Monday, 26 June 2017
Salon A-E (Marriott Portland Downtown Waterfront)
Motivated by the need to understand the influence of convection on tropical
variability, the interaction between gravity and Kelvin waves and moisture in a shallow water model is
analyzed with an emphasis on physical interpretation. Convection is representated by a simple Betts-Miller type
relaxation, 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 moisture and
convergence are necessarily in-phase at the SQE limit, and that this phase relationship necessarily changes when SQE
is relaxed. A relaxation timescale dependent ``gross moist stability'' and equivalent depth are derived for both
one-dimensional gravity waves and Kelvin waves. In particular, we show that rotation constrains moist Kelvin waves to be unconditionally
stable at the SQE limit in our system. 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, 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-convergence phasing. The phasing between the height, convergence 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, mechanistic
explanations are provided for previous work with 3-dimensional models showing acceleration and
damping of Kelvin waves as the relaxation time increases.
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