Axisymmetric Flows in the Boundary Layer of a Maintained Vortex

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Abstract
The three-dimensional flow in the boundary layer of a tornado-like vortex, with a core region of large vorticity and an outer region of nearly zero vorticity, is obtained by alternatingly solving the two nonlinear boundary-layer equations for the radial and the vertical distributions of the velocities. It is found that in the inner region the flow is of the Ekman-layer type, with an oscillatory distribution of the velocities in the vertical, while in the outer region the flow is of the ordinary boundary-layer type, with the velocity components approaching their respective values asymptotically without oscillation at a large distance from the boundary. This distribution of the radial velocity results in a weak descending motion in the outer region and a relatively strong ascending motion in the inner region with a sharp maximum upward motion occurring inside the radius of the maximum tangential wind where the boundary-layer thickness increases most rapidly outward. Abstract The three-dimensional flow in the boundary layer of a tornado-like vortex, with a core region of large vorticity and an outer region of nearly zero vorticity, is obtained by alternatingly solving the two nonlinear boundary-layer equations for the radial and the vertical distributions of the velocities. It is found that in the inner region the flow is of the Ekman-layer type, with an oscillatory distribution of the velocities in the vertical, while in the outer region the flow is of the ordinary boundary-layer type, with the velocity components approaching their respective values asymptotically without oscillation at a large distance from the boundary. This distribution of the radial velocity results in a weak descending motion in the outer region and a relatively strong ascending motion in the inner region with a sharp maximum upward motion occurring inside the radius of the maximum tangential wind where the boundary-layer thickness increases most rapidly outward.

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