卷 53, 编号 2 (2018): Suppl

The plane stationary flow of viscous gas is considered, which is induced by the jet impacting the unbounded space and the domain between two diverging flat walls. Existence criteria of the Landau self-similar solutions are established for the source of gas flowing from the apex of a wedge with the thermally insulated walls and of wedge with the prescribed walls temperature. The analytical solutions are constructed in the case when the gas temperature is constant along the lines of flow and when the transfer coefficients are power functions of temperature.

The basic conservation laws of the shallow water theory are deduced from the multidimensional integral conservation laws of mass and total impulse describing the flow of ideal incompressible fluid over the horizontal bottom. This derivation is based on the concept of the local hydrostatic approximation which generalizes the long wave approximation and is used to justify the application of the shallow water theory to modeling wave flows of fluid with hydraulic bores.

The problem of constructing an axisymmetric forebody with minimal wave drag with given constraints on volume and dimensions has been solved within the framework of the local linearization of the relationship between the geometric parameters and the gas-dynamic functions. The optimal fore-body has been determined by varying the shape of the cone with equivalent elongation, for which the approximation for the objective function (wave drag related with volume) has been determined on the basis of the known exact values of the flow parameters. Characteristic features of the optimal shape are bluntness of the nose across the front face and a smooth conjugation with closing cylinder for bodies with sufficiently large volume, the latter exceeding the value depending on the elongation and the Mach number. Comparison with the results of direct numerical optimization in the framework of Euler’s model has shown that the proposed analytical solution provides a near-minimum wave drag.

This work studies the plane-parallel unsteady shear of a homogeneous two-constant viscoplastic Bingham medium in the infinite layer. It was assumed that the axial velocity of the flow as a function of one spatial coordinate and time is known from the solution to the classical one-dimensional unsteady problem. The time variation in the thicknesses of the possible rigid zones is considered; their boundaries are parallel to the boundaries of the layer. The two-dimensional plane perturbations are superposed upon the main flow. The problem in terms of perturbations reduces to one linearized equation for the amplitude of the function of the flow with the corresponding set of four boundary conditions, and several variants of such quadruples are studied here. With the method of integral relationships, the problem reduces to the minimization problem of ratios of quadratic functionals depending on time in the space H₂(a;b), where a and b are functions of time determined by the motion of the rigid zones in the main flow. For different variants of imposition of the boundary conditions, the generalized Friedrichs inequalities are proved, and the sufficient integral estimates of stability are derived in which the Reynolds and Saint-Venant numbers and the maximum shear velocity in thickness in the main flow play a role. The dependence of the obtained estimates on the viscous and plastic properties of the medium is discussed.