viscous fluid

A fluid for which the molecular viscous effects of diffusion and dissipation can have significant effects on the flow.

The importance of viscosity depends on the relevant velocity and length scales of the flow and the viscosity of the fluid. The nondimensional measure of the relative importance of viscosity is the reciprocal of the Reynolds number, Re. For typical atmospheric flows, Re > 10⁷, implying that viscous effects may be neglected relative to the leading [O(1)] terms in the Navier–Stokes equations. However, in a turbulent flow, such as in the boundary layer, vortex stretching causes a continuous nonlinear cascade of turbulence kinetic energy, TKE, from large scales to smaller scales. The largest-scale eddies are responsible for the Reynolds stresses and conversion of mean flow energy into TKE. At some point in the cascade, the eddies will have length and velocity scales that are sufficiently reduced for the Reynolds number to be of order 1. At these scales the TKE of eddies can be converted into internal energy through viscous dissipation. These small eddies will have a much shorter timescale than the largest eddies in the flow and are thus statistically independent of the large-scale motion. For a developed turbulent flow, the rate at which the mean flow energy is converted into turbulence at the largest scales must be equal to the rate at which it is ultimately dissipated by viscosity by the small-scale eddies. These smallest eddies have scales that are very much larger than those of the molecular motions, and the continuum hypothesis is still valid for describing eddies of this size. Although dissipation occurs at the smallest possible eddies in the flow and the TKE is contained in the largest-scale eddies, the viscous dissipation is a leading term in the TKE budget and may not be ignored.
See turbulence spectrum, turbulence length scales.
Tennekes, H., and J. L. Lumley 1972. A First Course in Turbulence. MIT Press, . 256–262.

1. Regular markings on an instrument used to allow the reading of the measured quantity or setting.

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 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.

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 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.

The direction of a line over the earth with reference to north (true or magnetic).

1. Irregular fluctuations occurring in fluid motions.