The meridional scale of baroclinic waves with latent heat release

Abstract

An analytical theory of two-level, moist, quasi-geostrophic baroclinic waves with meridional variation, but without the fl-effect, is developed. The formulation is similar to that of Tang and Fichtl (1983) except that the meridional variation of the waves isallowed. The basic parameters are a rotational Froude number F = (where f is the Coriolis parameter, Sd the static stability in descending portion of the wave, p2 the pressure at the middle level, kd the zonal wave number in the descending portion of the wave, ℓ(=π/D) the meridional wave number and D the meridional extent of the wave) and a heating parameter e which is proportional to the midlevel vertical gradient of the mean flow saturation mixing ratio. For ε ≠ 0 the disturbances are characterized by an unequal zonal length of the ascending or wet portion of the wave (a) and zonal length of the descending or dry portion of the wave (b). The first mode has a small region of strong ascending motion and a large region of weak descending motion (a/b < 1) with the reverse for the second mode (a/b > 1). These features are similar to those obtained by Tang and Fichtl (1983). In the present paper a meridional-scale equation is derived, expressing three possibilities: (i) FORMULA = 0 (no meridional variation of baroclinic waves, discussed in Tang and Fichtl, 1983); (ii) ε = 0 (dry model, discussed in Phillips, 1954, with β-effect ignored, ℓ being arbitrary); and (iii) a biquadratic equation in ℓ/kd. This latter equation essentially contains the information of the influence of latent heat release on the meridional scale of baroclinic waves. The model of meridionally uniform baroclinic waves (ε = 0) and the dry model (e = 0) are singular in that the characteristics of these two models cannot be deduced by setting ℓ/kd → 0 or ε → 0 in this biquadratic equation. For ε < 0.464, the ratio of the meridional extent D of the zonal domain, a + b, is less than 0.7. For a given e and a given F, this ratio is larger for the first mode than for the second mode. The growth rate in the ascending region is equal to that in the descending region. The growth rate depends on both F and ℓ/kd. For a given F, the larger the heating parameter e, the larger the growth rate.

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