Cause-and-effect of linear mechanisms sustaining wall turbulence

Despite the nonlinear nature of turbulence, there is evidence that part energy-transfer mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from stability theory and comprise exponential instabilities, neutral modes, transient growth non-normal operators, parametric instabilities temporal mean-flow variations, among others. These mechanisms, each potentially capable leading observed structure, are rooted in theoretical conceptual arguments. Whether flow follows any or a combination them remains elusive. Here, we evaluate responsible for energy transfer streamwise-averaged ($\bf U$) fluctuating velocities u'$). We use cause-and-effect analysis based on interventions. This achieved by direct numerical simulation turbulent channel flows at low Reynolds number, which $\bf U$ u'$ constrained preclude targeted mechanism. show sufficient realistic turbulence. Self-sustaining persists when mean suppressed. further key component Orr/push-over mechanism induced spanwise variations base flow. Finally, demonstrate an ensemble simulations with various frozen-in-time arranged so only active, faithfully represent as Our approach provides evaluation energy-injection fully system simplifies model self-sustaining