On the effects of the Hadley circulation and westerly equatorial flow on planetary-wave reflection

Abstract

The nonlinear behaviour of quasi-stationary planetary waves that are excited by mid-latitude orographic forcing is considered in a global shallow-water model taken to represent the upper troposphere. The waves propagate toward low latitudes where the background flow is normally weak and the waves are therefore likely to break. Nonlinear pseudomomentum conservation relations are used to quantify the absorption-reflection behaviour of the wave-breaking region. Two different flow scenarios are represented: (i) initial states without a representation of the Hadley circulation, but where the axisymmetric equatorial background flow changes from being weak and easterly to moderate westerly; (ii) initial states that include a representation of the Hadley circulation and that have weak equatorial easterlies. Based on linear arguments, both (i) and (ii) are expected to influence the progression of the wave train. The nonlinear behaviour in the presence of low-latitude westerly background flows is different from linear predictions. For large-amplitude forcing, wave breaking takes place even though there is no zero-wind line in the initial slate, and the cross-equatorial wave propagation that look place for small-amplitude forcing is stopped before it can reach the equator. Nonlinear reflection is found to take place back into the hemisphere of origin but not across to the other hemisphere. In the presence of a Hadley circulation representative of winter conditions, the nonlinear reflection takes longer to get established, i.e. it requires more forcing, 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. A summer Hadley circulation allows wave activity to get to the winter hemisphere. As the forcing is increased, wave breaking occurs and eventually nonlinear reflection.