Approximate dynamical equations for fronts modified by the planetary boundary layer

The planetary boundary layer (PBL) strongly modifies the structure of surface fronts; yet standard theories of frontogenesis ignore the PBL. As a first step toward understanding the effects of the PBL on frontogenesis, dominant terms are estimated through a scale analysis in an attempt to identify approximations to the primitive equations that are useful near fronts and within the planetary boundary layer. The scaling reveals the absence of small parameters in such flows and emphasizes the importance of turning of the wind with height in determining the frontal dynamics. Although without small parameters the scale analysis is at most suggestive, it indicates that the geostrophic momentum and Ekman momentum approximations will not be accurate, and that the cross-front acceleration may in practice be negligible, as proposed by Cullen. Analysis of a thin viscous boundary layer beneath a front supports these conclusions, as do diagnostics applied to numerical simulations. The scale analysis and diagnostic results together suggest that the frontal PBL may have intrinsic dynamics, unlike an Ekman layer, which is directly slaved to the interior flow.