A Generalization of Petterssen's Frontogenesis Function and Its Relation to the Forcing of Vertical Motion

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Abstract
Petterssen' frontogenesis equation relates the Lagrangian rate of change of the magnitude of the horizontal potential temperature gradient, referred to as the frontogenesis function, to invariant kinematic properties of the horizontal velocity field. It is not uncommon in synoptic practice to infer the presence of vertical circulations in frontal regions from the spatial distribution of the scalar frontogenesis function. On the other hand, Hoskins and collaborators have introduced a form of the quasi-geostrophic omega equation in which the dynamical and forcing is proportional to the horizontal divergence of the so-called Q vector. The Q vector is defined as the Lagrangian rate of change following the geostrophic flow of the vector horizontal potential temperature gradient. The Q-vector formalism motivates us to generalize the Petterssen frontogenesis function to apply to the vector horizontal potential temperature gradient. This generalization, referred to as the vector frontogenesis function, c... Abstract Petterssen' frontogenesis equation relates the Lagrangian rate of change of the magnitude of the horizontal potential temperature gradient, referred to as the frontogenesis function, to invariant kinematic properties of the horizontal velocity field. It is not uncommon in synoptic practice to infer the presence of vertical circulations in frontal regions from the spatial distribution of the scalar frontogenesis function. On the other hand, Hoskins and collaborators have introduced a form of the quasi-geostrophic omega equation in which the dynamical and forcing is proportional to the horizontal divergence of the so-called Q vector. The Q vector is defined as the Lagrangian rate of change following the geostrophic flow of the vector horizontal potential temperature gradient. The Q-vector formalism motivates us to generalize the Petterssen frontogenesis function to apply to the vector horizontal potential temperature gradient. This generalization, referred to as the vector frontogenesis function, c...

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