The steady boundary layer due to a fast vortex

Andrew J. Bernoff; Harald J.H.M. Van Dongen; Seth Lichter

doi:10.1063/1.868823

The steady boundary layer due to a fast vortex

Andrew J. Bernoff, Harald J.H.M. Van Dongen, Seth Lichter^*

^*Corresponding author for this work

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A point vortex located above and convected parallel to a wall is an important model of the process by which a boundary layer becomes unstable due to external disturbances. Often it has been assumed that the boundary layer due to the passage of the vortex is inherently unsteady. Here we show that for a vortex convected by a uniform shear flow, there is a steady solution when the speed of the vortex c_v is sufficiently fast. The existence of the steady solution is demonstrated analytically in the limit of large vortex velocity (c_v→∞) and numerically at more moderate speeds. This solution may provide a useful base state about which to investigate the stability of a boundary layer induced by external disturbances.

Original language	English (US)
Pages (from-to)	156-162
Number of pages	7
Journal	Physics of Fluids
Volume	8
Issue number	1
DOIs	https://doi.org/10.1063/1.868823
State	Published - 1996

ASJC Scopus subject areas

Computational Mechanics
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering
Fluid Flow and Transfer Processes

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abstract = "A point vortex located above and convected parallel to a wall is an important model of the process by which a boundary layer becomes unstable due to external disturbances. Often it has been assumed that the boundary layer due to the passage of the vortex is inherently unsteady. Here we show that for a vortex convected by a uniform shear flow, there is a steady solution when the speed of the vortex cv is sufficiently fast. The existence of the steady solution is demonstrated analytically in the limit of large vortex velocity (cv→∞) and numerically at more moderate speeds. This solution may provide a useful base state about which to investigate the stability of a boundary layer induced by external disturbances.",

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AU - Bernoff, Andrew J.

AU - Van Dongen, Harald J.H.M.

AU - Lichter, Seth

PY - 1996

Y1 - 1996

N2 - A point vortex located above and convected parallel to a wall is an important model of the process by which a boundary layer becomes unstable due to external disturbances. Often it has been assumed that the boundary layer due to the passage of the vortex is inherently unsteady. Here we show that for a vortex convected by a uniform shear flow, there is a steady solution when the speed of the vortex cv is sufficiently fast. The existence of the steady solution is demonstrated analytically in the limit of large vortex velocity (cv→∞) and numerically at more moderate speeds. This solution may provide a useful base state about which to investigate the stability of a boundary layer induced by external disturbances.

AB - A point vortex located above and convected parallel to a wall is an important model of the process by which a boundary layer becomes unstable due to external disturbances. Often it has been assumed that the boundary layer due to the passage of the vortex is inherently unsteady. Here we show that for a vortex convected by a uniform shear flow, there is a steady solution when the speed of the vortex cv is sufficiently fast. The existence of the steady solution is demonstrated analytically in the limit of large vortex velocity (cv→∞) and numerically at more moderate speeds. This solution may provide a useful base state about which to investigate the stability of a boundary layer induced by external disturbances.

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The steady boundary layer due to a fast vortex

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