Analysis and Pollution Implications of the E — ∈ Turbulence Model Predictions of the Neutral ABL

Conclusion

The central result discussed in this paper was that condition (12) on closure constants should be satisfied in order for the E — ∈turbulence model to properly represent the solution for turbulence quantities near the NABL top (edge). This condition was derived from mathematical analysis of the E — ∈ model equations near the NABL top assuming a steady-state balance between diffusion and dissipation terms in the E and ∈ equations. The accuracy of numerical predictions of the NABL by the E —∈ model when the value of σ _e was changed from 1 to 0.6 to satisfy (12) supports the validity of this constraint. This stated, it should be emphasized that this change in the value of σ _e is not in and of itself suggested as a “fix” to the E — ∈ model for NABL prediction; the change was only made to satisfy (12) in attempts to demonstrate the predictive effects of the model’s analytic collapse to the proper NABL edge solution. It remains for future work to examine the physical implications of (12), and as a result to hopefully arrive at a means of satisfying this constraint consistent with the physics of the flow. In the meantime, the alteration σ _e =0.6 from the standard value σ _e =1 is seen as a practical solution to the problem of satisfying (12), and therefore of rectifying the oft-reported failure of the standard E — ∈ model for NABL prediction.

Future research will be directed towards performing analyses and computations with the E — ∈ model for prototypical stratified ABLs similar to those described in this paper for the NABL. The outcome of such efforts should aid considerably in understanding and improving the model so that its use in linked meteorological flow and air-pollution dispersion computations can be more frequently and confidently carried out.