Fully Nonlinear Simulations Of Internal Waves Due To Disturbance Sources Of Doublet And Vortex Pair Based On Boundary Integral Equation

In this thesis,interfacial waves caused by one point source / sink,doublet,as well as a pair of source-sink,vortex pair in two-dimensional two-layer flow are studied.Upper and lower fluids are ideal fluids,the motions are irrotational,and only steady flows are considered.The upper surface of the upper fluid satisfies the rigid-lid assumption,and the lower fluid is infinitely deep.The boundary integral equation method is used to establish the integral-differential equations,and the quasi-Newton method is used to solve it numerically.At the same time,linear analytical solutions of corresponding linearized problems are obtained,and are compared with the nonlinear method(boundary integral equation method).Different characteristics of internal waves caused by point vortex,doublet,as well as point source and point sink,vortex pairs are compared.The influence of related parameters on the results is discussed.Comparing steady downstream wave heights of the interfacial waves caused due to a single point vortex and that due to a doublet of the same strength,it is found that the latter is much larger than the former,but the positions of the crest/trough are close.As the strength increases,the difference of the steady downstream wave heights between that of the nonlinear results and that of the linear results due to a doublet is smaller,but this difference is larger in the case of point vortex.The downstream wave height of the linear solutions is independent of the sign of the point vortex as well as doublet,but this conclusion is not true for nonlinear results.The downstream wave height due to the negative point vortex/doublet is greater than that of the linear results,which is greater than that due to the positive point vortex/doublet.In the case of a doublet,when the far upstream flow encounters the doublet,a small depression(bulge)is formed then the first large crest(trough)appears.The amplitude of the first wave of interfacial waves due to one doublet is close to the amplitudes of corresponding downstream waves,and the difference between the amplitude of the first wave of interfacial waves and that of downstream waves due to one point vortex is much larger.The wave profiles caused by equal-strength source-sink is similar to that due to one doublet.When the distance between the point source and the point sink increases,the amplitude of the steady downstream waves changes periodically.The amplitude of the downstream wave of the nonlinear results due to one upstream point source and one downstream point sink is larger than that of the linear solutions,which is larger than that of nonlinear results due to one upstream point sink and one downstream point source.When the distance is taken certain values,the downstream wave is offset and the whole interface is composed of a symmetrical large wave crest/trough and depressions/bulges on both sides.For equal-strength counter-/co-rotating vortex pairs,when the distance between the two point vortices increases the steady downstream wave height changes periodically.The maximum/minimum is equal to the sum/difference of the wave heights due to two point vortices separately.Exchanging signs of counter-rotating vortex pairs does not affect the steady downstream wave heights,but the wave profiles due to co-rotating pairs changes significantly if signs of two vortices change.