Abstract: Pour a drop of milk into a cup of coffee. We know from experience that after a few moments of stirring, the mixture becomes homogeneous. In this talk, we study the advection of a passive scalar (the concentration of milk) under a random fluid (coffee) velocity on the torus. We prove, when the velocity solves the 2d stochastic Navier–Stokes equations on the torus, that the scalar converges exponentially to its mean. Our result applies even when only finitely many (as few as 4) Fourier modes are randomly forced. Joint with Keefer Rowan (EPFL).
