On the transfer of momentum by trapped Lee waves: Case of the IOP 3 of PYREX

The airplane data collected between 4 and 12 km above the Pyrenees during t he intensive observation period (IOP) 3 of the Pyrenees Experiment (PYREX) are analyzed again. A spectral analysis of the velocity and potential tempe rature series shows that the mountain waves are dominated by two oscillatio ns with well-defined horizontal wavenumbers. At nearly all altitudes, at le ast one among these two oscillations can be extracted: the short oscillatio n dominates the signal below 6 km and the long one above. These two oscilla tions contribute to the Reynolds stress below 5 km and not above. Linear steady nondissipative simulations show that the short oscillation is a trapped resonant mode and the long one a leaking, or partially leaking, resonant mode of the background flow. Pseudo-momentum flux budgets show tha t the short resonant mode only contributes to the Reynolds stress at low le vel (here below 3 to 4 km typically) while the long one contributes to the Reynolds stress at all levels. At low level, (below 4 to 6 km typically), t he long mode can induce a decay of the Reynolds stress amplitude, when it p artially leaks toward the stratosphere. Various tests, changing the inciden t flow profiles within limits provided by the different soundings available this day, reveal, on the one hand, that the above findings are quite robus t. On the other hand, they reveal that the resonant modes response is very sensitive to the background flow and orography specifications. In some of the steady linear simulations, the long resonant oscillation has a Reynolds stress that is constant with altitude. In all of them the downw ind extent of the lee waves is overestimated and the waves amplitude is too large. To explain these mismatches with the observations, we present simul ations that last 3 h only, so the resonant modes patterns are everywhere un steady. They show that during their build-up phase, all the leaking modes c an make the Reynolds stress amplitude decays with altitude at low level (he re below 4 to 6 km, typically). At this time, the downstream extent of the waves is also correctly predicted. These linear unsteady simulations also g ive realistic waves amplitude and Reynolds stress profiles if the mountain is cut off to parameterize nonlinear low-level flow splitting. By using a nonlinear model, the simulated waves are matched to that observe d through an adjustment of the parameters of the turbulent diffusion parame terization scheme: with enough dissipation, the model response can become q uite realistic. In these nonlinear simulations, the background flow is chos en so that there is only one resonant mode and this mode does not contribut e much to the Reynolds stress in the inviscid case. When increasing the mou ntain height and the dissipation, the overall structure of that mode stays unchanged, and it never contributes much to the Reynolds stress. This indic ates that the dissipative and nonlinear processes alone are not likely to p roduce the observed low-level stress variations associated with the resonan t modes.