Nice Animation of a Jetstream Source: NASA – GISS
Jetstreams are driven by atmospherical differences in temperature and thus in air pressure. There are horizontal gradients in air-temperature of atmosphere, for example between polar regions and mid latitudes, but there are also vertical gradients leading to convection and to cloud formation if air moisture is sufficient.
A Jetstream forms Rossby waves, troughs and ridges traveling streamwise and also eddies, the weather-making high and low pressure systems. These eddies arise from turbulences in jetstream like the vortexes of a raging river do.
Jens Christian Heuer
A nice animation: