Strongly Nonlinear Long Gravity Waves In A Type Of Shear Flows

Researches on the dispersion and nonlinearity of fluid waves help us to reveal the mechanisms of their formation, evolvement and attenuation. These can also guide us how to construct and maintain the underwater or coastal engineering in reality.In this thesis, we just consider irrotational, inviscid and incompressible fluids. Refering to the method from Choi [1], we use the depth-averaged velocities to derive a new model for surface wave solution with shear flow as the background. Theoretically, the derived new Boussinesq equation is solvable. In this model, we assume that the aspect ratio between water depth and wave length is small, but have nothing to do with the wave amplitude. Thus, the derived equations can be reduced to the case of Green&Naghi’s [2]; on the other hand, the model can be more widely applied to describe arbitrary amplitude waves. This study on the surface waves will give directions to the research of interfacial waves.