The energetics of wave-driven mean flow oscillations

Abstract

The celebrated laboratory experiment of Plumb and McEwan (J. Atmos. Sci. 1978; 35:1827–1839) represents a dynamical analogue to the quasi-biennial oscillation (QBO), the dominant variability in the equatorial stratosphere. The experiment demonstrates the influence of small-scale fluctuations on the long-time behaviour of larger-scale flows. In the direct numerical simulation of the laboratory experiment Wedi and Smolarkiewicz (Int. J. Numer. Methods Fluids 2005; 47:1369–1374) showed the occurrence of a number of internal gravity wave processes: wave reflection, wave–wave–mean flow interaction, critical-layer formation and subsequent wave breaking, all of which are found in the atmosphere. Here, a comprehensive investigation of the energetics of wave-driven mean flow oscillations is presented. The analysis confirms the accurate incorporation of the external forcing in the simulation, utilizing a generalized time-dependent coordinate transformation. An available potential energy analysis (J. Fluid Mech. 1995; 289:115–128) is used to assess the process of fluid mixing and potential to kinetic energy exchange in wave–mean flow interactions. The results aid to clarify the physical mechanisms as well as the role of numerical dissipation for the onset and the development of zonal mean zonal flow oscillations and distinguish the accuracy of particular numerical choices for the simulation of wave–driven flow phenomena, i.e. flux-form Eulerian or semi-Lagrangian advection algorithms. Copyright © 2005 John Wiley & Sons, Ltd.