The Role of Latent Heat Release in Baroclinic Waves-Without β-Effect

Chung-Muh Tang Fluid Dynamics Branch, NASA/Marshall Space Flight Center. AL 35812

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George H. Fichtl Fluid Dynamics Branch, NASA/Marshall Space Flight Center. AL 35812

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Abstract

In this paper we develop the analytical theory of two-level quasi-geostrophic baroclinic waves without β-effect aimed at understanding the role of latent heat release on the development of baroclinic waves.

When the release of latent heat is introduced with pseudo-adiabatic ascent and dry adiabatic descent the width a of the ascending region is different from the width b of the descending region and, furthermore, a static stability-vertical velocity correlation results in the mean state thickness increasing with time. However, the basic state shell is defined a priori, independent of the perturbations, in the formulation of the stability problem. Integro-differential equations for the perturbations are developed. Due to, the mass continuity constraint, the unstable waves in the dry and moist regions are stationary in a frame of reference which translates with the mean zonal wind at the middle level, and the growth rate in the moist region is equal to that in the dry region, the same as in the dry model. We define the parameter F = 2f2/Sdp22kd2, where f is the Coriolis parameter, Sd the static stability in the dry region, p2 the pressure at the middle level, and kd = π/b. The ratio a/b is a function of F. For F > 1, two unstable modes appear. The first mode has a narrow region of strong ascending motion and a wide region of weak descending motion (a/b < 1), and the second mode has a narrow region of strong descending motion and a wide region of weak ascending motion (a/b > 1). As F → 1, the modes become steady and neutral and are characterized by 1) a/b = (Sm/Sd)½ (Sm is static stability in the moist region), and 2) a/b → ∞. As F → ∞, the modes are steady and neutral and are characterized by 1) a/b → 0, and 2) a/b → 1. In comparison with the dry model, the structure of the first unstable mode shows that the ridge and trough of the streamlines shift slightly toward the region of sinking motion, and the warm advection occurs at the node of the vertical motion, while the structure of the second unstable mode shows that the ridge and trough of the streamlines shift slightly toward the region of rising motion, and the cold advection occurs at the node of the vertical motion.

An analysis of the energetics shows the presence of a latent heat release term which directly contributes to the generation of eddy available potential energy. Although this term is small compared to the vertical and horizontal heat transports, latent heat release causes a significant change in the structure of the waves such that large departure in the horizontal heat transport from dry atmospheric values can occur.

The multicomponent solution is also discussed. It is stressed that the first harmonic must be present and even harmonics are allowed provided the vertical motion is upward everywhere in the moist region of the width a and downward everywhere in the dry region of the width b. The solution is not Fourier decomposition in the normal sense because except for the first harmonic odd modes are not allowed.

Abstract

In this paper we develop the analytical theory of two-level quasi-geostrophic baroclinic waves without β-effect aimed at understanding the role of latent heat release on the development of baroclinic waves.

When the release of latent heat is introduced with pseudo-adiabatic ascent and dry adiabatic descent the width a of the ascending region is different from the width b of the descending region and, furthermore, a static stability-vertical velocity correlation results in the mean state thickness increasing with time. However, the basic state shell is defined a priori, independent of the perturbations, in the formulation of the stability problem. Integro-differential equations for the perturbations are developed. Due to, the mass continuity constraint, the unstable waves in the dry and moist regions are stationary in a frame of reference which translates with the mean zonal wind at the middle level, and the growth rate in the moist region is equal to that in the dry region, the same as in the dry model. We define the parameter F = 2f2/Sdp22kd2, where f is the Coriolis parameter, Sd the static stability in the dry region, p2 the pressure at the middle level, and kd = π/b. The ratio a/b is a function of F. For F > 1, two unstable modes appear. The first mode has a narrow region of strong ascending motion and a wide region of weak descending motion (a/b < 1), and the second mode has a narrow region of strong descending motion and a wide region of weak ascending motion (a/b > 1). As F → 1, the modes become steady and neutral and are characterized by 1) a/b = (Sm/Sd)½ (Sm is static stability in the moist region), and 2) a/b → ∞. As F → ∞, the modes are steady and neutral and are characterized by 1) a/b → 0, and 2) a/b → 1. In comparison with the dry model, the structure of the first unstable mode shows that the ridge and trough of the streamlines shift slightly toward the region of sinking motion, and the warm advection occurs at the node of the vertical motion, while the structure of the second unstable mode shows that the ridge and trough of the streamlines shift slightly toward the region of rising motion, and the cold advection occurs at the node of the vertical motion.

An analysis of the energetics shows the presence of a latent heat release term which directly contributes to the generation of eddy available potential energy. Although this term is small compared to the vertical and horizontal heat transports, latent heat release causes a significant change in the structure of the waves such that large departure in the horizontal heat transport from dry atmospheric values can occur.

The multicomponent solution is also discussed. It is stressed that the first harmonic must be present and even harmonics are allowed provided the vertical motion is upward everywhere in the moist region of the width a and downward everywhere in the dry region of the width b. The solution is not Fourier decomposition in the normal sense because except for the first harmonic odd modes are not allowed.

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