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

• Published in: Quarterly journal of the Royal Meteorological Society Vol. 146; no. 732; pp. 2981 - 2997
• Main Authors: Renaud, Antoine, Venaille, Antoine
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.10.2020; Wiley Subscription Services, Inc; Wiley
• Subjects: Boundary conditions; Boussinesq approximation; Chaos; Equatorial winds; Fluid dynamics; Fluids; Hydrodynamics; internal waves; Mechanics; Physics; Quasi-biennial oscillation; stratified fluid; Stratosphere; streaming; wave–mean flow interaction; Wind oscillations; Winds
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1002/qj.3821

The Holton–Lindzen–Plumb (HLP) 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 primary 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 HLP 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. Bifurcation diagram of the Holten‐Lindzen‐Plumb model.