NONNORMALITY INCREASES VARIANCE

Recently, a new theoretical and conceptual model of quasigeostrophic t urbulence has been advanced in which eddy variance is regarded as bein g maintained by transient growth of perturbations arising from sources including the nonlinear interactions among the eddies, but crucially without a direct contribution of unstable modal growth to the maintena nce of variance. This theory is based on the finding that stochastic f orcing of the subcritical atmospheric flow supports variance arising f rom induced transfer of energy from the background flow to the disturb ance field that substantially exceeds the variance expected from the d ecay rate of the associated normal modes in an equivalent normal syste m. Herein the authors prove that such amplification of variance is a g eneral property of the stochastic dynamics of systems governed by nonn ormal evolution operators and that consequently the response of the at mosphere to unbiased forcing is always underestimated when considerati on is limited to the response of the system's individual normal modes to stochastic excitation.