An Etymological Dictionary of Astronomy and Astrophysics
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A turbulent flow in which viscous forces are negligible compared to nonlinear advection terms, which characterize the variation of fluid quantities. The dynamics becomes generally turbulent when the Reynolds number is high enough. However, the critical Reynolds number for that is not universal, and depends in particular on boundary conditions.

→ large; → Reynolds number; → flow.

A → dimensionless quantity used in → magnetohydrodynamics to describe the relative balance of → magnetic advection to → magnetic diffusion. It is given by: R_m = σμ₀νLU₀, where σ is the → conductivity of the fluid, μ₀ is the → magnetic permeability of the fluid, L is he characteristic length scale of the fluid flow, and U₀ the characteristic velocity of the flow. A typical value for the Earth is R_m ~ 200.

→ magnetic; → Reynolds number.

A dimensionless quantity that governs the conditions for hydrodynamic stability and the occurrence of turbulence in fluids. It is defined by the ratio, R, of the inertial force (ρ u²) and the viscous force (μ u / L), i.e. R = L u ρ/μ, where L is a typical dimension of the system, u is a measure of the velocities that prevail, ρ the density, and μ the kinematic viscosity. At low Reynolds numbers the flow is steady, since the viscous forces are predominant in controlling the flow. At a critical value of R, corresponding to a critical velocity, the flow becomes turbulent.

Named after Osborne Reynolds (1842-1912), a British physicist who pioneered the study of turbulent flows; → number.