Canonical Transfer and Multiscale Energetics for Primitive and Quasigeostrophic Atmospheres

• Published in: Journal of the atmospheric sciences Vol. 73; no. 11; pp. 4439 - 4468
• Main Author: San Liang, X.
• Format: Journal Article
• Language: English
• Published: Boston American Meteorological Society 01.11.2016
• Subjects: Atmospheric models; Barotropic mode; Buoyancy; Classification; Computational fluid dynamics; Conversion; Decomposition; Dynamics; Energy consumption; External pressure; Fluid dynamics; Fluxes; Formalism; Fourier transforms; Friction; Geophysics; Hydrodynamics; Kinetic energy; Loads (forces); Madden-Julian oscillation; Mathematical models; Mechanics; Multiscale analysis; Nuclear electric power generation; Offshore engineering; Potential energy; Primitive equations; Reconstruction; Studies; Transport; Wavelet transforms
• ISSN: 0022-4928; 1520-0469
• DOI: 10.1175/JAS-D-16-0131.1

The past years have seen the success of a novel and rigorous localized multiscale energetics 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 and clarifications of some common misconceptions about multiscale energy. Multiscale equations are derived using a new analysis apparatus—namely, multiscale window transform—with respect to both the primitive equation and quasigeostrophic 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; hence, we 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 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 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 study of the Madden–Julian oscillation.