Force balances and dynamical regimes of numerically simulated cold fronts within the boundary layer

Abstract

The governing dynamics of numerically simulated cold fronts, as they collapse towards a minimum cross‐frontal scale, are identified by determining force balances and the Rossby and Ekman numbers in frontal regions. A hierarchy of numerical simulations of cold fronts is performed with the Weather Research and Forecasting model and individual terms in the horizontal momentum equations are calculated from the model output to construct force balances. An inviscid, three‐dimensional, idealized front is simulated at three different horizontal grid spacings (100, 20 and 4 km) and then the experiments are repeated with a planetary boundary layer (PBL) parametrization scheme included. Additionally, a full‐physics simulation of the cold front originally analyzed by Sanders is conducted. The leading edge of the idealized, inviscid cold front is characterized by small Rossby numbers and hence balanced dynamics at all three model resolutions. When the PBL scheme is included, large Rossby numbers and unbalanced flow develop at the leading edge of the cold front, but only when the front is simulated at high resolution; at coarse resolution, balanced dynamics remain. The acceleration is in the cross‐front direction and arises due to a localized pressure gradient force. Unlike the inviscid experiments or the coarse‐resolution PBL experiments, the front in the high‐resolution PBL experiment has a large cross‐front thermal gradient, strong forced ascent and sharp surface pressure trough, which enables a large cross‐front pressure gradient force to develop. The dynamics of the Sanders front agree qualitatively with the idealized PBL simulation, but much larger Rossby numbers occur at the leading edge of the Sanders front. This finding indicates that the dynamics of the Sanders front are more unbalanced than the dynamics of the idealized simulations.