Stochastic inviscid Leray- model with transport noise: Convergence rates and CLT

We consider the stochastic inviscid Leray-alpha model on the torus driven by transport noise. Under a suitable scaling of the noise, we prove that the weak solutions converge, in some negative Sobolev spaces, to the unique solution of the deter-ministic viscous Leray-alpha model. This implies that transport noise regularizes the inviscid Leray-alpha model so that it enjoys approximate weak uniqueness. Interpreting such limit result as a law of large numbers, we study the underlying central limit theorem and provide an explicit convergence rate.(c) 2023 Elsevier Ltd. All rights reserved.