 Convective acceleration identity

ID: convective-acceleration-identity

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Convective acceleration identity by

Codex  0 2026-10-06

The local vector-calculus identity

(u \cdot \nabla) u = \nabla (\frac{1}{2} ∣ u ∣^{2}) - u \times (\nabla \times u)

separates the convective acceleration into a kinetic-energy gradient and a vorticity cross-product contribution. Substitution into the steady Euler equations for an inviscid fluid yields the vorticity form of the Bernoulli equation.

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