## Reynolds number

The dimensionless ratio of the inertial force (∼

*U*^{2}/*L*) to the viscous force (∼ ν*U*/*L*^{2}) in the Navier–Stokes equations, where*U*is a characteristic velocity,*L*is a characteristic length, and ν is the kinematic viscosity of the fluid; thus,The Reynolds number is of great importance in the theory of hydrodynamic stability and the origin of turbulence. The inertia force generates vortex stretching and nonlinear interactions and hence creates randomness. Turbulence occurs when the inertia term dominates the viscous term, that is, when the Reynolds number is large. For many engineering flows, turbulence occurs when Re > Re

_{c}, where the critical Reynolds number is roughly Re_{c}= 2100.*See*large Reynolds number flow.