A quasi complex-lamellar solution for a hemispherically bounded cyclonic flowfield

This work describes an inviscid solution for a cyclonic flowfield evolving in hemispherical chamber configuration. In this context, vigorously swirling motion is triggered by gaseous stream that introduced tangentially to the inner circumference of chamber's equatorial plane. The resulting updraft spirals around while sweeping wall, reverses direction approaching headend, and then tunnels itself out through core portion chamber. Our analysis proceeds from Bragg–Hawthorne formulation, which proves effective treatment steady, incompressible, axisymmetric motions. Then using appropriate boundary conditions, we are able obtain closed-form expression Stokes streamfunction both spherical cylindrical coordinates. Other properties interest subsequently deduced, these include principal velocities pressure distributions, vorticity, swirl intensity, helicity density, crossflow velocity, location axial mantle; latter separates outer annular inner, centralized downdraft. Due large part overarching curvature, also exhibits polar mantle across flow becomes entirely radial inward. Along lower shorter interface, velocity vanishes switching angular direction. Interestingly, mantles coincide exit plane where ideal outlet size, prescribed position, found be approximately 70.7% radius. We thus recover same fraction analog right-cylindrical essentially complex-lamellar established.