ON SOME PROBLEMS OF SIMILARITY FLOW OF FLUID WITH A FREE SURFACE
ON SOME PROBLEMS OF SIMILARITY FLOW OF FLUID WITH A FREE SURFACE
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DOI：
10.1017/s0022112069001996
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发表时间：
1969-01-01
影响因子：
3.7
通讯作者：
DOBROVOLSKAYA, ZN
中科院分区：
文献类型：
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作者：
DOBROVOLSKAYA, ZN
提出了求解一类具有自由表面的不可压缩流体的相似流动二维问题的方法。假设流体是非粘性且无重量的。我们考虑具有无量纲流体动力学特征的二维无旋相似流，其仅取决于比率 x/v0t、y/v0t，其中 x、y 是笛卡尔坐标，t 是时间，v0 是速度维度的常数。所提出的方法基于使用 Wagner (1932) 引入的函数，并且可以应用于流动区域以自由表面为界和均匀移动（或固定）直线的问题不可渗透的边界。瓦格纳函数的引入使得将所考虑的每个问题简化为实函数的非线性奇异积分方程成为可能。该方法通过求解楔块均匀对称进入流体半平面的经典问题来说明。
The paper presents the method of solving a class of two-dimensional problems of the similarity flow of an incompressible fluid with a free surface. The fluid is assumed to be non-viscous and weightless. We consider two-dimensional irrotational similarity flows with dimensionless hydrodynamic characteristics depending only on the ratios x/v0t, y/v0t, where x, y are Cartesian co-ordinates, t is time and v0 is a constant of the velocity dimension.The proposed method is based upon using the function introduced by Wagner (1932) and can be applied to the problems where the flow region is bounded by free surfaces and uniformly moving (or fixed) rectilinear impermeable boundaries. Introduction of Wagner's function makes it possible to reduce each of the problems under consideration to a non-linear singular integral equation for the real function.The method is illustrated by solving the classical problem of the uniform symmetrical entry of a wedge into a half-plane of a fluid.