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1950•The Quarterly Journal of Mechanics and Applied MathematicsRequires access

A NOTE ON THE HODOGRAPH TRANSFORMATION FOR THE TWO-DIMENSIONAL VORTEX FLOW OF AN INCOMPRESSIBLE FLUID

S. GOLDSTEIN, Michael James Lighthill

Open publisher page 4 citations

Abstract

In the hodograph transformation of the two-dimensional vortex flow of an incompressible, inviscid fluid, branch lines arise, similar to those previously encountered in the theory of the irrotational supersonic flow of a gas. The result is of importance for the calculation of vortex flows with ‘free’ streamlines, and in particular for the calculation of jets with vorticity present. As a simple mathematical example the hodograph plane is described corresponding to the flow of a stream with uniform shear past a circular cylinder; the hodograph plane is a Riemann surface of six sheets.

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What this paper is about

In the hodograph transformation of the two-dimensional vortex flow of an incompressible, inviscid fluid, branch lines arise, similar to those previously encountered in the theory of the irrotational supersonic flow of a gas. The result is of importance for the calculation of vortex flows with ‘free’ streamlines, and in particular for the calculation of jets with vorticity present. As a simple mathematical example the hodograph plane is described corresponding to the flow of a stream with uniform shear past a circular cylinder; the hodograph plane is a Riemann surface of six sheets.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In the hodograph transformation of the two-dimensional vortex flow of an incompressible, inviscid fluid, branch lines arise, similar to those previously encountered in the theory of the irrotational supersonic flow of a gas. The result is of importance for the calculation of vortex flows with ‘free’ streamlines, and in particular for the calculation of jets with vorticity present. As a simple mathematical example the hodograph plane is described corresponding to the flow of a stream with uniform shear past a circular cylinder; the hodograph plane is a Riemann surface of six sheets.

Key concepts: Hodograph, Streamlines, streaklines, and pathlines, Inviscid flow, Conservative vector field, Potential flow around a circular cylinder, Vortex, Vorticity, Mechanics

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