有限深两层流中内孤立波的高阶解*
Higher-Order Theory of Internal Solitary Waves with a Free Surface in Two-Layer Fluid System of Finite Depth
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摘要: 本文研究有限水深两层流中孤立波的三阶近似理论,并考虑了自由表面对孤立波的影响,运用坐标变形方法得到了三阶内孤立波的发展方程,求得波速的解析表达式。对方程进行了数值计算,得到了几种参数下三阶解曲线,指出自由表面对波型和波速的影响是二阶的。计算表明三阶解对一阶、二阶解有明显的改进,使其更加接近试验结果。Abstract: A higher-order approximation theory of internal solitary waves with a free surface is presented.Using the method of strained co-ordinates,the third-order approximation evolution equation of interface has been found.An analytic expression of the wave velocity is given.The evolution equation has been solved numerically.It is found that the effects of free surface on the shape and wave velocity of solitary wave are O(ε2),and the third-order numerical solutions are closer to experimental data than the first-and second-order solutions.
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[1] Kubota,T.,D.R.S.Ko,and L.Dobbs,J.Hydronaut,AIAA 12(1978),157. [2] Koop,C.G.and G.Bulter,J.Fluid Mech.,112(1981),225-251. [3] Segur,H.and J.L.Hammack,J.Fluid Mech.,118(1982),285-304. [4] Joseph,R.I.and R.Egri,J.Phys.A.Math.and Gne.,11(1978). [5] Whitham,G.B.,Linear and Nonlinear Waves(1974). -
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