According to Newton’s second law, winds are driven by forces. The pressure-gradient creates a force, even in initially calm (windless) conditions. This force points from high to low pressure on a constant altitude chart (such as at sea-level), or points from high to low heights on an isobaric chart (such as the 50 kPa chart). Pressure-gradient force is the main force that drives the winds.
Other forces exist only when there is already a wind. One example is turbulent drag against the ground, which pushes opposite to the atmospheric boundary-layer wind direction. Another example is Coriolis force, which is related to centrifugal force of winds relative to a rotating Earth.
If all the forces vector-sum to zero, then there is no net force and winds blow at constant speed. Theoretical winds based on only a small number of forces are given special names. The geostrophic wind occurs when pressure-gradient and Coriolis forces balance, causing a wind that blows parallel to straight isobars. For curved isobars around lows and highs, the imbalance between these two forces turns the wind in a circle, with the result called the gradient wind. Similar winds can exist in the atmospheric boundary layer, where turbulent drag of the air against the Earth’s surface slows the wind and causes it to turn slightly to cross the isobars toward low pressure.
Waterspouts and tornadoes can have such strong winds that pressure-gradient force is balanced by centrifugal force, with the resulting wind speed known as the cyclostrophic wind. In oceans, currents can inertially flow in a circle.
The two most important force balances at midlatitudes are hydrostatic balance in the vertical, and geostrophic balance in the horizontal.
Conservation of air mass gives the continuity equation, for which an incompressible approximation can be used in most places except in thunderstorms. Mechanisms that cause motion in one direction (horizontal or vertical) will also indirectly cause motions in the other direction as the air tries to maintain continuity, resulting in a circulation.
Kinematics is the word that describes the behavior and effect of winds (such as given by the continuity equation) without regard to the forces that cause them. The word dynamics describes how forces cause winds (as given by Newton’s 2nd law).