Low Reynolds number version of k - ε model: Asymptotic Consistency

In general, the damping of turbulence near a solid surface due to molecular viscosity is simulated through some damping functions attached to various terms of the transport equations which allow a smooth change of the flow variable from the small laminar sublayer values very near the wall to the fully turbulent value away from the wall. The results of DNS (Kim et al. (1987)) and experimental data compiled by Patel et al. (1985) have shown the limiting forms of the turbulent quantities in the region close to the wall as following:

(30.2)

where O(y) represents the order of y , the normal distance from the wall. A model that duplicates these exact limiting forms of k , ε and is said to be Asymptotically Consistent with the near-wall behaviour of the exact equations of motion.