Kinematic wave
In gravity and pressure driven fluid dynamical and geophysical mass flows such as ocean waves, avalanches, debris flows, mud flows, flash floods, etc., kinematic waves are important mathematical tools to understand the basic features of the associated wave phenomena.[1] These waves are also applied to model the motion of highway
In these flows, mass and momentum equations can be combined to yield a kinematic wave equation. Depending on the flow configurations, the kinematic wave can be linear or non-linear, which depends on whether the wave
Kinematic wave for debris flow
Non-linear kinematic wave for debris flow can be written as follows with complex non-linear coefficients:
where is the generalized flux that depends on several physical and geometrical parameters of the flow, flow height and the hydraulic pressure gradient. For , this equation reduces to the Burgers' equation.
References
- ^ Takahashi, T. (2007). Debris Flow: Mechanics, Prediction and Countermeasures. Taylor and Francis, Leiden.
- ^ Lighthill, M.J.; Whitham, G.B. (1955). "On kinematic waves. I: Flood movement in long rivers. II: A theory of traffic flow on long crowded roads". Proceedings of the Royal Society. 229A (4): 281–345.
- .
Further reading
- ISBN 0-471-10945-2.