Multi-mode states in quasi-two-dimensional rotating flows

<p>The idea of the multiplicity of equilibrium states of the atmospheric circulation in geophysical hydrodynamics goes back to Charne and DeVore 1979, where, for a model with a small number of variables, solutions with significantly different values of the zonal and wave velocity components were obtained (see also Laurie, Bouchet 2015, Herbert et al. 2020). The results of similar studies for low-parameter approximations were given by Kallen 1980, Gluhovsky 2001, Koo, Ghil 2002 ... The circulation modes differed in the magnitude of the zonal component of the flow. At weak transport, the role of almost stationary atmospheric eddies is enhanced, which corresponds to circulation blocking modes. Laboratory confirmation of the effect was obtained from Weeks et al. 1997, Tian et al. 2001.</p><p>In the same years, in the experiments of A.M. Obukhov and coworkers, modes with differently directed axes of large-scale fluid rotation were observed in closed vessels at the same value of external generation - Obukhov et al. 1976, Gledzer et al. 1981.</p><p>In the present study, supported by Russian Science Foundation (Project 19-17-00248), the above types of multi-mode are considered based on laboratory and numerical experiments in circular rotating channels. It is known that the permanent magnet location configurations (source-sinks) could create an almost stationary vortex distribution pattern Gledzer et al. 2013,2014. The transition between different states is provided by a change in the value of the main parameter of electric current generation with subsequent restoration of its initial value.</p><p>The experimental results presented below are obtained for a rotating annular channel (rotation periods up to 1 minute) filled with an electrically conductive 10% copper sulfate solution. The bottoms of circular channels with inner and outer radii of 1) 5.5 cm and 18 cm  2) 5 cm and 36 cm have an axisymmetric conical shape with a height of 1 cm.</p><p>Depending on channel rotation periods or source configurations, it is possible: 1) Initial and final modes differ quantitatively in the number of generated vortices. 2) The number of vortex formations does not change, but differ in their spatial localization. 3) After changing and restoring the value of the defining parameter, the flow returns to the mode which is practically the same as the initial one.</p><p>Numerical experiments with the shallow water model confirmed the results obtained in laboratory experiments on the possibility of transition to new modes when the parameter determining the external force is changed for some time. For the source-sink method, a change in the number of large vortices (cyclones) is observed. At MHD generation it is possible to detect a change in the finite spatial position of vortices with preservation of their number.</p><p>Experiments support the conclusion that different modes of barotropic dynamics may exist. And it is unlikely to be associated with any low-parameter approximation of the velocity field in the model.</p><p>In our and earlier experiments and models, multi-mode is a property of dynamics in general. The mechanism of multi-mode may be an alternative to the traditional scenario of transition to other modes when external conditions change.</p>

Theoretical Method for Controlling the Flow Rate of the Pumped Medium by Positioning Locking Elements of the Pipe Fittings

Any object located in the pipeline, including the flow meter, leads to a drop in pressure in the pipeline and the need to increase the power of the pumps. Therefore, it seems promising to reduce energy consumption for pumping fluid in the pipeline by reducing the number of flow meters installed after shut-off and control valves and to predict the flow rate of the pumped medium by the position of the locking element in the valve. This will also lead to a reduction in the cost of transporting media by reducing the number of metering devices. In order to solve this complex problem in pipeline transport, the article solves a number of regional problems of hydromechanics based on the finite element method. In order to simplify the acquaintance with these solutions, as well as their practical application by engineers, the article proposes «parametric stationary vortex flow models in such types of shut-off and control valves as a ball valve, butterfly valve, wedge gate valve, angle valve. Without prejudice to generality of the technique, water is considered as an example of a pumped medium. The analysis was performed using FLOTRAN CFD software of ANSYS10 ED program». The article describes in detail the capabilities of both the graphical interface and the command line. Creating models is accompanied by full comments on the actions, which allows any user to master these models. All stages of building models are considered in detail: construction of a solid-state model, selection of elements, appointment of properties of the pumped media, appointment of boundary conditions, as well as solving the problem and viewing the results. «It has been established that the flow rate of the medium is affected both by the geometry of the considered types of shut-off and control valves», and the position of the locking element. The technique can be applied to any designs of pipe fittings associated with calculation of movement of a viscous fluid.

Non-stationary vortex streets in shear flows

Spatially periodic vortex systems that form due to unstable shear flows are called vortex streets. A number of exact and asymptotic solutions of two-dimensional hydrodynamic equations describing nonstationary vortex streets have been constructed. It is shown that the superposition of the flow with a constant horizontal shear and its perturbations in the form of a nonmodal wave provides an exact solution that describes a nonstationary vortex street with rotating elliptic current lines. The width of the zone occupied by such a vortex street has been determined. The equation of separatrix separating vortex cells with closed current lines from an external meandering flow has been obtained. The influence of the quasi-two-dimensional compressibility and beta effect on the dynamics of vortex streets has been studied based on the potential vorticity transport equation. The solutions describing the formation of vortex streets during the development of an unstable zonal periodic flow and a free shear layer have been constructed using a longwave approximation.

Исследование связанной динамики магнитных вихрей в трехслойном проводящем наноцилиндре

Solving numerically the generalized Landau–Lifshitz equation, we have carried out the micromagnetic investigation of the dynamics of two dipole-coupled magnetic vortices in a trilayer nanocolumn under the action of the external magnetic field directed perpendicular to the sample plane and spin-polarized electric field. The possible existence of different regimes of vortex motion, depending on the polarized current, is demonstrated. The current dependence of the oscillation frequency for the case of stationary dynamics of coupled vortices with the same frequency has been established. The possibility of controlling the frequency of the stationary vortex motion and tuning the control current amplitude by the external magnetic field is shown. Using the analytical method for simplified description of the dynamics of coupled vortices, the current and magnetic-field dependences of the frequency have been obtained, which are qualitatively consistent with the numerical data.