a valid perturbation equation in Eq. (28), we consider that it is valid to proceed with this approach.

Other justifications
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The author recognizes that the argument in the previous sub-section is somewhat [*ad hoc*]{}, and initially gives us no idea how to justify the choice of $\lambda$ or $\beta$, or, as we shall introduce, the relevant composite parameter $\epsilon$. However, there is another other route to justifying this approach. Let $\omega = \nabla^2 \psi$. Then the full 2D time-independent incompressible Navier–Stokes equation is precisely $$\nabla^2  \omega- R_e \frac{\partial(\psi,  \omega)}{\partial(x,y)}=0\ .$$ We already know from the existence of the Stokes paradox that simple linearization by setting $R_e=0$ is hopeless. We might therefore consider starting from other linearizations, for example, the Helmholtz linearization $$\nabla^2 \omega - \epsilon^2 \omega=0\ ,$$ where $\epsilon$ has to be determined either from experiment or from deeper theoretical considerations. The linear starting point for analysis is then not the biharmonic system but the Helmholtz-Laplace equation: $$\nabla^4 \psi - \epsilon^2 \nabla^2\psi=0\ .$$ In principle then we can consider justifying the choice of $\epsilon$ by matching $ \epsilon^2 \omega$ with $R_e \frac{\partial(\psi, \omega)}{\partial(x,y)}$ as closely as possible under a suitable norm. We will prove in the next section that 