When the relative vorticity of a parcel of air is observed by a person completely removed from the Earth, he or she observes an additional component of vorticity created by the rotation of the Earth. Thus, this

Figure 1-6-Illustration of shear effect opposing the curvature effect in producing vorticity. (A) Negative shear and positive curvature; (B) positive shear and negative curvature.

person sees the total or absolute vorticity of the same parcel of air.

The total vorticity, that is, relative vorticity plus that due to the Earths rotation, is known as the absolute vorticity. As was stated before, for practical use in meteorology, only the vorticity about an axis perpendicular to the surface of the Earth is considered.

In this case, the vorticity due to the Earths rotation becomes equal to the Coriolis parameter. This is expressed as 2oI sin , where w is the angular velocity of the Earth and is the latitude. Therefore, the absolute vorticity is equal to the Coriolis parameter plus the relative vorticity. Writing this in equation form gives: (Za = absolute vorticity)

In addition to locating the areas of convergence and divergence, we must also consider the effects of horizontal wind shear as it affects the relative vorticity, and hence the movement of the long waves and deepening or falling associated with this movement.

The two terms curvature and shear, which determine the relative vorticity, may vary inversely to each other. Therefore, it is necessary to evaluate both of them. Figures 1-7 through 1-10 illustrate some of the possible combinations of curvature and shear. Solid

lines are streamlines or contours; dashed lines are isotachs.

Figure 1-7 represents a symmetrical sinusoidal streamline pattern with isotachs parallel to contours. Therefore, there is no gradient of shear along the contours. In region I, the curvature becomes more anticyclonic downstream, reaching a maximum at the axis of the downstream ridge; that is, relative vorticity decreases from the trough to a minimum at the downstream ridge. The region from the trough to the downstream ridge axis is favorable for deepening. The reverse is true west of the trough, region II.

In figure 1-8 there is no curvature of streamlines; therefore, the shear alone determines the relative vorticity. The shear downstream in regions I and IV becomes less cyclonic; in regions II and III, it becomes more cyclonic. Regions I and IV are therefore favorable for deepening downstream.

In region I of figure 1-9 both cyclonic shear and curvature decrease downstream and this region is highly favorable for deepening. In region III both cyclonic shear and curvature increase downstream and this region is unfavorable for deepening. In region II the cyclonic curvature decreases downstream, but the cyclonic shear increases. This situation is indeterminate without calculation unless one term predominates. If the curvature gradient is large and the shear gradient small, the region is likely to be favorable for deepening.

In region IV, the cyclonic curvature increases downstream, but the cyclonic shear decreases, so that this region is also indeterminate unless one of the two terms predominates.

In region I of figure 1-10 the cyclonic shear decreases downstream and the cyclonic curvature increases. The region is indeterminate; however, if the shear gradient is larger than the curvature gradient, deepening is favored. Region II has increasing cyclonic shear and curvature downstream and is quite unfavorable. In region III, the shear becomes more cyclonic downstream and the curvature becomes less cyclonic. This region is also indeterminate unless the curvature term predominates. In region IV, the shear and curvature become less cyclonic downstream and the region is favorable for deepening.

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