Abstract
AbstractThis article establishes explicit non-asymptotic ergodic bounds in the renormalized Wasserstein–Kantorovich–Rubinstein (WKR) distance for a viscous energy shell lattice model of turbulence with random energy injection. The system under consideration is driven either by a Brownian motion, a symmetric $$\alpha $$
α
-stable Lévy process, a stationary Gaussian or $$\alpha $$
α
-stable Ornstein–Uhlenbeck process, or by a general Lévy process with second moments. The obtained non-asymptotic bounds establish asymptotically abrupt thermalization. The analysis is based on the explicit representation of the solution of the system in terms of convolutions of Bessel functions.
Funder
Facultad de Ciencias at Universidad de los Andes
Academy of Finland
Finnish Centre of Excellence in Randomness and STructures.
Publisher
Springer Science and Business Media LLC
Reference83 articles.
1. Frisch, U.: Turbulence: The Legacy of A.N. Kolmogorov. Cambridge University Press, Cambridge (1995)
2. Kolmogoroff, A.: The local structure of turbulence in incompressible viscous fluid for very large Reynold’s numbers. CR Acad. Sci. 30, 301–305 (1941)
3. Ditlevsen, P.: Turbulence and Shell Models. Cambridge University Press, Cambridge (2011)
4. Gledzer, E.: System of hydrodynamic type admitting two quadratic integrals of motion. Dokl. Akad. Nauk SSSR 209(5), 1046–1048 (1973)
5. Ohkitani, K., Yamada, M.: Lyapunov spectrum of a chaotic model of three-dimensional turbulence. J. Phys. Soc. Jpn. 56(12), 4210–4213 (1987)