9.3: Force Balances

The five forces from above affect aspects of horizontal wind speed and direction, and result in a number of common force balances found throughout Earth’s atmosphere.

Geostrophic Balance

Geostrophic balance is arguably the most important force balance in the atmosphere and holds nearly all the time, except for a few specific cases scenarios to be discussed later. When in geostrophic balance, wind in the atmosphere has a balance between the pressure gradient force and the Coriolis force. In geostrophic balance, \(PGF = CF\). The resulting wind is called a geostrophic wind. Setting the equation for \(CF\) and \(PGF\) equal to each other and solving for u gives the following equation for \(U_{\text {geos }}\).

\[U_{\text {geos }}=\frac{P G}{2 \cdot \rho \cdot \Omega \cdot \sin (\phi)} \nonumber \]

Because geostrophic winds are dependent on the pressure gradient, geostrophic winds are faster when isobars are closely spaced.

A number of assumptions are implicit to geostrophic balance. Geostrophic balance applies only under the following conditions: large temporal (>12 hrs) and large spatial (> a few km) scales; above the ABL when no surface friction is acting on the air; winds are steadily moving in a straight direction (no acceleration, negligible vertical velocity); finally, because the Coriolis force is important for the balance, it cannot hold at the equator when the \(CF\) is 0. The typical bounds are often given as >2° latitude.

The path of the geostrophic wind is parallel to the isobars. In the Northern Hemisphere, the wind direction is parallel to the straight isobars with the low pressure to the left side of wind. In the Southern Hemisphere, the direction is parallel to the straight isobars with the low pressure to the wind’s right. The image below shows the force balance present in a geostrophic wind in the northern hemisphere.

Geostrophic wind force diagram in the northern hemisphere (Image Created by Shintaro Russell via Paint.net).

To get into geostrophic balance, moving air will undergo 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 finds itself in a balance between the \(PGF\) and the \(CF\) moving parallel to the isobars instead of across them.

Gradient Wind

This 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 if they are curved, but a different name is needed because the force balance includes one more component. Compared to geostrophic winds, gradient winds feature a balance between the Coriolis force, the pressure gradient force, and the centrifugal force. The centrifugal force arises because the air is flowing on a curved path. The centrifugal force acts in the same direction as the coriolis force, opposite the pressure gradient force.

Gradient wind force diagram (Image Created by Shintaro Russell via Paint.net).

Atmospheric Boundary Layer

Balanced wind in the atmospheric boundary layer (ABL) occurs when there is a balance between the pressure gradient force, Coriolis force, and the frictional drag force. Both wind shear turbulence and convective turbulence cause drag, which results in the ABL wind being slower than geostrophic (subgeostrophic), and causes the wind to cross isobars toward the low pressure.

Atmospheric boundary layer wind force diagram (Image created by Shintaro Russell via Paint.net).

Again, the frictional drag force acts in the plane of motion and slows down the wind speed. The pressure gradient force doesn’t change, but because the wind speed is slower, the Coriolis force is weaker. When that happens the wind cannot balance the pressure gradient force, it is pulled more by the pressure gradient force, and turns toward the low pressure.

Cyclostrophic Wind

Cyclostrophic wind occurs at smaller cyclonic scales (at the mesoscale) such as tornadoes, waterspouts, and even the center of a tropical cyclone. Because the scale is small, the Coriolis force does not play a role. When a small cyclonic scale such as a tornado first forms, both tangential winds and centrifugal force increase much faster than the Coriolis force due to the very strong pressure gradient force. As a result, centrifugal force balances with the pressure gradient force, ignoring the negligible effects of Coriolis force. 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. For anticyclones or highs, however, they do not typically have strong pressure gradients. Thus, winds around the high are too weak to be in cyclostrophic balance.

Cyclostrophic wind force diagram where the pressure gradient force is balanced by the centrifugal force (Image Created by Shintaro Russell via Paint.net).

All of the wind balances discussed (geostrophic balance, gradient wind, ABL wind, and cyclostrophic wind) occur in Earth’s atmosphere under differing conditions. The following chapters will make these applications clearer and you can check back here for reference.

Chapter 10: Questions to Consider

1. Explain why wind occurs.
2. What are u, v, and w?
3. Which forces influence the direction and speed of horizontal winds?

4. Query \(\PageIndex{1}\)

5. Drag the terms to their correct position:

Query \(\PageIndex{2}\)

Selected Practice Question Answers:

Query \(\PageIndex{3}\)