| Summary: | Turbulence has remained an unsolved problem in physics, despite the availability of some numerical results. The onset and growth of disturbances leading to two- and three-dimensional turbulence have been theoretically and computationally shown for wall excitation with the response having modal and nonmodal components in the spectrum. The nonmodal component is seen to be dominant. Here, we conclusively show the nonmodal growth for a transition to turbulence, with the same equilibrium flow excited from the free stream with results from linearized and nonlinear two-dimensional Navier-Stokes equations. We establish that transition to turbulence definitely requires nonlinearity, even if the onset process is similar to a linear mechanism. Thus, the transition to turbulence in wall-bounded flows is due to a nonmodal nonlinear mechanism for any disturbance.
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