If there is substantial curvature in the flow pattern (or height field) surrounding a jet streak, then we must account for the centripetal accelerations. Actually, one must consider the curvature of an air parcel trajectory, not the streamline curvature, because the jet streak is propagating, but that requires more analysis than is practical in a forecast environment.

A highly curved trough and attendant westerly jet stream (yellow region) without a wind speed maximum (no along-stream variation of momentum). Solid lines denote geopotential height contours. Thick black vectors represent along-stream ageostrophic winds with magnitudes given by arrow length, as determined by the centripetal acceleration. The flow is in gradient wind balance.

This figure shows that the centripetal accelerations experienced by an air parcel can be substantial enough that the ageostrophic wind is determined primarily by those accelerations. According to the gradient wind equation, the relationship between curvature (K) and the actual wind speed (V) is:

This equation shows that in the presence of cyclonic curvature (K>0), the gradient wind speed is smaller than the geostrophic wind, or in other words, the winds are "subgeostrophic". Now, since the ageostrophic wind is the deviation of the gradient wind from the geostrophic wind:

then clearly the ageostrophic wind will be directed upstream at the base of the cyclonically curved trough, as shown in the above figure. Conversely, supergeostrophic flow at the anticyclonic ridge axis leads to downstream-directed ageostrophic flow there. Synthesis of this information leads to the pattern of divergence and convergence shown in the figure. Thus, the end result of this reasoning is that sinking (rising) motions are expected upstream (downstream) of the trough axis: a 2-cell pattern of vertical motions. This is very different than the pattern predicted by the simple straight jet streak model, yet the latter model is frequently used (in fact, overabused) by the operational forecast community!

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