On the Holton-Lindzen-Plumb model for mean flow reversals in stratified fluids

Abstract: The Holton-Lindzen-Plumb model describes the spontaneous emergence of mean flow reversals in stratified fluids. It has played a central role in understanding the quasi-biennial oscillation of equatorial winds in Earth's stratosphere and has arguably become a linchpin of wave-mean flow interaction theory in geophysical and astrophysical fluid dynamics. The derivation of the model's equation from primitive equations follows from several assumptions, including quasi-linear approximations, WKB expansion of the wavefield, simplifications of boundary layer terms, among others. Starting from the two-dimensional, non-rotating, Boussinesq equations, we present in this paper a self-consistent derivation of the Holton-Lindzen-Plumb model and show the existence of a distinguished limit for which all approximations remains valid. We furthermore discuss the important role of boundary conditions, and the relevance of this model to describe secondary bifurcations associated with a quasi-periodic route to chaos.