This paper considers the problem of the evolution of azimuthal perturbations in axisymmetric magnetohydrodynamic. flows of an ideally conducting inviscid fluid with circular streamlines. The fluid is. in a toroidal gap between two surfaces with constant values of the stream function. The equations of. fluid motion are derived in the approximation of infinitely a narrow gap. The parameters at which. spontaneous swirling is possible are determined numerically, and the properties of secondary swirling. flows resulting from instability of the initial steady-state poloidal flow are established.

The region of instability of the Hill-Shafranov viscous MHD vortex with respect to azimuthal axisymmetric perturbations of the velocity field is determined numerically as a function of the Reynolds number and magnetization in a linear formulation. An approximate formulation of the linear stability problem for MHD flows with circular streamlines is considered. The further evolution of the perturbations in the supercritical region is studied using a nonlinear analog model (a simplified initial system of equations that takes into account some important properties of the basic equations). For this model, the secondary flows resulting from the instability are determined.

Experimental estimates are obtained for the main parameters of tornado‐like vortices that arise from excitation of forced axisymmetric inertial oscillations of large amplitude in a rigidly rotating fluid.

It is shown that during excitation of forced, resonant, inertial oscillations of large amplitude in a rigidly rotating fluid, the mechanism of formation of tornado‐like vortices is primarily of a kinematic nature($advection of circulation of the azimuthal component velocity and stretching of vortex lines by the poloidal components of the velocity field that arise from excitation of inertial oscillations). The main parameters of the vortices are obtained by solutions of model problems. To excite such oscillations, it is necessary to deliver energy far exceeding the initial energy of the rotating fluid. Therefore, inertial oscillations by themselves cannot lead to the occurrence of intense atmospheric vortices. Nevertheless, such oscillations can apparently play the role of a trigger mechanism that activates more complex processes of vortex formation related to instability of the atmosphere.

The stability of steady axisymmetricMHD flows of an inviscid, incompressible, perfectly conducting fluid with respect to swirling—perturbations of the azimuthal components of the velocity field—is studied in a linear approximation. It is shown that for flows similar to a magnetohydrodynamic Hill-Shafranov vortex, the problem reduces to a one-dimensional problem on a closed streamline of the unperturbed flow (the arc length of the streamline is the spatial coordinate). A spectral boundary-value eigenvalue problem is formulated for a system of two ordinary differential equations with periodic coefficients and periodic boundary conditions. Sufficient conditions under which swirling is impossible are obtained. Numerical solution of the characteristic equation shows that, under certain conditions, for each streamline there is a real eigenvalue that yields monotonic exponential growth of the initial perturbations.

An approximate mathematical model, formulation of the problem, and its approximate solution are proposed for the far region of a turbulent vortex wake past a moving body, where the departure of the horizontal velocity component from the uniform flow is slight. It is assumed that the single important parameter that defines the main flow characteristics in this region is the vortex momentum per unit length produced in the fluid by the lift equal to the weigth of the moving body uncompensated by the buoyancy force. Thus, the flow is self-similar, and the self-similarity law determines the intensity, shape, and location of vortex lines as functions of the downstream distance with accuracy up to a constant factor, which cannot be determined theoretically and should be obtained by comparison of theory with experiment. A boundary-value problem is formulated to determine the flow structure of vortex lines (vorticity distribution). A solution of the problem is obtained numerically in the limit of “vanishing turbulent viscosity.” The variation in the maximum velocity of a vortex line with distance, determined by self-similarity, is in agreement with available experimental data.

A plane analog of the problem of spontaneous swirling—the occurrence of a free transverse flow due to disturbance of the initial plane-parallel flow—is considered. It is shown that in flows with circular streamlines between coaxial cylinders, loss of stability can result in the occurrence of axial flow that is axisymmetric on the average (averaging over the axial coordinate and the azimuthal angle) because of the countergradient transfer of the axial momentum component by Reynolds stresses.

A number of phenomena related to labqratory-produced tornado-like vortices are observed and discussed. These are the formation of a columnar vortex above evaporating fluid; appearance of multiple vortices in a single convergence system; a suppression of turbulence in fluid in rigid-body rotation; and the formation of a tornado-like vortex in rotating fluid heated from below. Qualitative explanations of these observed phenomena are given.

1. In connection with the development of the oil and gas deposits of Western Siberia, particular importance is attached to the question of protecting the drilling and extracting operations against fire hazards and to the question of rapidly extinguishing fires involving runaway wells. At the present there are two principal ways of extinguishing well fires: by means of powerful water jets directed at the base of the flame or by means of a gas-water jet created by an aircraft turbojet engine [1]. The use of these methods requires a great deal of manpower and special technology, large stocks of water and much preparation. Bringing the firefighting crews and their equipment to the scene of the fire under the conditions prevailing in Western Siberia, where aircraft are the principal means of transport, is an expensive proposition. Moreover, much time is lost in setting up the equipment. In some cases the weather conditions may impede the use of the existing methods of fighting well fires. The chief advantage of recently developed efficient methods of fighting well fires is their simplicity, speed and economy. These methods rely on the use of an explosive charge to create a vortex ring that acts on the flame as it travels along the axis of the gusher. The development of these techniques is the practical outcome of experimental and theoretical research into turbulent vortex rings carried out in recent years at the Institute of Hydrodynamics, Siberian Branch of the Academy of Sciences of the USSR, at the initiative of Lavrent'ev [2]. This article offers a qualitative explanation of the vortex-ring flame quenching mechanism and presents the results of laboratory, proving ground and field tests of the new method. 2. When the jet of gas escaping from the mouth of a damaged well ignites, it burns in the diffusion regime. In the first approximation, the structure of the flame takes the form shown in Fig. 1. The chemical reaction takes place in a thin layer, which may be regarded as the surface where the fuel and oxidizer concentrations vanish, the diffusion flows to the surface being in stoichiometric proportion [3]. This surface is called the flame front. The front begins at a certain distance from the well mouth and is stabilized along a curve, the position of which is determined by the composition of the air-fuel mixture at the edge of the jet and by the condition of equality of the turbulent burning rate and the jet velocity. In the case of a turbulent flow, which obtains under actual field conditions, the above picture applies to the average flow and the average position of the front. In well fires the height of the flame may reach 80-100 m and the maximum flame diameter 10-15 m.

This study deals with the motion of a gas bubble developing under the influence of surface-tension forces in an imponderable viscous liquid with a temperature gradient. A theory of steady-state motion of a bubble in a field with constant temperature gradient is given for the case of small Reynolds numbers. Experimental results that show qualitative agreement with the theory are presented.

A system of equation developed for so-called short waves and expressing the propagation velocity as a function of amplitude was previously used in an analysis of one-dimensional shock-wave asymptotics and of shock-wave reflection from a free surface and a hard wall. The same equations are applied in an analysis of explosions with a radius comparable to a water basin depth and of the flow produced by shock waves at distances remote from the explosion point. (R.V.J.)