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A new approach to the solution of the self-similar problem of the entry of a wedge into an ideal fluid at an arbitrary angle to the free surface is proposed. The method is based on the construction of the expressions for the complex velocity and the derivative of the complex potential in a parametric variable domain. An integral and an integro-differential equation are obtained for determining the absolute magnitude and the angle of the velocity vector at the free boundary. The calculated results for the free surface shape, the angles of contact between the free surface and the wedge, and the coefficients of the hydrodynamic forces are presented.

The obtaining of axisymmetric flows of incompressible and compressible fluids from plane-parallel flows by means of integral transformations relating harmonic and p-harmonic functions [1] is considered. A transformation is found that carries plane-parallel flows from elementary singularities into axisymmetric flows. It is shown that this transformation makes it possible to obtain the general form of the solution of axisymmetric problems of flow past bodies from the solution of plane-parallel problems.

where f(z) = U + iV is an analytic function in D, such that VI 1 = O, and is continued by symmetry to the domain D* of the half plane x < 0; L is a contour in D + I + D*, joining the points ~ = --x + iy and z = x + iy [I]. Formula (3) establishes a one-to-one correspondence between xk-analytic and analytic functions in D whose imaginary parts on l are equal to zero (the dependence of f on the parameter k is not reflected either here or in what follows).

The study discusses problems in the numerical modeling of axisymmetric flows of an incompressible fluid induced by a continuous vortex region or vortex sheet by means of a discrete system of vortex rings.

The method of discrete vortices is used for a numerical investigation of the nonlinear unsteady problem of passage of an axisymmetric body through a coaxial thin-walled cylindrical tube of finite length.

The article considers the supersonic unsteady-state motion of a plate with a finite (but infinitely small) angle of attack with an associated shock wave in an ideal gas. The laws governing the change of the velocity and the angle of inclination of the plate are assumed to be arbitrary, and the Strouhal numbers are assumed to be small. Under the latter assumption and with Mach numbers in the perturbed region not too close to unity, the prehistory of the motion is sufficiently well described by the instantaneous values of the parameters of the unsteady state and their derivatives. This fact permits a considerable simplification of the equations describing the perturbed unsteady-state motion, and an analytical solution.