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- Title
Atmospheric Predictability: Revisiting the Inherent Finite-Time Barrier.
- Authors
LEUTBECHER, MARTIN; REICH, SEBASTIAN; SHEPHERD, THEODORE G.; TSZ YAN LEUNG
- Abstract
The accepted idea that there exists an inherent finite-time barrier in deterministically predicting atmospheric flows originates from Edward N. Lorenz's 1969 work based on two-dimensional (2D) turbulence. Yet, known analytic results on the 2D Navier--Stokes (N-S) equations suggest that one can skillfully predict the 2D N-S system indefinitely far ahead should the initial-condition error become sufficiently small, thereby presenting a potential conflict with Lorenz's theory. Aided by numerical simulations, the present work reexamines Lorenz's model and reviews both sides of the argument, paying particular attention to the roles played by the slope of the kinetic energy spectrum. It is found thatwhen this slope is shallower than23, the Lipschitz continuity of analytic solutions (with respect to initial conditions) breaks down as the model resolution increases, unless the viscous range of the real systemis resolved--which remains practically impossible. This breakdown leads to the inherent finite-time limit. If, on the other hand, the spectral slope is steeper than 23, then the breakdown does not occur. In this way, the apparent contradiction between the analytic results and Lorenz's theory is reconciled.
- Subjects
KINETIC energy; COMPUTER simulation; TURBULENCE
- Publication
Journal of the Atmospheric Sciences, 2019, Vol 76, Issue 12, p3883
- ISSN
0022-4928
- Publication type
Article
- DOI
10.1175/JAS-D-19-0057.1