Journal of Fluid Mechanics

Structure of a linear array of hollow vortices of finite cross-section

G. R.  Baker a1, P. G.  Saffman a1 and J. S.  Sheffield a1
a1 Applied Mathematics, California Institute of Technology, Pasadena

Article author query
baker gr   [Google Scholar] 
saffman pg   [Google Scholar] 
sheffield js   [Google Scholar] 


Free-streamline theory is employed to construct an exact steady solution for a linear array of hollow, or stagnant cored, vortices in an inviscid incompressible fluid. If each vortex has area A and the separation is L, there are two possible shapes if A[fraction one-half]/L is less than a critical value 0.38 and none if it is larger. The stability of the shapes to two-dimensional, periodic and symmetric disturbances is considered for hollow vortices. The more deformed of the two possible shapes is found to be unstable while the less deformed shape is stable.

(Published Online March 29 2006)
(Received September 2 1975)