Three-Dimensional Unsteady Axisymmetric Viscous Beltrami Vortex Solutions to the Navier–Stokes Equations

This paper is aimed at eliciting consistency conditions for the existence of unsteady incompressible axisymmetric swirling viscous Beltrami vortices and explicitly constructing solutions that obey as well Navier–Stokes equations. By flow, it meant vorticity, i.e., curl velocity, proportional to velocity any local point in space time. The are derived proportionality coefficient, field external force. whose dimension [length−1], either constant or nonconstant. In former case, well-known exact nondivergent three-dimensional vortex obtained by solving evolution equations stream function directly. latter given nonlinear function, one which corresponds Bragg–Hawthorne equation steady inviscid flow. Solutions a novel type found numerically constraint fixed Time dependence recovered taking advantage linearity function. coefficient depend on A phenomenon partial restoration broken scaling invariance observed short distances.