Department of Earth System Science

The nonlinear behavior of quasi-stationary planetary waves excited by midlatitude orographic forcing is considered in a three-dimensional primitive equation model that includes a representation of the Hadley circulation. The Hadley circulation is forced by Newtonian cooling to a zonally symmetric reference temperature and vertical diffusion on the zonally symmetric component of the flow. To quantify the effect of the Hadley circulation on wave propagation, breaking, and nonlinear reflection, an initial state with no meridional flow, but with the same zonal flow as the Hadley state, is also considered. In order to allow the propagation of large-scale waves over extended periods, Rayleigh friction is applied at low levels to delay the onset of baroclinic instability.

As in the absence of a Hadley circulation, the waves in the Hadley state propagate toward low latitudes where the background flow is weak and the waves are therefore likely to break. Potential vorticity fields on isentropic surfaces are used to diagnose wave breaking. Nonlinear pseudomomentum conservation relations are used to quantify the absorption–reflection behavior of the wave breaking region. In the presence of a Hadley circulation representative of winter conditions, the nonlinear reflection requires more forcing to get established, but a reflected wave train is still present in the numerical simulations, both for a longitudinally symmetric forcing and for the more realistic case of an isolated forcing. The effect of the thermal damping on the waves is more severe in the current three-dimensional simulations than in the shallow water case considered in an earlier study. Both the directly forced wave train and the reflected wave train are quite barotropic in character; however, in the shallow water case one is essentially assuming an infinite vertical scale.