Nonmodal growth of three-dimensional disturbances on plane Couette–Poiseuille flows

The time development of three-dimensional disturbances superimposed on a variety of mean flow profiles representing plane Couette–Poiseuille flow is investigated numerically. Specifically, with y representing the wall normal coordinate, the mean flow profiles U(y) are represented by U(y)=A(1−y2)+By, where B=1 when 0⩽A⩽1∕2 and B=2A(1−A) when 1∕2⩽A⩽1. For streamwise independent disturbances, which are the most amplified ones, there is an increase of the disturbance peak amplification when the parameter A increases in the interval 1∕10⩽A⩽1∕2. In the interval 1∕2⩽A⩽9∕10, and especially for 9∕10⩽A⩽1, the disturbance peak amplification decreases rapidly when A is increased. For A close to 1, a slight reduction of A will therefore cause a strong increase of the disturbance amplification.