# Turbulence Kinetic Energy

In fluid dynamics, turbulence kinetic energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow. Physically, the turbulence kinetic energy is characterised by measured root-mean-square (RMS) velocity fluctuations.

In Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure method, i.e. a turbulence model. Generally, the TKE can be quantified by the mean of the turbulence normal stresses:

TKE can be produced by fluid shear, friction or buoyancy, or through external forcing at low-frequency eddie scales(integral scale). Turbulence kinetic energy is then transferred down the turbulence energy cascade, and is dissipated by viscous forces at the Kolmogorov scale. This process of production, transport and dissipation can be expressed as:

where:

• is the mean-flow material derivative of TKE;
• is the turbulence transport of TKE;
• is the production of TKE, and
• is the TKE dissipation.

The full form of the TKE equation is $underbrace{ frac{partial k}{partial t}}_{ begin{smallmatrix}text{Local}\text{derivative}end{smallmatrix}} + underbrace{overline{u}_j frac{partial k}{partial x_j}}_{ begin{smallmatrix}text{Advection}end{smallmatrix}} = - underbrace{ frac{1}{rho_o} frac{partial overline{u'_i p'}}{partial x_i} } _{ begin{smallmatrix}text{Pressure}\text{diffusion}end{smallmatrix}} - underbrace{ frac{partial overline{k u_i}}{partial x_j} }_{ begin{smallmatrix} text{Turbulent}\ text{transport} \ mathcal{T} end{smallmatrix}} + underbrace{ nufrac{partial^2 k}{partial x^2_j} }_{begin{smallmatrix} text{Molecular}\ text{viscous}\ text{transport} end{smallmatrix}} underbrace{ - overline{u'_i u'_j}frac{partial overline{u_i}}{partial x_j} }_{begin{smallmatrix} text{Production}\ mathcal{P} end{smallmatrix}} - underbrace{ nu overline{frac{partial u'_i}{partial x_j}frac{partial u'_i}{partial x_j}} }_{begin{smallmatrix} text{Dissipation}\ epsilon_k end{smallmatrix}} - underbrace{ frac{g}{rho_o} overline{rho' u'_i}delta_{i3} }_{begin{smallmatrix} text{Buoyancy flux}\ b end{smallmatrix}}$

By examining these phenomena, the turbulence kinetic energy budget for a particular flow can be found.

Read more about Turbulence Kinetic EnergyComputational Fluid Dynamics

### Other articles related to "turbulence kinetic energy, turbulence":

Turbulence Kinetic Energy - Computational Fluid Dynamics - Boundary Conditions
... Some possible examples are given below where is the initial turbulence intensity given below, and is the initial velocity magnitude Here is the turbulence or eddy ...

### Famous quotes containing the words energy, turbulence and/or kinetic:

The chief function of the city is to convert power into form, energy into culture, dead matter into the living symbols of art, biological reproduction into social creativity.
Lewis Mumford (1895–1990)

their eyes still fixed, hoping to find once more,
Being by Calvary’s turbulence unsatisfied,
The uncontrollable mystery on the bestial floor.
William Butler Yeats (1865–1939)

All my stories are webs of style and none seems at first blush to contain much kinetic matter.... For me “style” is matter.