The Kato-Launder modification is an ad-hoc modification of the turbulent production term in the k equation. The main purpose of the modification is to reduce the tendency that two-equation models have to over-predict the turbulent production in regions with large normal strain, i.e. regions with strong acceleration or decelleration.
The transport equation for the turbulent energy, , used in most two-equation models can be written as:
Where is the turbulent production normally given by:
is the turbulent shear stress tensor given by the Boussinesq assumption:
Where is the eddy-viscosity given by the turbluence model and is the trace-less viscous strain-rate defined by:
In incompressible flows, where the production term can be rewritten as:
Kato, M. and Launder, B. E. (1993), "The Modeling of Turbulent Flow Around Stationary and Vibrating Square Cylinders", Proc. 9th Symposium on Turbulent Shear Flows, Kyoto, August 1993, pp. 10.4.1-10.4.6.