The modulational stability of Taylor vortices in a curved channel

In this paper we use a multiple scales approach to derive an equation gover ning the modulational stability of Taylor vortices in a high Reynolds numbe r ow through a curved channel of small gap. The evolution equation governin g the two-dimensional modulation of Taylor vortices is found to be a modi e d Burgers equation with a new nonlinear term (A(T) + A(2)A(X) = +/-A(XX)). When finite but small curvature effects are accounted for, this modi ed Bur gers equation generalizes to A(T) + A(2)A(X) = +/-A(XX) + lambda A. Numeric al solutions of this equation show that a family of periodic traveling wave s exists, with profiles becoming increasingly steeper as the length of the system is increased.