O. V. Troshkin

Structurization of chaos

Vortex cascades of instabilities forming a core are studied. Large-scale linear waves in a fluctuating medium are described.

Nonlinear stability of a parabolic velocity profile in a plane periodic channel

An inviscid or viscous incompressible flow with a general parabolic velocity profile in an infinite plane periodic channel with parallel walls that can move is considered with the impermeability conditions (for the Euler equations) or the no-slip conditions (for the Navier-Stokes equations). The nonlinear (for the original equations) and nonlocal (for all Reynolds numbers) stability of the unperturbed flow with respect to arbitrary two-dimensional smooth perturbations of the initial velocity field is established.

On the theory of countercurrent flow in a rotating viscous heat-conducting gas

The countercurrent flow in a gas centrifuge is simulated. Mechanical and thermal methods for its excitation are discussed; thermal restructuring, the thermal control of the velocity field, and a shift in the inversion point are analyzed; and the formation of overtone flows in the rarefaction zone is studied.

On the theory of periodic layers in incompressible fluid

A conceptual error in the formally closed but physically incomplete Kim-Moin-Moser form of equations for viscous incompressible fluid in a horizontal periodic layer is corrected. This form, which has lately become popular, assumes that the vertical projections of the rotor and the second rotor of the field of accelerations vanish. This assumption considerably simplifies the calculations; however, it is insufficient for the equations of motion. In this paper, the fulfillment of these assumptions is ensured by the additional condition that the vector of the horizontal projection averaged over the period of the acceleration vorticity vanishes, which opens new possibilities. The resulting complete form of the equations with the rotors of three orders admits a reduction to two scalar equations (of the fourth and the sixth orders), which, however, are not less complicated than the equivalent Navier-Stokes equations.

A rotating gas tube: heating by torsion

A new exact solution of the Navier–Stokes equations is derived for a rotating gas tube. The solution improves the well-known rigid-like rotation at a constant temperature. The new temperature is shown to be variable. It increases from the boundary to the center of rotation due to the torsion strain produced by the swirl in the gas tube.

Numerical stability analysis of the Taylor-Couette flow in the two-dimensional case

The stability of the laminar flow between two rotating cylinders (Taylor-Couette flow) is numerically studied. The simulation is based on the equations of motion of an inviscid fluid (Euler equations). The influence exerted on the flow stability by physical parameters of the problem (such as the gap width between the cylinders, the initial perturbation, and the velocity difference between the cylinders) is analyzed. It is shown that the onset of turbulence is accompanied by the formation of large vortices. The results are analyzed and compared with those of similar studies.

Numerical simulation of a high-speed collision of metal plates

By means of single-, double-, and three-dimensional simulation, the dynamic processes occurring at a high speed impact of two metal plates of different densities are investigated. It is shown that in the process of collision, the Rayleigh-Taylor instability is developed on the boundary of the metals, which leads to the formation of three-dimensional ring structures on the surface of the metal with a lower density. The comparative characteristic of the deformation processes on the metal boundary in the spatial case is given by the use of various equations of the state of matter.

On the development of a wake vortex in inviscid flow

The evolution of an initial perturbation in an axisymmetric subsonic normal inviscid gas flow through a pipe is directly simulated. The basic (unperturbed) flow has a zero radial velocity component, while its axial velocity component (along the axis of symmetry) increases or decreases linearly with the radius. The perturbation is specified as a swirl (rotation about the axis) with a positive or negative velocity vanishing on the central axis and the lateral surface. Irrespective of its direction, the swirl gives rise to a steady-state vortex carried by the flow. It shape is spherical (contiguous to the rotation axis) or circular (sliding along the impermeable lateral surface).

On rotational gas heating

An exact solution of the Navier-Stokes equations for a normal state viscous heat conduct ing gas (with constant viscosity and heat conductivity) is obtained in the form of a stationary plane-parallel flow in a cylinder; the gas is heated by self-rotation at the angular velocity that monotonically increases (or decreases) along the central axis.

Stability theory for a two-dimensional channel

A scheme for deriving conditions for the nonlinear stability of an ideal or viscous incompressible steady flow in a two-dimensional channel that is periodic in one direction is described. A lower bound for the main factor ensuring the stability of the Reynolds–Kolmogorov sinusoidal flow with no-slip conditions (short wavelength stability) is improved. A condition for the stability of a vortex strip modeling Richtmyer–Meshkov fluid vortices (long wavelength stability) is presented.