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 traffic flows.[2][3]
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 phase speed is a constant or a variable. Kinematic wave can be described by a simple partial differential equation with a single unknown field variable (e.g., the flow or wave height, ) in terms of the two independent variables, namely the time () and the space () with some parameters (coefficients) containing information about the physics and geometry of the flow. In general, the wave can be advecting and diffusing. However, in simple situations, the kinematic wave is mainly advecting.
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.
- ^ Newell, G.F. (1993). "A simplified theory of kinematic waves in highway traffic, Part I: General theory". Transpn. Res. B. 27B (4): 281–287. doi:10.1016/0191-2615(93)90038-C.
Further reading
- Singh, Vijay P. (1996). "Linearization of Hydraulic Equations". Kinematic Wave Modeling in Water Resources : Surface-Water Hydrology. New York: John Wiley & Sons. pp. 211–253. ISBN 0-471-10945-2.
- v
- t
- e
- Airy wave theory
- Ballantine scale
- Benjamin–Feir instability
- Boussinesq approximation
- Breaking wave
- Clapotis
- Cnoidal wave
- Cross sea
- Dispersion
- Edge wave
- Equatorial waves
- Fetch
- Gravity wave
- Green's law
- Infragravity wave
- Internal wave
- Iribarren number
- Kelvin wave
- Kinematic wave
- Longshore drift
- Luke's variational principle
- Mild-slope equation
- Radiation stress
- Rogue wave
- Rossby wave
- Rossby-gravity waves
- Sea state
- Seiche
- Significant wave height
- Soliton
- Stokes boundary layer
- Stokes drift
- Stokes wave
- Swell
- Trochoidal wave
- Tsunami
- Undertow
- Ursell number
- Wave action
- Wave base
- Wave height
- Wave nonlinearity
- Wave power
- Wave radar
- Wave setup
- Wave shoaling
- Wave turbulence
- Wave–current interaction
- Waves and shallow water
- Wind setup
- Wind wave
- Atmospheric circulation
- Baroclinity
- Boundary current
- Coriolis force
- Coriolis–Stokes force
- Craik–Leibovich vortex force
- Downwelling
- Eddy
- Ekman layer
- Ekman spiral
- Ekman transport
- El Niño–Southern Oscillation
- General circulation model
- Geochemical Ocean Sections Study
- Geostrophic current
- Global Ocean Data Analysis Project
- Gulf Stream
- Halothermal circulation
- Humboldt Current
- Hydrothermal circulation
- Langmuir circulation
- Longshore drift
- Loop Current
- Modular Ocean Model
- Ocean current
- Ocean dynamics
- Ocean dynamical thermostat
- Ocean gyre
- Overflow
- Princeton ocean model
- Rip current
- Subsurface currents
- Sverdrup balance
- Thermohaline circulation
- Upwelling
- Wind generated current
- Whirlpool
- World Ocean Circulation Experiment
tectonics
- Acidification
- Argo
- Benthic lander
- Color of water
- DSV Alvin
- Marginal sea
- Marine energy
- Marine pollution
- Mooring
- National Oceanographic Data Center
- Ocean
- Explorations
- Observations
- Reanalysis
- Ocean surface topography
- Ocean temperature
- Ocean thermal energy conversion
- Oceanography
- Pelagic sediment
- Sea surface microlayer
- Sea surface temperature
- Seawater
- Science On a Sphere
- Stratification
- Thermocline
- Underwater glider
- Water column
- World Ocean Atlas
- Oceans portal
- Category
- Commons