The Effect of Viscosity on the Stability of Planar Vortices with Fine Structure

• Published in: Quarterly journal of mechanics and applied mathematics Vol. 56; no. 4; pp. 649 - 657
• Main Authors: Hall, Ian M., Bassom, Andrew P., Gilbert, Andrew D.
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01-11-2003; Oxford Publishing Limited (England)
• Subjects: Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Physics; Turbulent flows, convection, and heat transfer; Fine structure; Viscosity; Modelling; Vortex flow; Turbulence structure
• ISSN: 0033-5614; 1464-3855
• DOI: 10.1093/qjmam/56.4.649

We examine the viscous response of sharp‐edged vortices surrounded by fine structure. Such compact vortices admit normal mode solutions, and when weak vorticity is superimposed around the edge of the vortex a quasi‐mode appears. A critical layer is formed at the location at which the angular velocity of the fluid matches the frequency of the normal mode. Fine‐scale vorticity within this layer, combined with the presence of viscosity, can affect the stability of the quasi‐mode in a number of ways. Here we discuss briefly one situation for which viscosity can have a destabilizing effect.