The contest inside Navier-Stokes: (u·∇)u versus viscosity
jo_brandstetter · x · 2026-10-26
Inside the Navier-Stokes equations there is a competition: the flow carries and deforms its own motion while viscosity fights to smooth velocity differences. The term (u·∇)u describes how the flow acts on itself — enough to become very intricate even without complicated forcing. With the Reynolds number Re = UL/ν, inertia outweighs viscosity at high values and turbulence occurs.
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