The importance of each term in $$ \frac{\partial u^{*}}{\partial x^{*}}+\frac{\partial v^{*}}{\partial y^{*}}=0 $$ $$ u^{*}\frac{\partial u^{*}}{\partial x^{*}}+v^{*}\frac{\partial u^{*}}{\partial y^{*}} =-\frac{\partial p^{*}}{\partial x^{*}}+\frac{1}{\mathrm{Re}}\frac{\partial^{2}u^{*}}{\partial x^{*2}}+\frac{\partial^{2}u^{*}}{\partial y^{*2}} $$ $$ \frac{1}{\mathrm{Re}}\!\left(u^{*}\frac{\partial v^{*}}{\partial x^{*}}+v^{*}\frac{\partial v^{*}}{\partial y^{*}}\right) =-\frac{\partial p^{*}}{\partial y^{*}}+\frac{1}{\mathrm{Re}^{2}}\frac{\partial^{2}v^{*}}{\partial x^{*2}}+\frac{1}{\mathrm{Re}}\frac{\partial^{2}v^{*}}{\partial y^{*2}} $$ is determined by its coefficient

As $\mathrm{Re}\to\infty$, the terms with coefficients $1/\mathrm{Re}$ or $1/\mathrm{Re}^2$ drop out asymptotically

The relevant equations for laminar boundary-layer flow in dimensional form are $$ \frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0,\qquad u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y} =-\frac{1}{\rho}\frac{\partial p}{\partial x}+\nu\,\frac{\partial^2 u}{\partial y^2},\qquad 0=-\frac{\partial p}{\partial y} $$ This scaling exercise has shown which terms must be kept and which terms may be dropped under the boundary-layer assumption