Crocco's theorem

Crocco's theorem relates a fluid's velocity, vorticity, stagnation-enthalpy gradient, and entropy gradient in steady flow. It shows how entropy variation can generate vorticity and make stagnation enthalpy vary across streamlines.

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Vorticity: The curl of a velocity field, measuring local fluid rotation and shear. The theorem couples the velocity crossed with vorticity to stagnation-enthalpy variation.
Steady flow: A flow whose properties at each fixed point do not change with time. Steadiness removes local time dependence from the momentum relation behind Crocco's theorem.
Aerodynamics: The study of forces and motion involving air and other gases. Crocco's theorem relates aerodynamic velocity fields to entropy and stagnation-enthalpy distributions.
Luigi Crocco: An Italian fluid dynamicist known for work on gas dynamics and combustion. Crocco's name is attached to the steady-flow relation linking vorticity and enthalpy.
Stagnation enthalpy: The sum of a fluid's static enthalpy and kinetic energy per unit mass. Its spatial gradient appears directly in Crocco's steady-flow relation.
Enthalpy: A thermodynamic state function equal to internal energy plus pressure times volume. Stagnation enthalpy extends this thermodynamic quantity by including kinetic energy.
Boundary layer: A thin fluid region near a surface where viscosity strongly affects the flow. Entropy production in boundary layers helps explain downstream changes in stagnation enthalpy.
Gas dynamics: The study of gas motion, especially when compressibility and thermodynamic changes matter. Crocco's theorem became a useful identity within the development of compressible gas-flow theory.
Specific entropy: A thermodynamic state variable measuring energy dispersal per unit mass. Entropy gradients supply the theorem's thermodynamic contribution to the flow relation.
Equation of state: A relation connecting a substance's thermodynamic state variables. It helps express entropy and pressure gradients in forms used with Crocco's relation.