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Nonlinear unified equations for water waves propagating over uneven bottoms in the nearshore region |
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| Authors: | HUANG Hu DING Pingxing LU Xiuhong |
| Institution: | 1. State Key Laboratory of Estuarine Coastal Research, East China Normal University;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 2. State Key Laboratory of Estuarine Coastal Research, East China Normal University, 3. Division of Graduate Studies, Shanghai University, |
| Abstract: | Considering the continuous characteristics for water waves propagating over complex topography in the nearshore region, the unified nonlinear equations, based on the hypothesis for a typical uneven bottom, are presented by employing the Hamiltonian variational principle for water waves. It is verified that the equations include the following special cases: the extension of Airy's nonlinear shallow-water equations, the generalized mild-slope equation, the dispersion relation for the second-order Stokes waves and the higher order Boussinesq-type equations. |
| Keywords: | unified equations Hamilitonian variational principle for water waves extended mild-slope equation |
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