inviscidne

Inviscidne is a term used in fluid dynamics to denote the property or state of a fluid being inviscid, i.e., having negligible viscosity relative to other forces. The word is not widely standardized; more common terms are inviscid or inviscidity, and inviscidne may appear in theoretical discussions or as a neologism.

Definition and context

Inviscidne describes fluids in which viscous forces are neglected when formulating models. This allows the use of Euler equations and potential-flow theory. In such models, shear stresses and viscous dissipation are ignored, an approximation that is often valid in high Reynolds number flows away from solid boundaries.

Mathematical formulation

Under the inviscid assumption, the Navier–Stokes equations are replaced by the Euler equations: rho (du/dt + u · grad u) = -grad p + rho g, with div u = 0 for incompressible flow. The viscous term is omitted. In potential flow, the velocity field can be expressed as the gradient of a scalar potential, simplifying analysis.

Applications and implications

The inviscid framework supports many analytical results, such as Bernoulli’s equation along streamlines and qualitative lift predictions from potential-flow theory. It also leads to d’Alembert’s paradox, which states that a body experiences zero drag in a strictly inviscid, irrotational flow, highlighting the real-world necessity of viscous effects to account for drag and viscous dissipation.

Limitations

Real fluids have viscosity, and viscous effects are crucial near solid boundaries, in boundary layers, and in turbulent flows. Inviscid models cannot capture wall friction, flow separation, or energy loss due to viscosity, so they are used as idealizations or in regions away from surfaces.

See also

Inviscid flow, Euler equations, Navier–Stokes equations, boundary layer, potential flow.