Linked from

The 69 pages that link to Navier–Stokes equations, each with the reason it gives.

• Reynolds numberRelated: Their inertial and viscous terms supply the force balance represented by the Reynolds number.

• Computational fluid dynamicsNarrower topic: They supply the governing flow equations that most CFD methods approximate.

• AerodynamicsRelated: They form the governing equations for most continuous-flow aerodynamic models.

• Boundary layerNarrower topic: Boundary-layer equations are approximations of Navier–Stokes equations for thin near-wall regions.

• TurbulenceNarrower topic: Turbulence emerges from their nonlinear dynamics, though solving them remains difficult.

• HydrodynamicsRelated: They express how pressure, viscosity, and external forces govern liquid flow.

• Fluid mechanicsBroader topic: They combine pressure, viscosity, inertia, and external forces into a central flow model.

• Numerical weather predictionNarrower topic: Atmospheric dynamics are fluid motion governed by equations in this broader family.

• Partial differential equationBroader topic: They combine transport, pressure, and viscosity in a central nonlinear system.

• Vector fieldRelated: They evolve fluid velocity fields under pressure, viscosity, and external forces.

• MagnetohydrodynamicsNarrower topic: Magnetohydrodynamics extends fluid dynamics by adding electromagnetic forces and field evolution.

• Perturbation theoryRelated: Small departures from simple flows can be analyzed as corrections to known solutions.

• Bernoulli's principleNarrower topic: They describe viscous flows beyond Bernoulli's idealized energy balance.

• Fluid dynamicsRelated: They express the central momentum balance used to model fluid motion.

• Potential flowCompared with: They retain viscous effects omitted from classical potential-flow models.

• Nonlinear systemBroader topic: Their nonlinear advection term couples fluid velocity to its own spatial variation.

• Velocity fieldRelated: Their solutions include velocity fields that satisfy momentum and mass-balance constraints.

• Newtonian fluidRelated: For Newtonian fluids, their viscous term follows directly from the constitutive equation.

• Stokes' lawNarrower topic: Stokes' law follows from their creeping-flow limit around a sphere.

• Material derivativeRelated: Their acceleration term is the material derivative of velocity.

• Pressure gradientRelated: Their momentum equation balances pressure-gradient forces against inertia, viscosity, and other forces.

• Euler equationsCompared with: Setting viscosity to zero in this model yields the Euler equations.

• No-slip conditionNarrower topic: No-slip supplies a boundary condition needed to solve these equations near solid walls.

• Boltzmann equationCompared with: They emerge as macroscopic approximations under near-equilibrium conditions.

• CurlRelated: Taking curl of these equations yields evolution equations for fluid vorticity.

• Finite volume methodRelated: Finite volume balances handle their advective and diffusive fluxes on engineering meshes.

• Weak solutionRelated: Their global existence theory in three dimensions centers on suitably defined weak solutions.

• Eulerian descriptionBroader topic: Their standard form evolves velocity and pressure as spatial fields.

• Vector calculusRelated: They use vector derivatives to describe fluid acceleration, pressure, and viscosity.

• Rayleigh–Taylor instabilityNarrower topic: They describe how viscosity and inertia shape the unstable flow.

• Kinematic viscosityRelated: Kinematic viscosity sets the coefficient of the momentum-diffusion term in their standard form.

• Kelvin–Helmholtz instabilityNarrower topic: They provide the dynamical framework for modeling shear layers and their evolution.

• Transport phenomenaRelated: They combine momentum storage, advection, pressure forces, and viscous transport.

• Lattice Boltzmann methodRelated: These are the macroscopic equations the method is designed to recover.

• Ludwig PrandtlRelated: Prandtl's boundary-layer analysis extracts tractable approximations from these governing equations.

• Taylor–Couette flowRelated: They describe the fluid motion whose stability Taylor analyzed.

• Cauchy momentum equationBroader topic: A Newtonian-fluid stress law reduces the momentum balance to these equations.

• Cauchy stress tensorRelated: Their stress term relates fluid motion to internal forces and material response.

• Claude-Louis NavierBroader topic: Navier’s 1820s work introduced viscous terms into equations for fluid motion.

• Direct numerical simulationNarrower topic: DNS computes fluid evolution by numerically solving these governing equations.

• Hagen–Poiseuille equationNarrower topic: The equation follows from simplifying these fluid-motion equations for a pipe.

• Kutta–Joukowski theoremCompared with: Unlike the theorem’s ideal-flow setting, they account directly for viscosity.

• Large eddy simulationRelated: LES commonly starts from filtered forms of these governing fluid equations.

• Darcy's lawNarrower topic: At pore scale, fluid motion follows these equations rather than a bulk Darcy relation.

• Flow velocityRelated: They determine velocity evolution from pressure, viscosity, and applied forces.

• Osborne ReynoldsNarrower topic: Reynolds’s analysis interpreted their terms and derived averaged equations for turbulent motion.

• Sobolev inequalityRelated: Sobolev estimates control nonlinear terms in existence and regularity arguments.

• Solenoidal vector fieldRelated: Incompressible Navier–Stokes models impose a solenoidal velocity field.

• Astrophysical fluid dynamicsRelated: They provide the basic continuum equations for many astrophysical flows.

• Multiphase flowRelated: They supply the momentum framework extended by many multiphase-flow models.