For the present, a vortex will be defined as a two‐dimensional region containing nested closed streamlines. Such a vortex need not contain an extremal point of vorticity nor a minimal point of pressure. In the Stokes‐flow limit, a pressure minimum is not possible. A local criterion for the existence of a pressure minimum within a vortex is derived, leading to a transition Reynolds number above which the vortex contains a pressure minimum. In the limit of infinite Reynolds number, a pressure minimum must exist within the vortex. Specific data for a cavity flow and the flow past a circular cylinder are presented.
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Lugt previously concluded in Ref. 1 that, for nonzero Reynolds number, the line integral of the normal component of the steady two-dimensional momentum equations around a closed streamline implies that a pressure minimum always exists—it does not.
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© 1994 American Institute of Physics.
1994
American Institute of Physics
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