A&E Trounev IT Consulting, Toronto, Canada
Author list of organization
List of articles written by the authors of the organization
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BAER’S LAW AND EINSTEIN’S VORTEX HYPOTHESES
01.00.00 Physical-mathematical sciences
Description
We consider numerical solutions of the Navier-Stokes equations describing laminar and turbulent flows in channels of various geometries and in the cavity at large Reynolds numbers. An original numerical algorithm for integrating a system of nonlinear partial differential equations is developed, based on the convergence of the sequence of solutions of the Dirichlet problem. Based on this algorithm, a numerical model is created for the fusion of two laminar flows in a T-shaped channel. A new mechanism of meandering is established, which consists in the fact that when the two streams merge, a jet is formed containing the zones of return flow. Vortex motion in a rectangular cavity is studied. It is established that the numerical solution of the problem with discontinuous boundary conditions loses stability at Reynolds number Re> 2340. The trajectories of passive impurity particles in a cylindrical cavity are investigated. An explanation of the behavior of tea leaves in a cup of tea in the formation of a toroidal vortex because of circular stirring is confirmed, which is confirms the wellknown hypothesis of Einstein. A numerical model of flow in an open channel with a bottom incline in a rotating system is developed. It is shown that in both laminar and turbulent flow under certain conditions a secondary vortex flow arises in the channel due to the Coriolis force, which explains the well-known Baer law and confirms the Einstein hypothesis
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VORTEX TURBULENT FLOWS IN ATMOSPHERES OF PLANETS AND ON THE SUN
01.00.00 Physical-mathematical sciences
Description
In this work, we consider two types of vortex currents-cyclones and anticyclones in the Northern and Southern Hemispheres. Numerical modeling of turbulent flows of these types uses the model of the planetary boundary layer developed by the author. The purpose of the study is to test hypotheses about the influence of the Coriolis force on the formation of cyclones and anticyclones in the northern and southern latitudes. The first hypothesis on the direction of circulation in cyclones was verified in the case of axisymmetric radially converging and vertically rising turbulent flows with a natural Coriolis parameter and viscosity. From the obtained data of numerical experiments, it follows that the current in the northern latitudes circulates in a counter clockwise direction, and in the south - in a clockwise direction, in full accordance with the observational data. Thus, we have shown that a cyclonic flow is formed in a turbulent radially converging flow under the influence of the Coriolis force. The second hypothesis on the formation of anticyclones was verified in the case of radially divergent and vertically descending turbulent flows. Because of numerical experiments, it was established that in this case, the current in the northern latitudes circulates clockwise, and in the south - in a counter clockwise direction, which corresponds to observations for anticyclones. To test the effect of the cyclone (anticyclone) center velocity on circulation, a nonstationary 3D model of turbulent flow was developed. Within the framework of this model, flows in cyclones and anticyclones moving at a constant speed, as well as in shear flow, are studied. Some types of loop protuberances on the Sun are explained by the presence of a vortex turbulent flow starting in the bowels of the Sun and encompassing the chromosphere
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