The gradient wind is a balance of the Pressure Gradient Force, centrifugal and Coriolis. A geostrophic wind becomes a gradient wind when the wind begins flowing through curved height contours. The curving motion introduces a centrifugal (outward fleeing) force. The centrifugal effect can be felt when turning through a curve in a car. You stay with the car but it feels like you are being pushed sideways. The gradient wind occurs aloft (no friction) within curved height contours. The wind stays parallel to the height contours throughout the curve. The two examples below will be used to show how the flow stays parallel to the height contours. In the first diagram below (the trough), the outward fleeing centrifugal force is pointing in the same direction as the Coriolis (Northern Hemisphere, Coriolis is to right of path of motion). PGF must balance both centrifugal and Coriolis. For this to happen, the Coriolis needs to shorten so that Coriolis + centrifugal stays equal to the magnitude of the PGF. Since the Coriolis decreases, the wind speed decreases. This allows the wind to stay parallel to the height contours. Without this wind speed reduction the wind would follow a more straight line path that would cause it to move from lower toward higher height contours. Another way to think of this is that the PGF is greater in magnitude than the Coriolis thus the wind is going to bend more in the direction of PGF and this causes the flow to stay parallel to the height contours. In the second diagram below (the ridge), the outward fleeing centrifugal force is pointing in the same direction as the PGF (Northern Hemisphere, to left of path of motion). PGF and centrifugal must balance Coriolis (Northern Hemisphere, Coriolis is to right of path of motion). For this to happen, the Coriolis needs to get longer so that Coriolis = centrifugal + PGF. Since the Coriolis increases, the wind speed increases. This allows the wind to stay parallel to the height contours. Without this wind speed increase the wind would follow a more straight line path that would cause it to move from higher toward lower height contours. Another way to think of this is that the Coriolis is greater in magnitude than the PGF thus the wind is going to bend more in the direction of Coriolis and this causes the flow to stay parallel to the height contours.   |