Optimal perturbations for transient growth in a 3D stratified channel using nonlinear direct-adjoint looping

Laminar shear flows often transition to turbulence at Reynolds numbers smaller than that of their first linear instability. The underlying mechanism can be transient algebraic growth, either linear or nonlinear in nature. We obtain the maximum perturbation energy growth in a three-dimensional heated plane channel. A nonlinear technique of direct-adjoint-looping is employed to numerically achieve this. With this technique, we also obtain the initial velocity and temperature perturbation structure that leads to this growth. The energy growth associated with this optimal can be large enough to push the flow to turbulence. We study the effect of varying stratification strengths (gradient Richardson numbers), Reynolds numbers, and target times on the structure of the optimal. We show similarity or the lack thereof between the optimal perturbations for small (linear optimal) and large (non-linear optimal) initial energies.