Inviscid

Inviscid refers to a fluid with no viscosity or to an idealized model of such a fluid used in fluid dynamics. In an inviscid flow, viscous shear stresses are neglected, and the fluid is assumed to slide freely past itself and solid boundaries. This simplifying assumption leads to simpler governing equations and is useful for analyzing flow away from surfaces or at high Reynolds numbers where viscous effects are confined to thin boundary layers.

Inviscid flow is described by the Euler equations, which arise from the Navier-Stokes equations by setting the dynamic viscosity to zero. For an incompressible, inviscid fluid, the equations are ∂u/∂t + (u·∇)u = -∇p/ρ + g with ∇·u = 0. If the flow is irrotational, a velocity potential φ exists such that u = ∇φ and φ satisfies ∇²φ = 0 (potential flow). Bernoulli’s principle may be applied along a streamline in steady, inviscid flow.

Physical significance and limitations: Real fluids have viscosity, so inviscid models neglect energy dissipation through viscous stresses. Away from solid boundaries, viscous effects can be small, but near surfaces they form boundary layers and cause drag, separation, and heat transfer. A classic result, d’Alembert’s paradox, states that a perfectly inviscid, incompressible, and irrotational body experiences zero drag in steady potential flow; in practice, drag arises from the boundary layer and other viscous phenomena.

Applications and scope: Inviscid models underpin potential-flow theory and many aerodynamic analyses, especially for qualitative understanding or as a first approximation. They are used in computational methods that solve the Euler equations or use potential-flow approximations, and in high-speed aerodynamics where compressible inviscid flow is relevant. However, inviscid assumptions limit accuracy for flows with strong viscous effects or low Reynolds numbers.