The dimensionless ratio of the inertial force (∼U2/L) to the viscous force (∼ νU/L2) in the Navier–Stokes equations, where U is a characteristic velocity, L is a characteristic length, and ν is the ki
nematic viscosity of the fluid; thus, Re=ULv. 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 > Rec, where the critical Reynolds number is roughly Rec = 2100.
dimensionless quantity that is used to help predict similar flow patterns in different fluid flow situations. It is defined as the ratio of inertial forces to viscous forces and consequently quantifie
s the relative importance of these two types of forces for given flow conditions.
component of the total stress tensor in a fluid obtained from the averaging operation over the Navier-Stokes equations to account for turbulent fluctuations in fluid momentum.