A NOTE ON THE VISCOELASTIC INSTABILITY OF CIRCULAR-COUETTE FLOW

The linearised equations describing the onset of axisymmetric viscoela stic instability in Couette flows with negligible inertia (R.G. Larson , E.S.G. Shaqfeh and S.J. Muller, J. Fluid Mech., 218 (1990) 573) are reconsidered in the narrow gap limit. A simple proof is provided that the bifurcation parameter LAMBDA is purely imaginary, and it is shown how LAMBDA can be evaluated accurately using rapidly convergent series . A new lower bound is found for the behaviour of LAMBDA at large wave numbers.