Séminaire
Motivated by the need to interpret the influence of convection schemes on tropical variability, the interaction between gravity-driven waves and moisture in a shallow water model is analyzed with an emphasis on physical interpretation. A Betts-Miller type convective parameterization is used, and analytical solutions for the influence of moisture on wave speed and stability are obtained, both at the limit of a vanishing convective relaxation timescale (or “strict quasi-equilibrium” (SQE)) and for finite relaxation timescales. We show that the divergence and moisture fields are exactly out of phase only when the system is at the SQE limit. A relaxation timescale dependent “gross moist stability” and equivalent depth are derived for both one-dimensional gravity waves and Kelvin waves.
The wavenumber dependence of the effect of moisture is also analyzed, and it is seen that for any given value of the convective relaxation time, the larger scale waves are always closer to SQE than the smaller scale waves, as a natural consequence of the equivalence between SQE and the moisture-divergence phasing. The phasing between the height, divergence and moisture fields is calculated, and the behavior of moist gravity and Kelvin waves for finite relaxation timescales is explained using the phase differences between the various fields. Using this analysis, physically based explanations are provided for the results of prior GCM-based studies.
bruno.deremble@ens.fr