In the Navier-Stokes Equations, there is one term accounting for convective flow and one term for diffusive flow. At high flow rates, the diffusive term becomes much smaller compared to convective term, therefore can be neglected, leading to Euler's equations.
I can understand this in terms of mathematics: There is a multiplicative factor $\frac{1}{\text{Re}}$ in the diffusive term. With increasing flow rates, the inertial forces become larger than the viscous forces, so the Reynolds number increases and the term for diffusive flow becomes much smaller. But what is the physical interpretation of this? Does the influence of random motions decrease when the flow rate increases?
Best Answer
It's not that the random motion decreases when the flow rate increases. It is only that the random motion stays the same but the coherent motion dominates. If the diffusion velocity in a gas is 1 and the convective velocity of the flow is 1000 (units don't matter), then the diffusive action can be pretty safely ignored.
The important thing to remember is that there are limits to where the approximations can be applied. At high Reynolds number then one can use the Euler equations ignoring viscosity outside of the thin region around bodies where no matter how large the convective velocity is there will always be viscous effects there.