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Reynolds stress model (RSM)

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The Reynold's stress model (RSM) is a higher level, elaborate turbulence model. It is usually called a Second Order Closure. This modelling approach originates from the work by [Launder (1975)]. In RSM, the eddy viscosity approach has been discarded and the Reynolds stresses are directly computed. The exact Reynolds stress transport equation accounts for the directional effects of the Reynolds stress fields.


The Reynolds stress model involves calculation of the individual Reynolds stresses, \overline{u'_iu'_j} , using differential transport equations. The individual Reynolds stresses are then used to obtain closure of the Reynolds-averaged momentum equation.

The exact transport equations for the transport of the Reynolds stresses, \overline{u'_iu'_j} , may be written as follows:

Model constants

The constants suggested for use in this model are as follows:

C_s \approx 0.25, C_l \approx 0.25, C_\gamma \approx 0.25

Model variants

Performance, applicability and limitations

Implementation issues


Launder, B. E., Reece, G. J. and Rodi, W. (1975), "Progress in the Development of Reynolds Stress Turbulent Closure", Journal of Fluid Mechanics, Vol. 68, pp. 537-566.

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