horizontal pressure-gradient force

The horizontal pressure-gradient force is a fundamental concept in atmospheric science that describes the tendency for air to move from areas of high pressure to areas of low pressure. This force is a key component in understanding wind patterns, as described by Newton's second law of motion.1

In a simplified model, disregarding friction and acceleration, the pressure-gradient force is balanced by the Coriolis force, resulting in geostrophic balance and geostrophic wind. The pressure-gradient force itself is directly proportional to the difference in pressure over a given distance. When this pressure difference is large, meaning isobars are close together, the wind speed increases.1

The Coriolis force, an apparent force due to Earth's rotation, deflects winds to the right in the Northern Hemisphere and to the left in the Southern Hemisphere, causing winds to flow parallel to isobars in geostrophic motion. More complex models, like gradient wind, account for curved trajectories, providing a more accurate representation of actual wind, especially in phenomena like hurricanes and jet streams.123