PATTERN SELECTION IN THE PRESENCE OF A CROSS-FLOW

We study the pattern selection and the dynamics of a bifurcating syste m such as Taylor-Couette flow or Rayleigh-Benard convection, subject t o an externally imposed cross flow using the complex Ginzburg-Landau e quation as a qualitative model. We show that the bifurcation scenario is radically modified by the introduction of a cross flow, and that a nonlinear global mode, i.e., a nonlinear oscillating solution in a Sem i-infinite domain [0, +infinity), with a homogeneous condition at x = 0, exists only when the basic state is linearly absolutely unstable. W e derive the scaling law for the characteristic growth size, which var ies as epsilon(-1/2) (epsilon being the criticality parameter), and co mpares satisfactorily with numerical and experimental results from the literature.