6.2: Force Balances

Geostrophic Balance

The four forces affect horizontal wind speed and direction, resulting in several common force balances throughout Earth’s atmosphere. Geostrophic balance is arguably the most important force balance in the atmosphere and holds nearly all the time, except for a few specific cases, as discussed later. When the pressure-gradient force and the Coriolis force are equal and opposite, they balance each other out, and the wind is said to be in Geostrophic Balance. In geostrophic balance, \(PGF = CF\). The resulting wind is called a geostrophic wind, and it flows parallel to isobars. Because geostrophic wind speed depends on the pressure gradient, winds are faster when isobars are closely spaced. In the Northern Hemisphere, the wind direction is parallel to the straight isobars, with low pressure to the left of the wind. In the Southern Hemisphere, the direction is parallel to the straight isobars with the low pressure to the wind’s right. Figure \(\PageIndex{1}\) shows the force balance present in a geostrophic wind in the northern hemisphere.

Figure \(\PageIndex{1}\): Geostrophic wind force balance in the northern hemisphere includes the Pressure Gradient Force pulling the wind towards the low pressure and the Coriolis Force deflecting it to the right. As a result, geostrophic wind flows parallel to the isobars. (CC BY-SA 4.0; Shintaro Russell via Atmospheric Processes and Phenomena).

To achieve geostrophic balance, moving air undergoes geostrophic adjustment. First, air feels the pressure field (\(PGF\)) and begins moving from high to low pressure. Next, the Coriolis force (\(CF\)) deflects the object’s direction once it is in motion. Finally, the air is in balance between the \(PGF\) and the \(CF\), moving parallel to the isobars rather than across them.

Gradient Wind

The next force balance applies when air is not moving in a straight line. Gradient winds are winds flowing along curved isobars. Winds typically blow along isobars, even when they are curved, but a different name is needed because the force balance includes an additional component. Compared to geostrophic winds, gradient winds feature a balance between the Coriolis force, the pressure gradient force, and the centrifugal force. Centrifugal force arises because the air is flowing along a curved path. The centrifugal force acts in the same direction as the Coriolis force, and the pressure gradient force acts in the opposite direction, as shown in Figure \(\PageIndex{2}\).

Figure \(\PageIndex{2}\): Gradient wind force balance includes the Pressure Gradient Force pulling the wind towards the low pressure, the Coriolis Force, and the Centrifugal force deflecting it to the right and opposite the low pressure. As a result, Gradient wind flows along curved isobars. (CC BY-SA 4.0; Shintaro Russell via Atmospheric Processes and Phenomena)

Atmospheric Boundary Layer

Balanced wind near the surface occurs when the pressure-gradient force, the Coriolis force, and the frictional drag force are in balance. The frictional drag force acts in the opposite direction to the wind's motion, reducing wind speed at altitudes below 1000 m. The pressure gradient force doesn’t change, but because the wind speed is slower, the Coriolis force is weaker. When that happens, the Coriolis force cannot balance the pressure-gradient force. Thus, the wind is pulled more by the pressure gradient and turns toward the low-pressure system, as shown in Figure \(\PageIndex{3}\).

Figure \(\PageIndex{3}\): Atmospheric boundary layer or surface wind force balance includes the Pressure Gradient Force pulling the wind towards the low pressure, the Coriolis Force deflecting it to the right, and the Frictional Drag Force opposite to the direction of wind. As a result, surface wind angles towards the low-pressure system. (CC BY-SA 4.0; Shintaro Russell via Atmospheric Processes and Phenomena)

Cyclostrophic Wind

Cyclostrophic wind occurs at smaller cyclonic scales (mesoscale), such as tornadoes, waterspouts, and even at the center of a tropical cyclone. Because the scale is small, the Coriolis force is negligible. When a small cyclonic scale, such as a tornado, first forms, both the tangential winds and the centrifugal force increase much faster than the Coriolis force due to the very strong pressure gradient. As a result, the centrifugal force balances the pressure gradient force, as shown in Figure \(\PageIndex{4}\), with the Coriolis force neglected. Because the scale is small and independent of the Coriolis force, the direction of cyclostrophic winds can be either clockwise or counterclockwise in both hemispheres. Anticyclones (highs), however, typically lack strong pressure gradients. Thus, winds around the high are too weak to be in cyclostrophic balance.

Figure \(\PageIndex{4}\): Cyclostrophic wind force diagram where the centrifugal force balances the pressure gradient force. The Pressure Gradient Force pulls the wind towards the low pressure, while the Centrifugal Force pulls it outward. If they balance each other, the wind blows at a constant speed around the low-pressure system. (CC BY-SA 4.0; Shintaro Russell via Atmospheric Processes and Phenomena)

All of the wind balances discussed (geostrophic balance, gradient wind, surface wind, and cyclostrophic wind) occur in Earth’s atmosphere under differing conditions. The following chapters will clarify these applications.