Frontal circulations in the presence of small viscous moist symmetric stability and weak forcing

Abstract

AbstractThe Sawyer‐Eliassen (S‐E) equation for frontal circulation is extended to include the effects of eddy viscosity and small negative moist potential vorticity (MPV) under the condition of weak or, at least, not very strong frontogenetic forcing. When MPV is positive, viscosity can be neglected and this equation becomes the conventional S‐E equation. When forcing is absent and MPV is strongly negative, this equation degenerates into the equation of linear viscous conditional (moist) symmetric instability (CSI). By using an idealized distribution of frontogenetic forcing which attenuates exponentially away from the position of maximum forcing, the extended S‐E equation is solved both analytically and numerically for frontal circulations where frontogenetic forcing and negative MPV coexist (but the negative MPV is not so strong as to initiate viscous CSI). The solutions contain slantwise banded substructures on the warm side of the region of maximum forcing. The intensity, structure and scale of the bands are controlled by the competition between the frontogenetic forcing, negative MPV and eddy viscosity with the following characteristics: For a horizontally concentrated forcing whose attenuation length Lb (i.e. the length over which the forcing is reduced by a factor of eπ = 23.1 away from the region of maximum forcing) is less than Ls2 (where Ls is the semi‐geostrophic Rossby radius of deformation), the substructure is single‐banded. The band occurs even before MPV becomes negative. As MPV decreases and becomes negative, the band becomes narrow and intense. For a widespread forcing whose attenuation length Lb is larger than Ls, the substructure is multi‐banded. The multiple bands may occur only if MPV is negative enough, and the first occurring multi‐bands are characterized by wide bands of moist ascent with narrow and weak dry descents embedded between the moist bands. As MPV becomes further negative, the moist bands become narrow, intense and widely spaced. For a moderately widespread forcing whose attenuation length Lb is between Ls/2 and Ls, the substructure changes from wide and weak multiple bands to a narrow and strong single band as MPV becomes increasingly negative. As the coefficient of eddy viscosity increases within a moderately wide range (5‐100m2s−1), the band (or bands) become weak and wide. The theoretical findings are explained physically and compared with observations.