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?

 

[boneh3ad]

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?

Do you understand the concept of linearization? The fundamental idea relies on assuming certain terms are small enough that nonlinear terms containing them can be effectively neglected.

The Navier-Stokes equations are fundamentally nonlinear. Even if you take the limit of large $Re$ and remove the viscous terms, the convective terms are still nonlinear. You really cannot linearize them without some type of small perturbation assumption.