An analytical solution is given for a time-decay Rankine vortex profile due to viscous effects. The vortex filament is assumed to be isolated, strong, concentrated and having zero-meridional flow （i.e. radial and axi...An analytical solution is given for a time-decay Rankine vortex profile due to viscous effects. The vortex filament is assumed to be isolated, strong, concentrated and having zero-meridional flow （i.e. radial and axial velocities are equal to zero）. Zero-meridional renders the governing equations for an unsteady, incompressible and axisymmetric vortex in a simple form. Based on the tangential momentum equation, the spatial-temporal distributions of the swirl velocity are given in terms of Fourier-Bessel series by using separation of variables technique. A general formula is derived by total differentiation of the swirl velocity with respect to time, depicting the viscous dissipation for Oseen and Taylor-like vortex profiles. This analysis is validated by comparison with previous experimental data.展开更多
文摘An analytical solution is given for a time-decay Rankine vortex profile due to viscous effects. The vortex filament is assumed to be isolated, strong, concentrated and having zero-meridional flow （i.e. radial and axial velocities are equal to zero）. Zero-meridional renders the governing equations for an unsteady, incompressible and axisymmetric vortex in a simple form. Based on the tangential momentum equation, the spatial-temporal distributions of the swirl velocity are given in terms of Fourier-Bessel series by using separation of variables technique. A general formula is derived by total differentiation of the swirl velocity with respect to time, depicting the viscous dissipation for Oseen and Taylor-like vortex profiles. This analysis is validated by comparison with previous experimental data.
