## Abstract

The airplane data collected between 4 and 12 km above the Pyrénées during the intensive observation period (IOP) 3 of the Pyrénées Experiment (PYREX) are analyzed again. A spectral analysis of the velocity and potential temperature series shows that the mountain waves are dominated by two oscillations with well-defined horizontal wavenumbers. At nearly all altitudes, at least one among these two oscillations can be extracted: the short oscillation dominates the signal below 6 km and the long one above. These two oscillations 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 that the short resonant mode only contributes to the Reynolds stress at low level (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), the long mode can induce a decay of the Reynolds stress amplitude, when it partially leaks toward the stratosphere. Various tests, changing the incident flow profiles within limits provided by the different soundings available this day, reveal, on the one hand, that the above findings are quite robust. 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 downwind extent of the lee waves is overestimated and the waves amplitude is too large. To explain these mismatches with the observations, we present simulations that last 3 h only, so the resonant modes patterns are everywhere unsteady. They show that during their build-up phase, all the leaking modes can make the Reynolds stress amplitude decays with altitude at low level (here below 4 to 6 km, typically). At this time, the downstream extent of the waves is also correctly predicted. These linear unsteady simulations also give 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 observed through an adjustment of the parameters of the turbulent diffusion parameterization scheme: with enough dissipation, the model response can become quite realistic. In these nonlinear simulations, the background flow is chosen so that there is only one resonant mode and this mode does not contribute much to the Reynolds stress in the inviscid case. When increasing the mountain height and the dissipation, the overall structure of that mode stays unchanged, and it never contributes much to the Reynolds stress. This indicates that the dissipative and nonlinear processes alone are not likely to produce the observed low-level stress variations associated with the resonant modes.

*Corresponding author address:* François Lott, Laboratoire de Météorologie Dynamique du CNRS, UPMC Paris 6, case 99, 4 Place Jussieu, 75252 Paris Cedex 05, France. Email: flott@lmd.jussieu.fr