Numerical studies of frontal motion in the atmosphere-I

Abstract

The motion of frontal disturbances in the atmosphere is studied by the numerical solution of differential equations based upon a two-layer model of an incompressible fluid on a rotating earth. The density of each layer is assumed to be constant. The upper and lower fluids correspond respectively to warm and cold air. In this first attempt, only the motion of the lower cold air layer is studied by assuming, in effect, that the dynamics of the perturbations in the upper warm air layer can be neglected. The numerical study of this simple mechanical model shows that even though thermodynamic processes have been ignored, the occlusion process, characteristic for warm and cold fronts, develops from an initially sinusoidal frontal pattern. Two cases of different initial conditions are examined. Case A: Only the east-west component of wind velocity is initially geostrophic. Case B: Both east-west and north-south components are initially geostrophic. In both cases, computations indicate that the cold front propagates faster than the warm front and that a relatively strong mass convergence zone appears behind the cold front only. This fact suggests the occurrence of severe storms associated with cold fronts, but not with warm fronts in the atmosphere. The numerical method developed here to calculate the movement of the front is based on following the motion of the material “particles” at the front. This method has applications to the numerical solution of a certain class of hydrodynamic flow problems in which the entire boundary of the domain of integration is not given a priori, but must be determined (so-called free-boundary problems).