Analytical and Numerical Analyses for Synoptic Eddy and Low-Frequency Flow Feedback

The two-way interaction between synoptic eddy and low-frequency flow (SELF) has been recognized to be important for the low-frequency variability of the atmosphere circulation. By considering a stochastic basic flow that captures the observed synoptic eddy statistics, we obtained both first and higher order approximations for a linear closure of the SELF feedback. The validity of the first order approximation depends on the intensity of the eddy variance. The first order approximation breaks down only when the level of eddy variance is unrealistically large. Under observed level of the synoptic eddy variance, we demonstrated that the first-order approximation is largely as good as high order approximations. Direct numerical ensemble simulations of the linearized model with stochastic basic state also confirm the validity of the first order approximation. Moreover, forced solutions under the external forcing are analyzed to delineate the importance of the SELF feedback in generating the patterns of low-frequency modes.