Construction of axisymmetric steady states of an inviscid incompressible fluid by spatially discretized equations for pseudo-advected vorticity

摘要

An infinite number of generalized solutions to the stationary Euler equations with axisymmetry and prescribed circulation are constructed by applying the finite difference method for spatial variables to an equation of pseudo-advected vorticity. They are proved to be different from exact solutions which are written with trigonometric functions and a Coulomb wave function.