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http://dx.doi.org/10.9765/KSCOE.2012.24.1.010

Linear Shallow Water Equations for Waves with Damping  

Jung, Tae-Hwa (Division of Civil, Environment and Urban Engineering, Hanbat National University)
Lee, Chang-Hoon (Department of Civil and Environmental Engineering, Sejong University)
Publication Information
Journal of Korean Society of Coastal and Ocean Engineers / v.24, no.1, 2012 , pp. 10-15 More about this Journal
Abstract
Wave characteristics in the presence of energy damping are investigated using the linear shallow water equations. To get the phase and energy velocities, geometric optics approach is used and then these values are validated through numerical experiments. Energy damping affects wave height, phase and energy velocities which result in wave transformation. When the complex wavenumber is used by the Eulerian approach, it is found that the phase velocity decreases as the damping increases while the energy velocity increases showing higher values than the phase velocity. When the complex angular frequency is used by the Lagrangian approach, the energy-damping wave group is found to propagate in the energy velocity. The energy velocity is found to affect shoaling and refraction coefficient which is verified through numerical experiments for waves on a plane slope.
Keywords
Energy damping; Linear shallow water equations; Phase velocity; Energy Velocity; Shoaling; Refraction;
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