The research reported in this work has been sponsored by the Air Force Cambridge Research Laboratories, under Contract No. AF 19 (628)–5826.
The predictability of a flow which possesses many scales of motion
Article first published online: 18 MAR 2010
1969 Blackwell Munksgaard
Volume 21, Issue 3, pages 289–307, June 1969
How to Cite
LORENZ, E. N. (1969), The predictability of a flow which possesses many scales of motion. Tellus, 21: 289–307. doi: 10.1111/j.2153-3490.1969.tb00444.x
- Issue published online: 18 MAR 2010
- Article first published online: 18 MAR 2010
- Manuscript received October 31, 1968, revised version December 13, 1968
It is proposed that certain formally deterministic fluid systems which possess many scales of motion are observationally indistinguishable from indeterministic systems; specifically, that two states of the system differing initially by a small “observational error” will evolve into two states differing as greatly as randomly chosen states of the system within a finite time interval, which cannot be lengthened by reducing the amplitude of the initial error. The hypothesis is investigated with a simple mathematical model. An equation whose dependent variables are ensemble averages of the “error energy” in separate scales of motion is derived from the vorticity equation which governs two-dimensional incompressible flow. Solutions of the equation are determined by numerical integration, for cases where the horizontal extent and total energy of the system are comparable to those of the earth's atomsphere.
It is found that each scale of motion possesses an intrinsic finite range of predictability, provided that the total energy of the system does not fall off too rapidly with decreasing wave length. With the chosen values of the constants, “cumulus-scale” motions can be predicted about one hour, “synoptic-scale” motions a few days, and the largest scales a few weeks in advance. The applicability of the model to real physical systems, including the earth's atmosphere, is considered.