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The energy method, also known as the Reynolds-Orr equation, is widelyutilized in predicting the unconditional stability threshold of shear flowsowing to the zero contribution of nonlinear terms to the time derivative ofperturbation kinetic energy. However, it often underestimates the criticalReynolds numbers compared to experimental measurements. On the other hand,linear stability analysis tends to yield impractically high limits due to theoccurrence of subcritical transitions.  A novel methodology is introduced to enhance and validate the generalizedkinetic energy formulation, aiming to provide a more accurate estimation oftransition.  This method considers the influence of nonlinear terms in calculating thethreshold amplitude.  The efficacy of this approach is showcased through the utilization of basiclow-order turbulence models and the Poiseuille flow as illustrative examples.  Through the proposed technique, the objective is to bridge the disparitybetween theoretically predicted critical Reynolds numbers and experimentalobservations, thus providing a more precise evaluation of shear flow stability.This research contributes to the advancement of stability analysis methods,offering practical implications for diverse fluid flow scenarios.

Advancing Fluid Dynamics Stability Analysis: Construction of Lyapunov Functions via the Generalized Kinetic Energy Approach