The linear stability of a doubly periodic array of vortices to three-dimensional perturbations is studied. The instabilities are separated into symmetric and antisymmetric modes. For two-dimensional disturbances only the symmetric mode is found to be unstable. The antisymmetric mode shows a peak in growth rate at long wavelengths. This is attributed to the Crow instability. For short wavelengths both symmetric and antisymmetric modes are found to have similar growth rates. This is attributed to the elliptical instability and it is found to occur even when the vortex cells are square, a physical explanation for which is provided, but for elongated vortex cells the growth rates are higher. Viscosity is found to have a strong stabilizing influence on short wavelength perturbations.
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Research Article|
May 11 2010
Linear stability of a doubly periodic array of vortices to three-dimensional perturbations Available to Purchase
A. K. Pathak;
A. K. Pathak
Department of Mechanical Engineering,
Indian Institute of Technology
, Kharagpur 721302, West Bengal, India
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S. N. Bhattacharyya
S. N. Bhattacharyya
Department of Mechanical Engineering,
Indian Institute of Technology
, Kharagpur 721302, West Bengal, India
Search for other works by this author on:
A. K. Pathak
Department of Mechanical Engineering,
Indian Institute of Technology
, Kharagpur 721302, West Bengal, India
S. N. Bhattacharyya
Department of Mechanical Engineering,
Indian Institute of Technology
, Kharagpur 721302, West Bengal, India
Physics of Fluids 22, 054105 (2010)
Article history
Received:
December 05 2008
Accepted:
March 16 2010
Citation
A. K. Pathak, S. N. Bhattacharyya; Linear stability of a doubly periodic array of vortices to three-dimensional perturbations. Physics of Fluids 1 May 2010; 22 (5): 054105. https://doi.org/10.1063/1.3415135
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