Abstract
AbstractMomentum transport by boundary layer turbulence causes a weak synoptic‐scale vertical motion. The classical textbook solution for the strength of this Ekman pumping depends on the curl of the surface momentum flux. A new solution for Ekman pumping is derived in terms of the curl of the geostrophic wind and a term that depends in a nontrivial way on the vertical profile of the turbulent momentum flux. The solution is confined to a boundary layer regime that is vertically well mixed and horizontally homogeneous. The momentum flux is computed from a commonly used bulk surface drag formula and a flux jump relation to capture the entrainment flux of momentum at the top of the boundary layer. It is found that the strength of Ekman pumping is bounded. The weakening of Ekman pumping for enhanced turbulent surface friction can be explained from the fact that it will reduce the magnitude of the horizontal wind. It is demonstrated that entrainment of momentum across the top of the boundary layer tends to diminish the large‐scale divergence of the wind. As momentum transport is parameterized in large‐scale models, the analysis is relevant for the understanding and interpretation of the evolution of synoptic‐scale vertical motions as predicted by such models.
Highlights
Geostrophic flow is at the heart of dynamical meteorology
A new solution for Ekman pumping is derived in terms of the curl of the geostrophic wind and a term that depends in a nontrivial way on the vertical profile of the turbulent momentum flux
The weakening of Ekman pumping for enhanced turbulent surface friction can be explained from the fact that it will reduce the magnitude of the horizontal wind
Summary
Geostrophic flow is at the heart of dynamical meteorology It elucidates why in a synoptic system of (low) high pressure on the Northern Hemisphere the wind vector is tangent to the isobars in a (counter)clockwise direction. The presence of synoptic-scale vertical motion requires the consideration of turbulent boundary layer eddies that act as a drag on the mean flow. As depicted schematically, this friction effect gives rise to a net horizontal transport of air from high to low pressure. Boundary layer eddies cause a cross-isobaric flow in which a net transport of air from high to low pressure occurs This leads to a convergence of air in the low-pressure system and a subsequent large-scale ascending motion. It will be demonstrated that this solution predicts a maximum value for the large-scale divergence of the horizontal wind
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