Numerical simulation studies of two-Dimensional turbulence: II. Stability and predictability studies

The theoretical predictability of statistically steady two-dimensional turbulence is examined by means of numerical simulations of the time evolution of pairs of almost identical initial flow realizations. It is found that the amplitude of the difference flow field, obtained by subtraction of one realization from the other, typically grows exponentially and maintains a shape-preserving scalar energy spectrum. This difference energy spectrum has its peak at a higher wave number than the spectra of the individual realizations, and the difference vorticity field appears to be highly intermittent. Comparison of the results with Lorenz's recent ideas on flow predictability and Leith's related calculations show partial but inconclusive agreement. Comparisons of the results for models using different forcing mechanisms indicate that the growth of difference, or loss of predictability, does not depend much on the method of forcing.A special perturbation simulation experiment is conducted, in which the mean flow is taken to be a state of two-dimensional turbulence but is artificially held constant in time. The perturbation eventually reaches a shape-preserving exponentially growing form which can be interpreted as the most rapidly growing normal mode for the mean flow and an upper bound to the growth of difference amplitude.