Modeling Error of $\alpha$-Models of Turbulence on a Two-Dimensional Torus

Luigi C. Berselli (1) , Argus Adrian Dunca (2) , Roger Lewandowski (3, 4) , Dinh Duong Nguyen (3)

1 DMA - Dipartimento di Matematica Applicata [Pisa]
2 UniBuc - University of Bucharest
3 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
4 IRMAR - Institut de Recherche Mathématique de Rennes

This paper is devoted to study the rate of convergence of the weak solutions $u_\alpha$ of $\alpha$-regularization models to the weak solution $bu$ of the Navier-Stokes equations in the two-dimensional periodic case, as the regularization parameter $\alpha$ goes to zero. More specifically, we will consider the Leray-$\alpha$, the simplified Bardina, and the modified Leray-$\alpha$ models. Our aim is to improve known results in terms of convergence rates and also to show estimates valid over long time intervals.

Mots clés: Rate of convergence; $α$-turbulence models; Navier-Stokes Equations

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Luigi C. Berselli, Argus Adrian Dunca, Roger Lewandowski, Dinh Duong Nguyen. Modeling Error of $\alpha$-Models of Turbulence on a Two-Dimensional Torus. Discrete and Continuous Dynamical Systems - Series B, 2021, 26 (9), pp.4613-4643. ⟨10.3934/dcdsb.2020305⟩. ⟨hal-02469048v3⟩