Variational Approach to Closure of Nonlinear Dynamical Systems: Autonomous Case

• Published in: Journal of statistical physics Vol. 179; no. 5-6; pp. 1073 - 1160
• Main Authors: Chekroun, Mickaël D., Liu, Honghu, McWilliams, James C.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2020; Springer; Springer Nature B.V
• Subjects: Analysis; Approximation; Atmospheric models; Backscattering; Closures; Computer simulation; Cut off wavelength; Direct numerical simulation; Fields (mathematics); Invariants; Mathematical and Computational Physics; Nonlinear systems; Numerical analysis; Optimization; Parameterization; Parameters; Physical Chemistry; Physics; Physics and Astronomy; Primitive equations; Quantum Physics; Statistical Physics and Dynamical Systems; Theoretical; Approximate invariance formulas; Parameterizing manifold; Backward–forward systems; Dynamical closure; Optimization

A general approach for the derivation of nonlinear parameterizations of neglected scales is presented for nonlinear systems subject to an autonomous forcing. In that respect, dynamically-based formulas are derived subject to a free scalar parameter to be determined per mode to parameterize. For each...