A tale of two paradigm changes, with remarks on unconscious assumptions (Invited Presentation)

Since the writing of Haurwitz's 1941 classic "Dynamic Meteorology", our understanding of global-scale atmospheric circulations, jet formation and other fundamentals has been revolutionized by two mutually-relevant paradigms that took over from the old turbulent momentum-mixing paradigm. Both paradigm changes went in fits and starts over the best part of a century. There was no "Einstein moment" after which everything became clear. The first of the new paradigms says that the global-scale atmosphere is radiation-stress-dominated. That is, large-scale momentum transports are dominated not by turbulent but by wave-induced momentum transports. The second paradigm -- I'll call it the "inhomogeneous PV-mixing paradigm" -- can be traced back nearly a full century to seminal work by G. I. Taylor yet even today is still being evolved, debated, and clarified, as computing power improves. It says not only that potential vorticity (PV) tends to be mixed along stratification surfaces, but also that the mixing tends to be spatially inhomogeneous. Indeed, observed phenomena, including the observed structure of strong jets, show that the spatial inhomogeneity is often strong. It lies entirely outside the scope of standard homogeneous-turbulence theory. The very phrase "turbulence theory" is a misnomer because the reality is often a highly inhomogeneous wave-turbulence jigsaw, with turbulent and wavelike regions closely adjacent and in dynamical symbiosis. The jigsaw fits together dynamically as well as geometrically. Without the wave part one cannot begin to understand even gross angular-momentum budgets. The simplest idealized example that illustrates the symbiosis is not homogeneous-turbulence theory but, rather, the nonlinear Rossby-wave critical layer theory first fully developed by Stewartson, Warn and Warn. A further payoff from these insights has been a breakthrough in understanding the Sun's internal differential rotation.