Leung, T.Y. and Leutbecher, M. and Reich, S. and Shepherd, Th.G. (2019) Atmospheric Predictability: Revisiting the Inherent FiniteTime Barrier. Journal of the Atmospheric Sciences, 76 (12). pp. 38833892. ISSN Online: 15200469 Print: 00224928

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Official URL: https://journals.ametsoc.org/doi/pdf/10.1175/JASD...
Abstract
The accepted idea that there exists an inherent finitetime barrier in deterministically predicting atmospheric flows originates from Edward N. Lorenz’s 1969 work based on twodimensional (2D) turbulence. Yet, known analytic results on the 2D Navier–Stokes (NS) equations suggest that one can skillfully predict the 2D NS system indefinitely far ahead should the initialcondition 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 that when this slope is shallower than −3, 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 system is resolved—which remains practically impossible. This breakdown leads to the inherent finitetime limit. If, on the other hand, the spectral slope is steeper than −3, then the breakdown does not occur. In this way, the apparent contradiction between the analytic results and Lorenz’s theory is reconciled.
Item Type:  Article 

Additional Information:  SFB1114 Preprint: 04/2019 (PrintTitel weicht ab vom PreprintTitel: "Atmospheric predictability: the origins of the finitetime behaviour") 
Subjects:  Physical Sciences > Physics > Environmental Physics > Atmospheric Physics Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
ID Code:  2386 
Deposited By:  Silvia Hoemke 
Deposited On:  04 Dec 2019 13:57 
Last Modified:  24 Nov 2020 14:36 
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