Rossby waves and two-dimensional turbulence in the presence of a large-scale zonal jet

Abstract

This dissertation represents a theoretical, numerical, and observational study of barotropic waves and turbulence in an inhomogeneous background flow environment. The theoretical aspects of the work are simplified by restricting attention to the two-dimensional doublyperiodic beta-plane, and in nearly every respect to large-scale zonal flows which are barotropically stable (in a normal-mode sense). The role of the flow inhomogeneity is investigated by considering both nonlinear and linear theory of wave, mean-flow interaction; the key concept to emerge is that of induced spectral transfer of conserved wave quantities by the basic-state flow. Along the way, some new nonlinear conservation laws are derived. In the special case examined of a large-scale zonal jet, the wave enstrophy is approximately conserved in a fully nonlinear sense, and the wave, mean-flow interaction may be characterized as an induced spectral transfer of the wave enstrophy along lines of constant zonal wavenumber k. Because of the scale separation, the linear part of the interaction problem can be closed by applying WKB ray-tracing theory. The turbulent dynamics act to smooth the spectral gradients by irreversible mixing of wave enstrophy; their closure is less easily quantified. The theoretical ideas are tested by performing numerical simulation experiments of both the spin-down and forced-dissipative equilibrium variety. In particular, the nature of the wave, mean-flow interaction can be identified by examining the interaction terms as functions of the meridional wavenumber X for fixed k. In so doing one can determine the point at which irreversible nonlinear dynamics take over from reversible linear dynamics; while the latter are characterized by induced transfer of enstrophy along lines of constant k, the former operate by diffusing energy and enstrophy across such contours. Finally the ideas of the thesis are applied to atmospheric data, and the results used to interpret the observed nonlinear spectral fluxes of kinetic energy and of enstrophy, as well as the interaction between the stationary (viz. one-month time-mean) and transient flow components.