Editing Navier–Stokes equations (section)

===Turbulence===

[[Turbulence]] is the time-dependent [[Chaos theory|chaotic]] behaviour seen in many fluid flows. It is generally believed that it is due to the [[inertia]] of the fluid as a whole: the culmination of time-dependent and convective acceleration; hence flows where inertial effects are small tend to be laminar (the [[Reynolds number]] quantifies how much the flow is affected by inertia). It is believed, though not known with certainty, that the Navier–Stokes equations describe turbulence properly.<ref>Encyclopaedia of Physics (2nd Edition), [[Rita G. Lerner|R.G. Lerner]], G.L. Trigg, VHC publishers, 1991, {{ISBN|3-527-26954-1}} (Verlagsgesellschaft), {{ISBN|0-89573-752-3}} (VHC Inc.)</ref>

The numerical solution of the Navier–Stokes equations for turbulent flow is extremely difficult, and due to the significantly different mixing-length scales that are involved in turbulent flow, the stable solution of this requires such a fine mesh resolution that the computational time becomes significantly infeasible for calculation or [[direct numerical simulation]]. Attempts to solve turbulent flow using a laminar solver typically result in a time-unsteady solution, which fails to converge appropriately. To counter this, time-averaged equations such as the [[Reynolds-averaged Navier–Stokes equations]] (RANS), supplemented with turbulence models, are used in practical [[computational fluid dynamics]] (CFD) applications when modeling turbulent flows. Some models include the [[Spalart–Allmaras turbulence model|Spalart–Allmaras]], [[k-omega turbulence model|{{mvar|k}}–{{mvar|ω}}]], [[turbulence kinetic energy|{{mvar|k}}–{{mvar|ε}}]], and [[SST (Menter’s Shear Stress Transport)|SST]] models, which add a variety of additional equations to bring closure to the RANS equations. [[Large eddy simulation]] (LES) can also be used to solve these equations numerically. This approach is computationally more expensive—in time and in computer memory—than RANS, but produces better results because it explicitly resolves the larger turbulent scales.