Validation of the optimal vector for

Re=100, α=0.5, β=2

The non-modal analysis yields an optimal vector which can be given as an initial state to an Initial Value Problem (IVP) solver. For that we calculate the optimal initial vector based on the extracted vectors corresponding to the discrete part (red dots on the Fig. 1).

Fig. 1

Then, we obtain the growth of its energy norm, |q_opt|²(t), from the numerical solution of the IVP.  If the energy norm growth is identical to that predicted by the non-modal analysis, G_E(t), then we argue that the discrete spectrum was extracted correctly (Fig. 2).

Correctly extracted eigenvectors can be used for non-modal analysis in both the energy and the enstrophy norms.

Fig. 2