Navier–Stokes equationn.
/ˌneɪvɪəˈstəʊks ᵻkweɪʒn/, /ˌnavɪeɪˈstəʊks ᵻkweɪʒn/, U.S. /ˈˌneɪviərˈstoʊks əˌkweɪʒ(ə)n/ Physics.
Each of the one-dimensional equations of motion for a viscous fluid. Also: the vector equation combining these, which may be written dV/ dt = − 1/ ρ∇p + F + ν∇2V + 1/ 3ν∇(∇·V) where V is the fluid velocity, ρ the density, p the pressure, F the total force per unit mass, and ν the kinematic viscosity.
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Stokes' law1910
Navier–Stokes equation1942
1933 Proc. Royal Soc. A. 142 622 The expressions must satisfy the Stokes–Navier equations.
1934 J. P. den Hartog tr. O. G. Tietjens Appl. Hydro- & Aeromechanics i. 5 The general differential equations of fluid motion including the effect of viscosity are known as ‘the equations of Navier–Stokes’.]
1942 Amer. Jrnl. Math. 64 754 The demonstration is based on an exact treatment of the Navier–Stokes equations.
1956 A. A. Townsend Struct. Turbulent Shear Flow ii. 23 The problem of obtaining from the Navier–Stokes equations of motion complete solutions of any problem in turbulence appears impossibly difficult.
1976 Nature 15 July 162/2 The atmosphere may be regarded as a compressible fluid, its behaviour being described by the Navier–Stokes equation and the thermodynamic equations concerned with sources, sinks and the transfers of energy.
1996 Daily Tel. 18 Sept. 18/4 A basic mathematical description of fluids such as air and water has been around for donkey's years, in the form of the Navier–Stokes equation.
This entry has been updated (OED Third Edition, June 2003; most recently modified version published online March 2022).
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n.1942