Three-dimensional disturbances in channel flows

In this paper we conduct a linear stability analysis of three-dimensional two-fluid flows and use an energy method to comment on its stability. The governing equations are solved using a Chebyshev-tau D-2 method that reduces the order of the coupled governing Orr-Sommerfeld and Squire equation and hence achieves more accurate results. A new norm, called the M-norm, is defined to overcome the problem of nonconvergence of the disturbance energy. The maximum amplification of O(10(3)) is achieved for streamwise independent disturbances due to the "lift-up effect," as is the case of three-dimensional single-fluid flow. In contrast to two-dimensional flows, where the adjoint of the leading mode influences the growth, the three-dimensional single-fluid flow growth is influenced by the adjoint of the second mode. Although most growth in three-dimensional two-fluid flow is due to the contribution of the adjoint of the second mode, at large time the interfacial mode contributes to most growth. (c) 2007 American Institute of Physics.