Reynolds Number
A dimensionless number in fluid mechanics that measures the relative strength of inertial forces to viscous forces, defined as Re = UL/ν. It is used to determine whether a flow state is laminar or turbulent.
Timeline (last 90 days)
The Reynolds number is a dimensionless parameter for determining flow regime, defined as the ratio of inertial forces to viscous forces.
In pipe flow, when the Reynolds number exceeds a critical value (about 2000-4000), the flow transitions from laminar to turbulent.
In turbulence, the ratio of scales can reach on the order of Re^{3/4}, which is the physical root of its multiscale nature.
The computational cost of DNS scales roughly with Re^{3}; for an aircraft wing (Re~10^7), the required grid points can reach more than 10^{12}, far beyond current supercomputer capabilities.
A small Reynolds number means smooth, viscosity-dominated flow; a large Reynolds number means inertia dominates and the flow tends to become unstable and develop into turbulence.
The Navier-Stokes equations can describe a wide range of phenomena from blood flow to weather, because different values of the Reynolds number cover the entire spectrum from laminar flow to turbulence.
The Reynolds number Re = UL/ν (U is the characteristic velocity, L is the characteristic length) measures the relative strength of inertial forces and viscous forces.
All Facts (7)
The Reynolds number is a dimensionless parameter for determining flow regime, defined as the ratio of inertial forces to viscous forces.
50%UnverifiedIn pipe flow, when the Reynolds number exceeds a critical value (about 2000-4000), the flow transitions from laminar to turbulent.
50%UnverifiedIn turbulence, the ratio of scales can reach on the order of Re^{3/4}, which is the physical root of its multiscale nature.
50%UnverifiedThe computational cost of DNS scales roughly with Re^{3}; for an aircraft wing (Re~10^7), the required grid points can reach more than 10^{12}, far beyond current supercomputer capabilities.
50%UnverifiedA small Reynolds number means smooth, viscosity-dominated flow; a large Reynolds number means inertia dominates and the flow tends to become unstable and develop into turbulence.
50%UnverifiedThe Navier-Stokes equations can describe a wide range of phenomena from blood flow to weather, because different values of the Reynolds number cover the entire spectrum from laminar flow to turbulence.
50%UnverifiedThe Reynolds number Re = UL/ν (U is the characteristic velocity, L is the characteristic length) measures the relative strength of inertial forces and viscous forces.
50%