= Solution
The <Reynolds number> is
$$
\boxed{\operatorname{Re}=\frac{\mathcal U\mathcal L}{\nu}}.
$$
When it is large, viscosity is negligible in most of the flow, but the inviscid outer solution cannot generally satisfy the <no-slip boundary condition> at a rigid wall. A thin <boundary layer> resolves this mismatch: tangential gradients remain of outer scale $\mathcal L$, normal gradients have the much shorter scale $\delta$, and the small viscous coefficient is offset by $u_{yy}=O(\mathcal U/\delta^2)$. Matching a viscous inner solution to an inviscid outer solution retains the leading viscous effects without solving the full equations uniformly everywhere.
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