Concentration of Stationary Measures onto Large Scales in the Fast-Advection Limit of the Stochastically Forced Two-Dimensional Navier-Stokes EquationsNew

This paper investigates the fast-advection limit (ε→0) of stochastically forced two-dimensional incompressible Navier-Stokes equations on the torus. The authors perform numerical simulations at resolution N=128 for four different forcing shells on both square and thin tori, with the advection parameter ε varied over approximately one decade. The study reveals that stationary distributions become increasingly concentrated as the advection parameter approaches zero, providing insights into the statistical behavior of 2D turbulent flows under rapid advection conditions.