A key subject of global circulation is interaction between eddies and mean flow. Taylor Identity provides a viable starting point. It soon extended to the elegant formulation of Eliassen-Palmer flux. The EP flux works best within a potential vorticity framework whereas eddies are confined in linear regime. Nevertheless the nonacceleration theorem puts a severe constraint that steady waves can only force meridional overturning circulation, but not the zonal mean flow itself. Therefore a valid eddies-mean flow interaction theory has to include O(η 3) part; where η 3 represent the third or higher order of eddy amplitude. Several attempts (e.g., the generalized Lagrangian mean (GLM) formulation of Andrews and McIntyre 1978) had been made to remedy this deficiency. They are deemed either mathematically too intractable or computationally too complicated to be in use. Over the past decade Noboru Nakamura’s group has been developing a series of works to overcome these obstacles. The doctrine of finite-amplitude wave activity (FAWA), based on the Stokes theorem, can apply to situations where the mean PV gradients are nearly vanishing and eddies become non-linear. These are situations exactly addressing some most important weather events. The FAWA appears to be a revolutionary approach which has been applied to blocking, heat wave, wave guide, Arctic amplification, stratospheric sudden warming, even wild fire climatology, all with various degree of, yet remarkable, successes.

A totally different approach comes from the formalism of geostrophic turbulence, centered by Held and his students. By combining wave and weakly inhomogeneous turbulence it leads to statistical balance between eddies and mean flow. These two schools may be internally related.

This course is aimed to pursuit a research-oriented environment. Literature reviews, dotted with some formal lectures, are designed to steer participants to engaging practical problems. Highly motivated students are encouraged to enjoy the beauty of global circulation’s core thinking..