Editing Navier–Stokes equations (section)

===Nonlinearity===

The Navier–Stokes equations are [[Nonlinearity|nonlinear]] [[partial differential equations]] in the general case and so remain in almost every real situation.<ref>{{cite book |title=Fluid Mechanics |first1=M. |last1=Potter |first2=D. C. |last2=Wiggert |series=Schaum's Outlines |publisher=McGraw-Hill |year=2008 |isbn=978-0-07-148781-8}}</ref><ref>{{cite book |title=Vectors, Tensors, and the basic Equations of Fluid Mechanics |first=R. |last=Aris |publisher=Dover Publications |year=1989 |isbn=0-486-66110-5 }}</ref> In some cases, such as one-dimensional flow and [[Stokes flow]] (or creeping flow), the equations can be simplified to linear equations. The nonlinearity makes most problems difficult or impossible to solve and is the main contributor to the [[turbulence]] that the equations model.

The nonlinearity is due to [[convective]] acceleration, which is an acceleration associated with the change in velocity over position. Hence, any convective flow, whether turbulent or not, will involve nonlinearity. An example of convective but [[laminar flow|laminar]] (nonturbulent) flow would be the passage of a viscous fluid (for example, oil) through a small converging [[nozzle]]. Such flows, whether exactly solvable or not, can often be thoroughly studied and understood.<ref>{{cite book |title=McGraw Hill Encyclopaedia of Physics |edition=2nd |first=C. B. |last=Parker |year=1994 |publisher=McGraw-Hill |isbn=0-07-051400-3 }}</ref>