 Kinematic wave

A kinematic wave is a disturbance whose propagation speed is determined by the local relation between a conserved density and its flux. In a scalar conservation law $u_t+f(u{)}_x=0$, smooth values travel at speed $f^{\prime }(u)$.

A kinematic wave refers to a type of wave that is characterized by the transport of information or movement through a medium without requiring a physical medium for conveyance, specifically in the context of fluid dynamics and systems where the flow or movement can be described mathematically. These waves arise in various applications, including traffic flow, shallow water waves, and even in the context of geophysical flows.