  The past years have seen the success of a novel multiscale energetic
formalism in a variety of ocean and engineering fluid applications. In a
self-contained way, this study introduces it to the atmospheric dynamical
diagnostics, with important theoretical updates. Multiscale energy equations
are derived using a new analysis apparatus, namely, multiscale window
transform, with respect to both the primitive equation and quasi-geostrophic
models. A reconstruction of the "atomic" energy fluxes on the multiple scale
windows allows for a natural and unique separation of the in-scale transports
and cross-scale transfers from the intertwined nonlinear processes. The
resulting energy transfers bear a Lie bracket form, reminiscent of the Poisson
bracket in Hamiltonian mechanics, we hence would call them "canonical". A
canonical transfer process is a mere redistribution of energy among scale
windows, without generating or destroying energy as a whole. By classification,
a multiscale energetic cycle comprises of available potential energy (APE)
transport, kinetic energy (KE) transport, pressure work, buoyancy conversion,
work done by external forcing and friction, and the cross-scale canonical
transfers of APE and KE which correspond respectively to the baroclinic and
barotropic instabilities, among others, in geophysical fluid dynamics. A
buoyancy conversion takes place in an individual window only, bridging the two
types of energy namely KE and APE, it does not involve any processes among
different scale windows, and is hence basically not related to instabilities.
This formalism is exemplified with a preliminary application to the
Madden-Julian Oscillation (MJO) study.
