Vol 89, No 5 (2025)

The results of a numerical study of unsteady viscous fluid flow in the area of the branching of a circular cross-section channel at an angle of 60° are presented for four values of the inlet Re number that are less than or equal to 1475; in the upstream region, the channel flow is assumed to be unperturbed and fully-developed. The main results relate to the case of equality of the flow rates in two branches, with flow separation regions in both branches. It was shown, in particular, that at Re = 750, intense quasi-periodic oscillations develop in the computational domain due to the Kelvin-Helmholtz instability. At Re = 1475, a zone of locally turbulent motion is formed in the flow, the size of which depends on the proportion of the flow going into the side branch. The vortex pattern of the flow and the type of the velocity pulsation spectrum at various points in the region are analyzed.

The hydrodynamic stability of the flow with S-shaped spanwise velocity profiles simulating an incompressible flow in three-dimensional boundary layers is analyzed in a wide range of Reynolds numbers. The existence of an instability different from the known crossflow vortices and Tollmien-Schlichting waves is confirmed. The boundaries of the instabilities are estimated in terms of the wave vector angle.

This paper studies the compatibility conditions for a system of equations describing nonuniform helical flows of an inviscid incompressible fluid. The class of flows considered traces back to the works of I. S. Gromeka and E. Beltrami, who independently discovered stationary solutions of the Euler equations satisfying the collinearity condition between the velocity and vorticity vectors. Their results laid the foundation for the theory of helical flows, identifying special solution classes of hydrodynamic equations. The system under consideration comprises the Euler equations supplemented by differential constraints that relate the velocity and vorticity vectors. Gromeka showed that if the function α is constant, the system becomes involutive. However, when α(x, y, z) is variable, the analysis becomes significantly more complex, and in general, the system is not involutive. A group analysis is performed for the resulting closed nonlinear system relating the velocity components and the function α\alpha. An optimal system of subgroups of the six-dimensional Lie algebra admitted by the system is constructed. Invariant solutions with respect to one-parameter subgroups are derived and are described by quasilinear equations with two independent variables.

The present paper is devoted to the study concerning partially invariant multidimensional solutions of gas dynamics equations, generalizing classical stationary two-dimensional gas flows. It is proved that the gas dynamics equations for such solutions reduce to a third-order dynamical system on a manifold. The singular manifolds of this system are investigated. The main attention is paid to the structure of invariant and non-invariant components of the solution, as well as the features of solutions near singular points. The existence of solutions conjugated through a shock wave, which correspond to the transition of integral curves from one sheet of the manifold to another, is proved.

Within the framework of the theory of jets flows in an ideal fluid, the combustion of a liquid monopropellant jet flowing out of a vessel with flat walls is investigated. An exact solution to the problem is obtained and a parametric study of the influence of the vessel geometry and combustion parameters on the shape, flow rate coefficient and length of the jet is carried out. This work expands the class of problems solved by methods of the theory of plane potential jets in an ideal fluid.

This paper considers the stability of a flow of a weak polymer solution between concentric cylinders, the inner of which rotates. A case of Kelvin–Voight model, frequently called Oskolkov model, was used to describe the movement of the fluid. This model is applicable for highly diluted solutions, where the relaxation time is much less than the typical flow time scale and the elastic forces are much less the viscous. The stability was investigated by the linear approach using the differential sweep numerical method. It is found that for axisymmetric perturbations, as well as in the case of small gap between the cylinders, the critical Reynolds numbers are close to the case of Newtonian fluid. In the case of medium and small values of the inner cylinder radius, the viscoelastic fluid is less stable with respect to the non-axisymmetric disturbances than the viscous one. The critical Reynolds numbers for the non-axisymmetric spiral perturbations may be lower than for the axisymmetric Taylor vortices.