Numerical analysis of the asymptotic representation of solitary waves

Novosibirsk. Translated from Prikladnaya Mekhanika i Technicheskaya Fizika, No. 5, pp. 44–54, September–October, 1994.     

Fourier method in the problem of small perturbations of colliding jets

Small unsteady perturbations of the solution of the known problem of a steady collision of two jets of an ideal incompressible fluid having identical velocities are studied. A discrete spectrum of the linear problem is found through direct calculations. It is demonstrated that the Fourier method is inapplicable because the eigenfunctions are not bounded.     

Exact Solutions to the Problem of Dynamics of a Liquid with a Free Surface between Two Approaching Vertical Walls

Doklady Physics - Exact solutions of the classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite...     

Higher-order approximations of cnoidal-wave theory

A solution of the problem of gravity waves on a liquid surface is sought in the form of a series whose first term corresponds to shallow-water theory. Such series have been previously studied numerically and analytically but their structure remains unclear because of the complicated initial formulation of the problem. In the present paper, instead of the strongly linear boundary-valua problem with a free boundary containing several unknown functions, we solve an ordinary quadratic-nonlinear differential-difference equation of the first order containing an unknown function. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 92–104, January–February, 2000.     

The problem of the failure of a dam in two-layer shallow water (linear approximation)

The flows that occur in the solution, in the linear approximation, of the problem of the failure of a dam for the model of two-layer shallow water with a free boundary are analysed qualitatively. It is shown that, apart from symmetry, four basic processes and four transients exist. They are distinguished by the type of jumps in the levels on the lines of discontinuity and by the direction of the velocities in the liquid layers. Examples of the profiles of all these flows are presented.     

Physical nature of the Kerr-Newman gravitational field in the relativistic theory of gravitation

Scientific-Research Institute of Nuclear Physics at the Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 83, No. 3, pp. 470–475, June, 1990.     

Arc Discharge in a Channel with Transparent Walls at Intense Flow Rates of a Plasma Forming Gas

The arc discharge was studied in a transparent channel at an intense flow rate of nitrogen, hydrogen, air, carbon dioxide in the current range 100–1500 A. The internal diameter of the porous channel varied from 10 to 34 mm, the length - from 50 to 150 mm, the air and nitrogen flow rates - from 0.05 to 1.5 kg/s, hydrogen - from 0.005 to 0.05 kg/s. The electric field strength in the arc channel reached a value of 300 V/cm for N₂ and 500 V/cm for H₂. The effect of plasma thermochemical non-equilibrium was discovered.     

Small perturbation in the problem of jet impingement: Constitutive equations

The well-known steady-state problem of impingement of two plane jets of an ideal incompressible fluid moving with the same velocity is refined and extended to the case of unsteady interaction. Equations describing perturbation propagation on the free surface of the impinging jets are obtained and linearized on the steady-state solution.