalar, there are three non-zero Lya-punov exponents; because of incompressibility, the sum of those exponents is zero. Using direct numerical simulation of the advection-diffusion equation, we show that when one is positive and the two others are negative, spatial structures of the scalar field in the form of filaments are generated by the flow. When reversing the flow in time, we change the sign of all Lyapunov exponents, and obtain sheets. While dimensional analysis suggests that diffusion by thinner structures is larger, so that the sheets, associated to the most negative Lyapunov exponent, should dissipate more rapidly the scalar energy, we find numerically that the scalar energy decay is the same for both types of structures. We prove this result using a symmetry argument on the advection-diffusion operator. This evidences that the decay of the variance of a scalar field is not linked to the sign of the intermediate exponent.

Domaines: Mécanique des fluides [physics.class-ph]

Grimaud Pillet, Stephan Fauve, Florence Raynal. Backwards mixing. 2020. ⟨hal-02426167⟩