  The energy method, also known as the Reynolds-Orr equation, is widely
utilized in predicting the unconditional stability threshold of shear flows
owing to the zero contribution of nonlinear terms to the time derivative of
perturbation kinetic energy. However, it often underestimates the critical
Reynolds numbers compared to experimental measurements. On the other hand,
linear stability analysis tends to yield impractically high limits due to the
occurrence of subcritical transitions.
  A novel methodology is introduced to enhance and validate the generalized
kinetic energy formulation, aiming to provide a more accurate estimation of
transition.
  This method considers the influence of nonlinear terms in calculating the
threshold amplitude.
  The efficacy of this approach is showcased through the utilization of basic
low-order turbulence models and the Poiseuille flow as illustrative examples.
  Through the proposed technique, the objective is to bridge the disparity
between theoretically predicted critical Reynolds numbers and experimental
observations, 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.
