Do Breaking Mountain Waves Deceierate the Local Mean Flow?

Abstract

Numerical simulations are examined in order to determine the local mean flow response to the generation, propagation, and breakdown of two-dimensional mountain waves. Realistic and idealized cases are considered, and in all instances the pressure drag exerted by flow across an O(40 km) wide mountain fails to produced a significant net mean flow deceleration in the O(400 km) region surrounding the mountain. The loss of momentum in the local patches of decelerated flow that appear in regions of wave overturning directly above the mountain is approximately compensated by momentum gained in other nearby patches of accelerated flow. The domain-average mean flow deceleration in the O(400 km) domain is not determined solely by the divergence of the horizontally averaged momentum flux, ???u?w??, because differences in the upstream and downstream values of ?u2+p provide nontrivial contributions to the total domain-averaged momentum budget. As confirmed by additional simulations in an O(1000 km) wide periodic domain, terrain-induced perturbations in the pressure and horizontal velocity fields are rapidly transmitted hundreds of kilometers away from the mountain and distributed as a small-amplitude signal over a very broad area far away from the mountain. These results suggest that both ???u?w?? and information about the wave-induced horizontal momentum fluxes need to be parameterized in order to completely define the local subgrid-scale forcing associated with mountain wave propagation and breakdown. The forcing for the globally averaged mean flow deceleration can, nevertheless, be determined solely from the vertical divergence of ???u?w??. A simpler description of the local mean flow response to gravity wave propagation and breakdown may be obtained using pseudomomentum diagnostics. When the velocities in the unperturbed cross-mountain flow are positive, the vertical pseudomomentum flux is negative and may be regarded as an upward flux of negative pseudomomentum whose source is the cross-mountain pressure drag. In regions where the waves are steady and not undergoing dissipation the horizontal average of the vertical pseudomomentum flux is constant with height. The sinks for this flux are located in the regions of wave dissipation. Unlike the conventional perturbation momentum, the pseudomomentum perturbations generated by breaking mountain waves are all negative. According to the pseudomomentum viewpoint, the signature of gravity wave drag is a secular increase in the strength of the negative pseudomomentum anomalies generated by wave dissipation. In contrast to the behavior of the perturbation momentum, the average rate of pseudomomentum loss in an O(400 km) domain surrounding the mountain is a significant fraction of the total decelerative forcing provided by the cross-mountain pressure drag. Since pseudomomentum is a second-order quantity that decays rapidly upstream and downstream of the mountain, the horizontally averaged pseudomomentum budget can be closed in open domains of reasonable finite size without explicitly accounting for the pseudomomentum fluxes through the lateral boundaries, and thus, the temporal changes in the horizontally averaged pseudomomentum can be determined solely from the divergence of the vertical pseudomomentum flux. Momentum and pseudomomentum perturbations in trapped mountain lee waves are also investigated. These waves generate nontrivial domain-averaged pseudomomentum perturbations in the low-level flow and should be considered an important potential source of low-level gravity wave drag. These waves are, however, inviscid, and the pseudomomentum perturbations do not grow as a result of dissipation but rather as a result of wave transience through the continued downstream expansion of the wave train.