Hysteresis and precession of a swirling jet normal to a wall

Interaction of a swirling jet with a no-slip surface has striking features of fundamental and practical interest. Different flow states and transitions among them occur at the same conditions in combustors, vortex tubes, and tornadoes. The jet axis can undergo precession and bending in combustors; this precession enhances large-scale mixing and reduces emissions of NOx. To explore the mechanisms of these phenomena, we address conically similar swirling jets normal to a wall. In addition to the Serrin model of tornadolike flows, a new model is developed where the flow is singularity free on the axis. New analytical and numerical solutions of the Navier-Stokes equations explain occurrence of multiple states and show that hysteresis is a common feature of wall-normal vortices or swirling jets no matter where sources of motion are located. Then we study the jet stability with the aid of a new approach accounting for deceleration and nonparallelism of the base flow. An appropriate transformation of variables reduces the stability problem for this strongly nonparallel flow to a set of ordinary differential equations. A particular flow whose stability is studied in detail is a half-line vortex normal to a rigid plane-a model of a tornado and of a swirling jet issuing from a nozzle in in a combustor. Helical counter-rotating disturbances appear to be first growing as Reynolds number increases. Disturbance frequency changes its sign along the neutral curve while the wave number remains positive. Short disturbance waves propagate downstream and long waves propagate upstream. This helical instability causes bending of the vortex axis and its precession-the effects observed in technological flows and in tornadoes.V. Shtern, J. M

Hysteresis and precession of a swirling jet normal to a wall

Interaction of a swirling jet with a no-slip surface has striking features of fundamental and practical interest. Different flow states and transitions among them occur at the same conditions in combustors, vortex tubes, and tornadoes. The jet axis can undergo precession and bending in combustors; this precession enhances large-scale mixing and reduces emissions of NOx. To explore the mechanisms of these phenomena, we address conically similar swirling jets normal to a wall. In addition to the Serrin model of tornadolike flows, a new model is developed where the flow is singularity free on the axis. New analytical and numerical solutions of the Navier-Stokes equations explain occurrence of multiple states and show that hysteresis is a common feature of wall-normal vortices or swirling jets no matter where sources of motion are located. Then we study the jet stability with the aid of a new approach accounting for deceleration and nonparallelism of the base flow. An appropriate transformation of variables reduces the stability problem for this strongly nonparallel flow to a set of ordinary differential equations. A particular flow whose stability is studied in detail is a half-line vortex normal to a rigid plane-a model of a tornado and of a swirling jet issuing from a nozzle in in a combustor. Helical counter-rotating disturbances appear to be first growing as Reynolds number increases. Disturbance frequency changes its sign along the neutral curve while the wave number remains positive. Short disturbance waves propagate downstream and long waves propagate upstream. This helical instability causes bending of the vortex axis and its precession-the effects observed in technological flows and in tornadoes.V. Shtern, J. M

Some results of cislunar plasma research

The main results of plasma cislunar investigations, carried out during Luna-19 and Luna-22 spacecraft flights by means of dual frequency dispersion interferrometry, are briefly outlined. It is shown that a thin layer of plasma, with a height of several tens of kilometers and a maximum concentration of the order 1,000 electrons/cu cm exists above the solar illuminated lunar surface. A physical model of the formation and existence of such a plasma in cislunar space is proposed, taking into account the influence of local magnetic areas on the moon

The nighttime ionosphere of Mars from Mars-4 and Mars-5 radio occultation dual-frequency measurements

Dual frequency radio sounding of the Martian nighttime ionosphere was carried out during the exits from behind the planet of the Mars-4 spacecraft on February 2, 1974 and the Mars-5 spacecraft on February 18, 1974. In these experiments, the spacecraft transmitter emitted two coherent monochromatic signals in decimeter and centimeter wavelength ranges. At the Earth receiving station, the reduced phase difference (or frequencies) of these signals was measured. The nighttime ionosphere of Mars measured in both cases had a peak electron density of approximately 5 X 1,000/cu cm at an altitude of 110 to 130 km. At the times of spacecraft exit, the solar zenith angles at the point of occultation were 127 deg and 106 deg, respectively. The height profiles of electron concentration were obtained assuming spherical symmetry of the Martian ionosphere

Multivariate p-dic L-function

We construct multivariate p-adic L-function in the p-adic number fild by using Washington method.Comment: 9 page

SOME ABSTRACT PROPERTIES OF SEMIGROUPS APPEARING IN SUPERCONFORMAL THEORIES

A new type of semigroups which appears while dealing with $N=1$ superconformal symmetry in superstring theories is considered. The ideal series having unusual abstract properties is constructed. Various idealisers are introduced and studied. The ideal quasicharacter is defined. Green's relations are found and their connection with the ideal quasicharacter is established.Comment: 11 page

Разбиение железнодорожного состава на отдельные вагоны

The problem of the decomposition of a train into its cars is considered in this paper. This problem arises while making automatic systems of train registration. The input data is a film that visualizes the train motion. An algorithm for solving the problem is proposed. An experiment is conducted using 16 different films to test the algorithm.Рассматривается задача, возникающая при создании автоматизированных систем регистрации железнодорожных составов, а именно: разбиение состава на отдельные вагоны (цистерны). Приводится описание алгоритма, предназначенного для решения данной задачи. Входными данными для него служит фильм, в котором можно видеть движение железнодорожного состава. Для тестирования алгоритма проводится эксперимент с использованием 16 различных фильмов

Generalized Bloch analysis and propagators on Riemannian manifolds with a discrete symmetry

We consider an invariant quantum Hamiltonian $H=-\Delta_{LB}+V$ in the $L^{2}$ space based on a Riemannian manifold $\tilde{M}$ with a countable discrete symmetry group $\Gamma$. Typically, $\tilde{M}$ is the universal covering space of a multiply connected Riemannian manifold $M$ and $\Gamma$ is the fundamental group of $M$. On the one hand, following the basic step of the Bloch analysis, one decomposes the $L^{2}$ space over $\tilde{M}$ into a direct integral of Hilbert spaces formed by equivariant functions on $\tilde{M}$. The Hamiltonian $H$ decomposes correspondingly, with each component $H_{\Lambda}$ being defined by a quasi-periodic boundary condition. The quasi-periodic boundary conditions are in turn determined by irreducible unitary representations $\Lambda$ of $\Gamma$. On the other hand, fixing a quasi-periodic boundary condition (i.e., a unitary representation $\Lambda$ of $\Gamma$) one can express the corresponding propagator in terms of the propagator associated to the Hamiltonian $H$. We discuss these procedures in detail and show that in a sense they are mutually inverse