Effect of Overturning Circulation on Long Equatorial Waves: A Low-Frequency Cutoff

Abstract

Zonally long tropical waves in the presence of a large-scale meridional and vertical overturning circulation are studied in an idealized model based on the intraseasonal multiscale moist dynamics (IMMD) theory. The model consists of a system of shallow-water equations describing barotropic and first baroclinic vertical modes coupled to one another by the zonally symmetric, time-independent background circulation. To isolate the effects of the meridional circulation alone, an idealized background flow is chosen to mimic the meridional and vertical components of the flow of the Hadley cell; the background flow meridionally converges and rises at the equator. The resulting linear eigenvalue problem is a generalization of the long-wave-scaled version of Matsuno's equatorial wave problem with the addition of meridional and vertical advection. The results demonstrate that the meridional circulation couples equatorially trapped baroclinic Rossby waves to planetary, barotropic free Rossby waves. The meridional circulation also causes the Kelvin wave to develop an equatorially trapped barotropic component, imparting a westward-tilted vertical structure to the wave. The total energy of the linear system is positive definite, so all waves are shown to be neutrally stable. A critical layer exists at latitudes where the meridional background flow vanishes, resulting in a minimum frequency cutoff for physically feasible waves. Therefore, linear Matsuno waves with periods longer than the vertical transport time of the meridional circulation do not exist in the equatorial waveguide. This implies a low-frequency cutoff for long equatorial waves.

Effects of Rotation on the Multiscale Organization of Convection in a Global 2D Cloud-Resolving Model

“…In particular, the multi-scale models in the weak and order-one rotation regimes are derived under the standard physical scaling in the tropics (Majda 2007). Consequently, the governing equations across synoptic-and meso-scales are similar to the mesoscale equatorial synoptic dynamics (MESD) model (Majda 2007), and those across planetary-and synoptic-scales resemble the intraseasonal multi-scale moist dynamics (IMMD) model (Biello and Majda 2010;Back and Biello 2018). Notably, the MESD model has been used to study the upscale impact of MCSs on convectively coupled Kelvin waves (CCKWs) Majda 2017, 2018) and 2-day waves .…”