Viscous fluid: Difference between revisions

Latest revision as of 17:12, 25 April 2012

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.

INDEX
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
0
1
2
3
4
5
6
7
8
9

@@ Line 9: / Line 9: @@
    </div>
-<div class="definition"><div class="short_definition">A fluid for which the molecular viscous effects of [[diffusion]] and [[dissipation]] can have  significant effects on the flow.</div><br/> <div class="paragraph">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 &gt; 10<sup>7</sup>, implying  that viscous effects may be neglected relative to the leading [''O''(1)] terms in the [[Navier&ndash;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. <br/>''See'' [[turbulence spectrum]],  [[turbulence length scales]].</div><br/> </div><div class="reference">Tennekes, H., and J. L. Lumley 1972. A First Course in Turbulence. MIT Press, . 256&ndash;262. </div><br/>
+<div class="definition"><div class="short_definition">A fluid for which the molecular viscous effects of [[diffusion]] and [[dissipation]] can have  significant effects on the flow.</div><br/> <div class="paragraph">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 &gt; 10<sup>7</sup>, implying  that viscous effects may be neglected relative to the leading [''O''(1)] terms in the [[Navier&ndash;Stokes equations|Navier&ndash;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. <br/>''See'' [[turbulence spectrum]],  [[turbulence length scales]].</div><br/> </div><div class="reference">Tennekes, H., and J. L. Lumley 1972. A First Course in Turbulence. MIT Press, . 256&ndash;262. </div><br/>
 </div>