Lift-up effect ($u(y,t)=u_0(y)-t{U}^{\prime }(y)v_0(y)$)

A streamwise-independent cross-stream disturbance in an inviscid parallel shear flow has time-independent wall-normal velocity. It advects the base streamwise momentum, producing the displayed linear growth of streamwise velocity and quadratic growth of perturbation kinetic energy. This is algebraic amplification, not an exponentially unstable normal mode; it exemplifies transient growth from non-normal modes.