Linearization of the Navier–Stokes equations for real airflow conditions

[Pharal]

TL;DR

Navier Stokes equations are hard to solve analytically; numerical methods are used for real airflow.

How can the Navier Stokes equations be linearized to study real airflow behavior, rather than just small perturbations? Even at speeds as close as 500 km/h and 501 km/h, there can be significant differences in the flow patterns and turbulence. What approaches exist to handle such real-world variations in velocity when attempting a linear approximation?