Atmospheric Frontogenesis: A Numerical Experiment

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  • 1 Massachusetts Institute of Technology, Cambridge
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Abstract

The objective of this study is to produce a narrow frontal zone from a field which initially contains only large-scale variations. In the model, all quantities except the temperature and pressure are independent of y (latitude), and these have y derivatives which are only functions of z. The hydrostatic Boussinesq equations are employed, and friction, heating, and the variation of f are neglected. In the experiment a growing baroclinic wave distorts itself in such a way that a cold frontal zone is produced. Comparative integrations with two different values of Δx indicate that the front would become discontinuous within a finite period of time if Δx were made arbitrarily small.

A crude analytical solution is obtained which has the main characteristics of the numerical solutions. Mathematically, the analytical solution is similar to those which describe the formation of shocks and pressure jumps. Physically, the frontal case is quite different because the vorticity is always much larger than the divergence.

Abstract

The objective of this study is to produce a narrow frontal zone from a field which initially contains only large-scale variations. In the model, all quantities except the temperature and pressure are independent of y (latitude), and these have y derivatives which are only functions of z. The hydrostatic Boussinesq equations are employed, and friction, heating, and the variation of f are neglected. In the experiment a growing baroclinic wave distorts itself in such a way that a cold frontal zone is produced. Comparative integrations with two different values of Δx indicate that the front would become discontinuous within a finite period of time if Δx were made arbitrarily small.

A crude analytical solution is obtained which has the main characteristics of the numerical solutions. Mathematically, the analytical solution is similar to those which describe the formation of shocks and pressure jumps. Physically, the frontal case is quite different because the vorticity is always much larger than the divergence.

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