Boundary Layer Effects on Frontogenesis

Charney and Eliassen (1949) first presented a mechanism to communicate the integrated effect of the Ekman boundary layer to the relatively inviscid free atmosphere above. Horizontal convergence in regions of cyclonic vorticity and horizontal divergence in regions of anticyclonic vorticity produce, respectively, ascent and descent at the base of the free atmosphere. This vertical motion, the Ekman suction velocity, serves as a lower boundary condition for flow in the upper layer.

Although this boundary layer parameterization only provides a low-order depiction of boundary layer influence on free atmospheric flows, its usefulness as a valuable research tool has not abated. The reason is that it is simple to implement, and fundamental relationships between the frictionally forced secondary circulation and free atmospheric dynamics may be revealed with relatively little effort. The present talk describes the effect of the Ekman boundary layer on three different models of frontogenesis. 1)Semigeostrophic frontogenesis in a horizontal deformation flow and in a 2)vertical shear flow (the Eady model), and 3)frontogeneis forced by an unbalanced initial state. The effect on frontogenesis, in each case will be described.

1) A confluent horizontal velocity field increases the thermal gradient across the front, but the effect of the Ekman layer is frontolytic. The latter effect appears in the model as a horizontal difluent flow. A finite frontal width may be realized when the frontal gradient and deformation flow are relatively weak, and when the friction is relatively large (Twigg and Bannon, 1998).

2) Eady instability in a semigeostrophic model produces a temperature and a velocity discontinuity in a finite time (Hoskins and Bretherton, 1972). The inclusion of the Ekman layer is frontolytical, but the front will eventually become discontinuous. The frontogenesis is enhanced by a cross front convergent flow, whose intensity increases with frontogenesis. Ekman friction alters the phase relationship between the upper and lower baroclinic wave disturbances, equivalently the unstable growth rate, and the intensity of the cross front circulation diminishes, but not enough to prevent the frontal discontinuity from forming.

3) The initial state consists of an unbalanced horizontal temperature gradient and no motion. At time t>0, frontogenesis occurs with warmer air overlying colder air (Blumen, 2000). The time-dependent Ekman layer spins up quickly, but has relatively little effect on the equally rapid frontogenesis that occurs. The frictionally forced interior circulation will, however, produce frontogenesis in anticyclonic flow where downwelling into the boundary layer occurs.

Each model of frontogenesis responds differently to the same boundary layer parameterization. Other boundary layer parameterizations, which may be used in numerical model forecasts and simulations, should be carefully examined to insure that the model response is physically realizable in each case.