| Popis: |
A study was made of the class of solutions of the NavierStokes equations wherein the radial, tangential, and axial velocities in cylindrical coordinates (r, theta , z) are of the forms u = u(r), v' v(r), and w = zw-(bar)(r). These solutions are found to represent a rather large class of three-dimensional viscous vortex motions. The class of solutions contains Burger's analytic solution for an unconstrained one-celled vortex as a special limiting case. The solutions obtained show that vortex motions are possible which have more than ons ""cell.'' That is, the flow may not simply spiral in toward an axis and out along it as in a one-celled configuration but may have nested regions of successively reversed axial flow. The behavior of the solutions, in passing from single to multiple-celled configurations, is discussed and the solution for the extremely interesting case of a twocelled analog to Bungers' unconstrained vortex, which probably occurs quite often in nature, is given in closed form. An interesting outcome of the investigation discussed is that, for a given narrow range of dimensionless parameters governing the flow, no steady solutions of the NavierStokes equations of the type under investigation are possible. (auth) |
