Accelerating diffusion on compact Riemannian surfaces by incompressible drift

We construct divergence free vector-fields on compact Riemannian surfaces which push the spectral gap of some diffusion generator above some prescribed value. The resulting diffusion describes some Brownian particle in a stationary incompressible fluid. The spectral gap is an indicator for the speed at which this diffusion converges toward its equilibrium, which corresponds to the uniform distribution. In other terms, we describe efficient fluid motion, to accelerate the convergence to equilibrium of some Brownian particle in a two-dimensional liquid.