Study On The Generation And Evolution Of The Nonlinear Wave On Uneven Bottoms

The research on the nonlinear wave is an advanced subject in mechanics, physics, applied mathematics and engineering practice and it is of great practical and theoretical significance. In the thesis, some aspect on the evolution and generation of the wave in flow and even stratified flow on several kinds of uneven bottom are investigated by the method of combination of the theoretical analysis, symbolical computation and numerical simulation. The results we obtain as follows.The evolution equation for the finite amplitude internal solitary in stratified fluids of finite depth with uneven bottom is educed. The first-order and second-order evolution equation of the internal solitary wave amplitude for the finite depth stratified fluid on general uneven bottom are both derived from the Euler equation, by introducing the Gardner-Morikawa transformation and asymptotic expansions, and the matching of the solutions for the upper and lower-layer of fluid. The mixed stratified fluid model is adopted, that is, the density of the upper-layer fluid is uniform, and the distribution of density in lower-layer fluid is varied with depth, and the depth of the upper-layer fluid is much higher than lower-layer one. And then, the first-order evolution equation that seems a variable-coefficient ILW (Intermediate Long Wave) for the amplitude with slowly bottom is yielded, and the coefficient of the equation is computed with specific density distribution.The effect of the different surface tension on the evolution and generation of the surface solitary wave for the flow with uneven bottom is investigated by numerical simulation. Considering basic flow, surface tension and uneven bottom, the equation of the surface solitary wave for incompressible and inviscid fluid is derived from potential theory by adopting small parameter perturbation method when the Bond number is closed to 1/3 and the equation contain not only the third-order positive dispersion term, but also the fifth-order positive dispersion term. And then, the equations of the surface solitary wave derived from different Bond number are numerically analyzed by the combination of the pseudo spectral method and numerical simulation software, so the waterfall of the wave is drawn. The effects of some factors, such as different flow state and different bottom, on the generation evolution of the surface solitary wave is discussed.The effect of the waving bottom on the evolution and generation of the nonlinear surface wave is researched. Based on the two-dimension motion of incompressible and inviscid fluid, the first-order and the second-order equation of the nonlinear surface wave with waving bottom and surface tension are both derived from potential theory by adopting small parameter perturbation method. The numerical simulation on the first-order equation is made by the pseudo spectral method, so the evolutional character of the nonlinear surface wave is obtained. And the generational feature of the nonlinear surface wave under the waving bottom or ordinary bottom is compared. At last, the nonlinear first-order surface wave equation under different bottom is simulated numerically for different flow state including the resonant state, supercritical state and subcritical state, and the evolutional law of the solitary is analyzed.