17.13: Geostrophic Flow

Essential to Know

• Horizontal pressure gradients exert a force that accelerates fluid molecules in the direction of pressure decrease on the gradient. The acceleration increases as the strength of the pressure gradient increases.
• The Coriolis effect deflects fluids that flow on a pressure gradient until they flow across the gradient. The flow then continues along a line of constant pressure (isobar) as a geostrophic flow.
• Geostrophic flow conditions occur when the pressure gradient force is balanced by the Coriolis deflection.
• Geostrophic wind and current speeds are determined by the steepness of the pressure gradient. Wind or current speed increases as the steepness of the gradient increases.
• Geostrophic wind or current speed and direction can be determined from contour maps. The direction of flow is parallel to the isobars, and the speed is higher where the pressure gradient is steeper (isobars are closer together).
• Geostrophic winds and currents flow counterclockwise around low-pressure zones and clockwise around high-pressure zones in the Northern Hemisphere. In the Southern Hemisphere, they flow clockwise around low-pressure zones and counterclockwise around high-pressure zones.

Understanding the Concept

The atmosphere and ocean waters are stratified fluids (CC1), in each of which density decreases with increasing distance from the Earth’s center. The only exceptions are in limited areas where stratification is unstable. It is in these areas of unstable stratification that density-driven vertical motions of the fluid occur.

If the oceans or atmosphere were at equilibrium, density would be uniform at any one depth or altitude. The vertical density gradient would be the same everywhere, so the total weight of the overlying water and/or air column at a specific depth or altitude would be the same everywhere. Because this total weight determines atmospheric or water pressure, pressure would be uniform at any depth or altitude.

Neither the atmosphere nor the oceans is at equilibrium, because the density of atmospheric gases and ocean water is altered locally by changes in such factors as air or water temperature, dissolved salt concentration in the water, and water vapor pressure in the air (Chaps. 5, 7). Consequently, the vertical distribution of density in both oceans and atmosphere varies from place to place, and there are horizontal variations of pressure at any given height in the atmosphere or depth in the oceans.

Surfaces that consist of points of equal altitude or depth are referred to as horizontal or level surfaces. However, these surfaces are actually spherical because the Earth is a sphere. Horizontal pressure gradients develop in the oceans as a result of density differences between water masses and also because winds tend to move ocean surface waters, causing the water to pile up in some locations (Chap. 8).

Where there is a horizontal pressure gradient, the fluid is subject to a force that tends to accelerate molecules from high-pressure areas toward low-pressure areas. The acceleration is greater when the pressure gradient is steeper. We perform one of the simplest demonstrations of acceleration along a pressure gradient every time we open a soda bottle or can. Once they are free to do so, the gas molecules in the high-pressure zone within the bottle are accelerated toward the lower pressure outside.

In our soda bottle experiment, the density gradient is extremely steep because the pressure difference between the air outside the bottle and the gas in the bottle is large, and the distance between the high-pressure zone inside the bottle and the low-pressure zone of the surrounding air is very short. When we open the bottle, gas molecules in the high-pressure zone are accelerated very rapidly and must move only a short distance to reach the low-pressure zone. As a result, the pressure equalizes almost instantaneously. In contrast, the pressure differential between horizontally separated high- and low-pressure zones in the oceans and atmosphere is very small, and these zones are separated by much greater distances. Consequently, the accelerations produced by atmospheric and oceanic horizontal pressure gradients are small. In addition, air or water does not flow directly from the high-pressure zone to the low-pressure zone, because the air and water molecules are subject to the Coriolis effect (CC12) once they have been set in motion.

To understand how motions induced by the pressure gradient and Coriolis effect interact, consider the following facts. Freely moving objects, including air or water molecules, actually travel in straight paths unless acted on by another force, such as the pressure gradient. The Coriolis deflection is only a perceived deflection seen by an observer on the rotating Earth. However, from our rotating frame of reference, the freely moving object is deflected cum sole. In Figure CC12-11, we can see that the magnitude of the deflection and the rate of increase both increase with time. These are the characteristics of an acceleration in the direction 90° cum sole to the direction of motion, and this “acceleration” increases with the object’s speed (Fig. CC12-11).

We can now examine what happens when a fluid begins to flow in response to a horizontal pressure gradient. The fluid is accelerated down the pressure gradient from the high-pressure region toward the low-pressure region. As it begins to move, it is deflected by the Coriolis effect. The faster it moves, the greater is the Coriolis deflection (CC12). The direction of motion thus turns away from the direct path down the pressure gradient, to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. As the moving fluid is deflected, the pressure gradient acceleration continues to act toward the low-pressure region while the Coriolis deflection continues to act at 90° cum sole to the changed direction of flow. The speed increases as the molecules are accelerated, thus increasing the Coriolis deflection.

The molecules continue to accelerate while the direction of flow is progressively turned cum sole until the flow is directed across the pressure gradient along a contour of equal pressure (Fig. CC13-1). When the flow is in this direction, the pressure gradient, acceleration, and Coriolis deflection act in opposite directions and balance each other. The speed of the fluid at this balance point is determined by the steepness of the pressure gradient because stronger pressure gradients cause greater accelerations that must be balanced by greater Coriolis deflections, which increase with increasing speed (CC12).

Figure CC13-1. When a current is initiated on a horizontal pressure gradient, the initial direction of motion is directly down the gradient. However, as it moves, the water mass is deflected by the Coriolis effect. It accelerates and is deflected until it flows directly across the pressure gradient, and the pressure gradient force is balanced by the Coriolis deflection. This is a “geostrophic” current. If the pressure gradient is steeper, the acceleration is greater, and the geostrophic current is faster, but it is still balanced by the greater Coriolis deflection associated with the higher speed.

This type of flow, in which the pressure gradient and Coriolis deflection are balanced, is called geostrophic flow, and the moving air or water masses are geostrophic winds or geostrophic currents. The most important features of geostrophic winds or currents are that the flow is directed along contours of equal pressure within a pressure gradient, and that wind or current speed is determined by the steepness of the pressure gradient.

Geostrophic flows are almost never aligned exactly along the contours of equal pressure on the pressure gradient. The reason is that pressure gradients are continuously changing in response to changes in the factors that create them, such as wind stress on the oceans and convection in the atmosphere (CCS3). In addition, friction between moving air masses and the ground or ocean surface, or between ocean water and the seafloor, reduces the Coriolis deflection. Thus, geostrophic winds at the surface and currents near the seafloor do not flow exactly along contours of equal pressure. Instead, they are aligned generally along these contours but offset toward the center of low-pressure zones and away from the center of high-pressure zones.

Horizontal pressure gradients are usually shown as maps of lines of equal pressure called isobars. Most weather maps in newspapers and on television are of this type. The isobaric maps in Figure CC13-2 show high- and low-pressure zones and the pressure gradients between these zones. The pressure difference between adjacent isobars is the same for all adjacent isobars at all locations on each map. The gradient is steeper where the isobars are closer together. Therefore, the spacing of the isobars reveals the steepness of the pressure gradient (the change in pressure per unit distance).

Figure CC13-2. Isobaric contour maps can be used to deduce the wind (or current) speeds and directions associated with the isobars. The contour map examples in this figure show circulation at (a) a low-pressure zone in the Northern Hemisphere, (b) a high-pressure zone in the Northern Hemisphere, (c) a low-pressure zone in the Southern Hemisphere, and (d) a high-pressure zone in the Southern Hemisphere. Note that the directions of rotation are opposite for the two hemispheres. Winds blow counterclockwise around a low-pressure zone and clockwise around a high-pressure zone in the Northern Hemisphere, and in the reverse directions in the Southern Hemisphere. 

Most upper-air wind and ocean current systems are geostrophic, and their flow direction is nearly parallel to the pressure contours. As a result, pressure contour maps can be used to estimate both the speed and direction of winds or currents. The wind or current direction is parallel to the isobars, and the speed can be estimated from the pressure gradient. Because the Coriolis deflection is to the right in the Northern Hemisphere, winds and currents in this hemisphere flow counterclockwise around low-pressure zones (Fig. CC13-2a) and clockwise around high-pressure zones (Fig. CC13-2b). In the Southern Hemisphere, the deflection is to the left, and winds and currents flow clockwise around low-pressure zones (Fig. CC13-2c) and counterclockwise around high-pressure zones (Fig. CC13-2d). The wind or current speed is determined by the steepness of the pressure gradient. Accordingly, wind or current speeds are higher where isobars are closer together and slower where they are more widely separated (Fig. CC13-2).