This answer provides a good explanation why cyclones (e.g. hurricanes, typhoons, and tornadoes) have rotary motion. However, cyclones usually also have translational motion -- they move from place to place.
This seems counter-intuitive. The center of mass of the air ought to stay in place. Even worse, some cyclones meander instead of following a straight-line path.
So, why do cyclones have translational motion?
The earth rotates around its axis and the atmosphere is a gas, not rigidly connected to the ground or oceans. Motions are generated in the atmosphere which combined with the different velocities according to latitude, induce the systematics of weather systems.
Here is an article analyzing the weather fronts.
Dynamic meteorology is the branch of fluid dynamics concerned with the meteorologically significant motions of the atmosphere. It forms the primary scientific basis for weather and climate prediction, and thus plays a primary role in the atmospheric sciences. Most of the meteorologically important motions studied in dynamic meteorology are profoundly influenced by the facts that the Earth is a rapidly rotating planet, and that the atmosphere on average has stable density stratification. These facts make the fluid dynamics of the atmosphere very different from traditional engineering fluid dynamics. Planetary rotation places strong constraints on large-scale horizontal motions; stable stratification places strong constraints on vertical motions. These constraints can be understood by considering the fundamental physical laws governing motions of the atmosphere.
The motions of the atmosphere are governed by the laws for conservation of mass, conservation of momentum, and conservation of thermodynamic energy. Application of these laws to motions with horizontal scales of several hundred kilometers or greater leads to simple relations among the horizontal wind, pressure, and temperature distributions. These relations form a set of diagnostic relations essential for understanding the motions that generate weather disturbances. Such motions are generally rotational in character. They can be characterized by a conservable property known as the potential vorticity, which is the fluid dynamical analogue of spin angular momentum in solid mechanics
The latitudinal gradient of potential vorticity provides the mechanism for generation of global-scale planetary waves, which are primary features of the climate system. Superposed on these global waves are transient cyclones and anticyclones, whose energy is derived primarily from the potential energy associated with the mean Pole-to-Equator temperature gradient. Study of the development and evolution of transient weather disturbances, and of dynamical mechanisms for producing intraseasonal and interannual climate variations, are among the principal areas of study in dynamic meteorology.
The are advected with the mean flow, which is generally eastwards in the equatorial zone.
