On the Axisymmetric Steady Incompressible Beltrami Flows  

作　　者：Pavel Bělík Xueqing Su Douglas P. Dokken Kurt Scholz Mikhail M. Shvartsman Pavel Bělík;Xueqing Su;Douglas P. Dokken;Kurt Scholz;Mikhail M. Shvartsman(Department of Mathematics, Statistics, and Computer Science, Augsburg University, Minneapolis, MN, USA;Department of Statistics, University of Michigan, Ann Arbor, MI, USA;Department of Mathematics, University of St. Thomas, Saint Paul, MN, USA)

机构地区：[1]Department of Mathematics, Statistics, and Computer Science, Augsburg University, Minneapolis, MN, USA [2]Department of Statistics, University of Michigan, Ann Arbor, MI, USA [3]Department of Mathematics, University of St. Thomas, Saint Paul, MN, USA

出　　处：《Open Journal of Fluid Dynamics》2020年第3期208-238,共31页流体动力学（英文）

摘　　要：In this paper, Beltrami vector fields in several orthogonal coordinate systems are obtained analytically and numerically. Specifically, axisymmetric incompressible inviscid steady state Beltrami (Trkalian) fluid flows are obtained with the motivation to model flows that have been hypothesized to occur in tornadic flows. The studied coordinate systems include those that appear amenable to modeling such flows: the cylindrical, spherical, paraboloidal, and prolate and oblate spheroidal systems. The usual Euler equations are reformulated using the Bragg-Hawthorne equation for the stream function of the flow, which is solved analytically or numerically in each coordinate system under the assumption of separability of variables. Many of the obtained flows are visualized via contour plots of their stream functions in the <em>rz</em>-plane. Finally, the results are combined to provide a qualitative quasi-static model for a progression of tornado-like flows that develop as swirl increases. The results in this paper are equally applicable in electromagnetics, where the equivalent concept is that of a force-free magnetic field.In this paper, Beltrami vector fields in several orthogonal coordinate systems are obtained analytically and numerically. Specifically, axisymmetric incompressible inviscid steady state Beltrami (Trkalian) fluid flows are obtained with the motivation to model flows that have been hypothesized to occur in tornadic flows. The studied coordinate systems include those that appear amenable to modeling such flows: the cylindrical, spherical, paraboloidal, and prolate and oblate spheroidal systems. The usual Euler equations are reformulated using the Bragg-Hawthorne equation for the stream function of the flow, which is solved analytically or numerically in each coordinate system under the assumption of separability of variables. Many of the obtained flows are visualized via contour plots of their stream functions in the <em>rz</em>-plane. Finally, the results are combined to provide a qualitative quasi-static model for a progression of tornado-like flows that develop as swirl increases. The results in this paper are equally applicable in electromagnetics, where the equivalent concept is that of a force-free magnetic field.

关 键 词：Axisymmetric Beltrami Flow Trkalian Flow Bragg-Hawthorne Equation Cylindrical Coordinates Spherical Coordinates Paraboloidal Coordinates Prolate Spheroidal Coordinates Oblate Spheroidal Coordinates Vorticity 

分 类 号：O17[理学—数学]