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Reynolds stress : ウィキペディア英語版
Reynolds stress
In fluid dynamics, the Reynolds stress is the component of the total stress tensor in a fluid obtained from the averaging operation over the Navier-Stokes equations to account for turbulent fluctuations in fluid momentum.
==Definition==
For a homogeneous fluid and an incompressible flow, the flow velocities are split into a mean part and a fluctuating part using Reynolds decomposition:
:u_i = \overline + u_i',\,
with \mathbf(\mathbf,t) being the flow velocity vector having components u_i in the x_i coordinate direction (with x_i denoting the components of the coordinate vector \mathbf). The mean velocities \overline are determined by either time averaging, spatial averaging or ensemble averaging, depending on the flow under study. Further u'_i denotes the fluctuating (turbulence) part of the velocity.
The components ''τ''ij'' of the Reynolds stress tensor are defined as:
:\tau'_ \equiv \rho\,\overline,\,
with ''ρ'' the fluid density, taken to be non-fluctuating for this homogeneous fluid.
Another – often used – definition, for constant density, of the Reynolds stress components is:
:\tau''_ \equiv \overline,\,
which has the dimensions of velocity squared, instead of stress.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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