Analytic Study of Shell Models of Turbulence
Peter Constantin, Boris Levant, Edriss S. Titi
Abstract
In this paper we study analytically the viscous `sabra' shell model of energy turbulent cascade. We prove the global regularity of solutions and show that the shell model has finitely many asymptotic degrees of freedom, specifically: a finite dimensional global attractor and globally invariant inertial manifolds. Moreover, we establish the existence of exponentially decaying energy dissipation range for the sufficiently smooth forcing.
Create a lesson
Related papers
High-order stabilized matrix-free simulation of rotating mixing devices using the Mortar Element Method
B. Campos, P. Munch, V. O. Ferreira et al.
How well can Diffusion Models learn Lagrangian-Tracer Statistics in Non-reciprocal Turbulence?
Pratyush Jha, Biswajit Maji, Rahul Pandit
Dynamical slowdown, bottlenecks, and multiscaling in Voigt-regularised turbulence
Anikat Kankaria, Bikram Pal, Edriss S. Titi et al.
Energy transfer and scale organisation in dense canopy turbulence
Riccardo Bertoncello, Alessandro Chiarini, Giulio Foggi Rota et al.
Stochastic Transport and Wave Interactions for Multiscale Surface Gravity Waves: Part II: Kinetic Theory and Ocean-Wave Applications
E. Mémin, B. Chapron, A. Debussche et al.
High-resolution in situ analysis of biomass pyrolysis by combining quantitative synchrotron μCT and 3D particle-resolved simulations
Emeric Boigné, Mohamed M. Ahmed, Collin Foster et al.