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Absolute instabilities in eccentric Taylor-Couette-Poiseuille flow

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Absolute instabilities are investigated in the Taylor–Couette system with axial flow and eccentricity of the cylinder axes, using the Briggs–Bers criterion with a pseudospectral method. Domains of absolute instability are determined for a ratio of radii eta = 0.5, and eccentricities e<=0.7. Reynolds numbers based on the inner cylinder rotation Re_Omega and mean axial advection Re_z are taken below 50 and 400 respectively. Five modes of instability are studied, respectively the toroidal Taylor vortex, and the left- and right- handed helical vortices of “pseudo-azimuthal” wavenumber 1 and 2, which include the critical modes of the convective instability. A general criterion is presented to discriminate genuine pinches from spurious saddle points in the vicinity of third-order saddle points D^2D=Dk^2= 0 of the dispersion relation D in the complex wavenumber k plane.

Author(s):

Colin Leclercq    
LMFA - Ecole Centrale de Lyon
France

Benoît Pier    
LMFA - CNRS
France

Julian Scott    
LMFA - Ecole Centrale de Lyon
France