Turbulent Excitation of the Tropical Background and Wave Spectrum

Abstract:

In the Tropics, the upward motion of air within small-scale convection cells not only generates clouds and convection, but also impacts the large-scale flow. Specifically, variations in outgoing longwave radiation in the Tropics peaks at wavenumber-frequency combinations given by the theoretical dispersion curves of zonally propagating equatorial waves, as compared to the background spectrum in between these dispersion curves. The precise mechanism whereby the small-scale convection triggers large-scale waves and forms the background spectrum is not yet fully understood. The goal of this work is to reconsider these process using concepts developed in the fields of nonlinear fluid dynamics and turbulence. A standard practice in studies of the response of turbulent dynamical systems to forcing is to add a stochastic, inhomogeneous, forcing term to the homogeneous nonlinear equations whose linear counterpart is employed in the derivation of the properties of free waves. In the present context, such a stochastic forcing can be thought of as randomly distributed convection scattered about the tropics. Here, the stochastic forcing is applied to the rotating shallow water equations. We demonstrate that turbulent transfer of energy can account for both the wave and the background spectra. The main results consist of a parameter sweep where the magnitude of the applied stochastic forcing, which is concentrated in the zonal wavenumber range 30≤k≤40, is gradually increased from near zero to near-observed values. In these simulations we eventually develop a background and wave spectra that resemble the observed ones, but with these simulations we can use the results of classical turbulent theory to explain why the background spectrum is red and how power becomes concentrated at the wavenumber-frequency combinations where linear theory mandates that waves should develop. These simulations also demonstrate that in the parameter-regime of Earth's tropics, nonlinear turbulent processes are crucial, and a linearized perspective employed in earlier studies misses key aspects of the dynamics.