The Stability of Wet and Dry Bent-Over Plumes

1 February 1973

journal article
Published by American Meteorological Society in Journal of Applied Meteorology

Vol. 12 (1) , 133-139
https://doi.org/10.1175/1520-0450(1973)012<0133:tsowad>2.0.co;2

Abstract

Let (Γ^*_aP/T_P) − (Γ^*/T_E^*) = k_P and (Γ^*_aE/T_E) − (Γ^*/T_E^*) = k_E, where suffix P denotes a plume element and E the surroundings of the element, T is absolute temperature, Γ_a^* a modified adiabatic lapse rate, T_E^* an absolute virtual temperature of the surroundings, and Γ^* the lapse rate of T_E^*. It is argued that the path of the plume element is unstable either if, in a sufficiently deep layer of the atmosphere surrounding the plume, k_E < 0, or if k_E ≥ 0 and k_P < 0. If k_E ≥ 0 and k_P = 0, the element is neutrally stable; if k_E ≥ 0 and k_P > 0, the element is stable. If k_E ≥ 0 and k_P is a positive constant, the plume element oscillates in the vertical with frequency N^*/(2π), where N^*2 = gΛ_P²k_P, g is the gravitational acceleration, and Λ_P is a constant. Also 0.32 < Λ_P < 0.86 approximately. The theory does not apply either if k_E > 0 and a great deal of the gravitational potential energy is transformed into energy of internal gravity wives, or if the plume sheds a great deal of fluid at a sharp inversion.

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