Nonlocal turbulent transport in a buoyant vortex ring during the ascent of a thermal in a stratified atmosphere

The flow initiated by a hot gas cloud (thermal) in a stratified atmosphere is calculated on the basis of theκ-ε turbulence model and the transport model for the Reynolds stresses and turbulent fluxes and the results obtained are compared The nonlocal nature of the turbulent transport in a vortex ring and its effect on certain flow characteristics are explained In particular, the calculations carried out using the Reynolds stress model show much slower cooling of the temperature-vortex torus than those based calculated on theκ-ε-model Modification of theκ-ε-model to take the effect of curvature of the streamlines approximately into account makes it only partially possible to reproduce the results obtained on the basis of the Reynolds stress model Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 12–20, January–February, 1999. The research was carried out with support from the Russian Foundation for Basic Research (project No. 95-01-00544a).     

Formation of a tripolar vortex in a stratified fluid

This paper reports on an experimental study of vortices in a stratified fluid. The vortices were generated by two different stirring devices, viz. a rotating sphere and a rotating bent rod. It was found that the vortices created with the rotating sphere are mostly axisymmetric and stable, whereas the vortices produced with the bent rod generally show instabilities, under certain conditions leading to the formation of a tripolar vortex. This report concentrates on this tripolar structure and presents quantitative information about the flow obtained through streak photography of tracer particles.     

Associated disturbances around a vortex ring in a stratified fluid

A motion of a vortex ring in a stratified fluid is accompanied by associated disturbances which, in the schlieren visualization in the field of a horizontal density gradient, have the shape of a symmetric four-petal configuration. The criterion of the existence of the disturbances is the Froude number Fr based on the motion velocity and the vertical vortex size. On the range Fr > 1, the disturbances are stable with respect to the variation of themotion regime and the distortion of the vortex shape. For Fr < 1 the disturbances disappear. Computer processing of the schlieren photographs showed that the experimental spatial dependences of the disturbance amplitude are close to the functions describing the distribution of the vertical velocity component in the inviscid flow past a sphere.     

Loss of energy during the motion of a vortex ring

Experimental estimates of energy and energy dissipation of a vortex ring are presented. The energy losses during the motion of a vortex ring and a streamlined solid are compared. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 24–30, January–February, 2008.     

Formation of a regular sequence of vortex loops around a rotating disk in stratified fluid

A regular system of vortex loops in annular flow behind the edge of a disk of 6–11 cm in diameter rotating in stratified fluid is first visualized using the shadowgraph techniques (classical method with the Foucault knife and the “filament-in-focus” method). Clearly outlined vortex loops are observed in strongly and weakly stratified fluids over a wide range of the angular disk rotation velocities. The dimensions of the vortex flow region depend on the stratification (buoyancy period), the angular velocity of rotation, and the disk diameter. Extended lengthy filaments which form spiral and irregular patterns inside the loops are clearly expressed in the fine flow structure. The filaments connect the neighboring loops. The trajectories of motion of the upper edges of the loops, i.e., the sources of short internal waves, are traced.     

Turbulent thermal in a stratified atmosphere

An approximate analytical model of a turbulent thermal in a stratified atmosphere is proposed. This model makes it possible to predict the dynamics of the ascent, suspension and oscillation processes of a buoyant cloud both within the troposphere and on entering the stratossphere. The values of the heat energy needed for the thermal to penetrate the tropopause in northern and southern latitudes are estimated. Estimates are obtained for the amount of material dumped into the stratosphere. A method of determining the thermal energy of volcanic eruptions of the explosive type is proposed. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 141–153, November–December, 1986.     

Motion of thermics in a stratified atmosphere

Regular features of motion of thermics in a stratified atmosphere are considered. Thermics are single and multiple free volumes of floating gas, which successively arise with a certain frequency near a horizontal surface. In a real atmosphere, large-scale thermics of this type appear, for example, as a result of powerful pulse actions on the ambient medium that are successively produced at one point near the Earth surface. Deceased. Institute of Physicotechnical and Radiotechnical Measurements, Moscow Region, Mendeleevo 141570. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 33–39, September–October, 1999.     

Diffusion of a ring vortex

The diffusion of a ring vortex is investigated in the present paper with allowance for the influence of the initial radius of the toroidal vorticity distribution on the flow structure. The statement of the problem in such a formulation makes it possible to classify and reinterpret results obtained previously. A vortex pair is studied together with a vortex ring. The toroidal vorticity and stream function distributions are obtained analytically. The self-induced lift velocity of the ring vortex is found. The influence of inertial terms is investigated numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 10–15, November–December, 1987.     

Turbulent floating jet in a stratified atmosphere

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 61–72, July–August, 1989.     

Analytical and numerical investigation of formation of a vortex ring in the process of rising of a thermal in the atmosphere

Formation of a vortex ring in the process of rising a heated light volume of air medium in the Earth’s gravity field is investigated. The results of calculations carried out on various computational grids are compared both with each other and with solutions of the approximate analytical theory of formation and motion of a buoyant vortex ring approved by the available experimental data. A good agreement between all the data is obtained.     

Transport in a turbulent vortex ring

Transport in a turbulent vortex ring is considered; the mass of a passive impurity transported by the vortex is found as a function of distance traveled via a formula that agrees closely with experiment. A method is indicated for filling the part of the vortex that transports the impurity without loss. The effects of the following factors on the transport have been examined: initial Reynolds number, roughness in walls of the exit hole, and density difference between the solution and the medium. The transport of aerosols and suspended particles by vortex rings is considered. Two methods of transport measurement are compared.     

Instability of a vertical columnar vortex in a stratified fluid

In this article, we study experimentally the evolution of a vertical columnar vortex in a stratified fluid. Three different measurement techniques are used. Particle image velocimetry allows us to monitor the time evolution of the characteristics of the vortex (Froude and Reynolds numbers). Dye visualizations reveal the existence of an instability for Froude numbers smaller than one, which creates an undulation of the vortex centerline. Synthetic schlieren visualization shows that the density structure of the unstable mode is very similar to the structure found recently numerically for the radiative instability of a Lamb–Oseen vortex (Riedinger et al. in J Fluid Mech, 2010). The experimental stability diagram and unstable wavelengths are compared with these numerical results. A secondary instability associated with the presence of critical layers is also observed for Froude numbers larger than one.     

Long-wave instability of a vortex ring

The instability of barrel-shaped vibrations of a vortex ring in an ideal fluid is investigated. These vibrations, stable for a vortex ring with a piecewise-uniform vorticity profile, appear to be unstable for a vortex ring with a smooth vorticity profile. The instability growth rate is found on the basis of the energy balance equation determining the energy transport from perturbations with negative energy in the critical layer to perturbations with positive energy in the rest of the flow. The curvature of the vortex ring, by virtue of which the perturbations with energies of different signs appear to be connected, plays a prominent role in the mechanism under consideration.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 72–78, November–December, 1995.     

Hydrodynamic structure of a vortex ring

Hot-wire anemometry and high-speed motion-picture photography have been used in an experimental study of the structure of a vortex ring in air. The velocity field and streamline pattern have been determined, together with the vorticity distribution. It has been shown that the vorticity is almost entirely localized in the region of the core of the vortex ring and quickly diminishes with distance from the core. Analysis of the experimental results permits a conclusion concerning the nonstationarity of vortex rings.The authors thank V. K. Sheremetov and V. A. Kosinov for their assistance.     

Rising vortex ring in a viscous fluid

Most theoretical results for thermals, whose motion is determined by the complex interaction between dynamics and buoyancy, have been obtained numerically [1–4]. The analytic solutions for a convection element have been limited to consideration of the self-similar regime [5]. At the same time, the preself-similar stage of development of a vortex ring of dynamic origin has been described analytically [6]. This approach is now extended to a rising vortex ring. In this case a modification of the traditional formulation of the problem makes it possible to obtain an analytic solution of the problem of a weak thermal in the form of unsteady temperature, vorticity and stream function fields that tend in the limit to the self-similar regime. The rate of ascent of the convective vortex ring is found. A solution is obtained for the two-dimensional analog of the problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–48, May–June, 1989.