Boundary-Layer Meteorology

, Volume 144, Issue 2, pp 199–215

The Apsley and Castro Limited-Length-Scale \({{k-\varepsilon}}\) Model Revisited for Improved Performance in the Atmospheric Surface Layer


DOI: 10.1007/s10546-012-9724-7

Cite this article as:
Sumner, J. & Masson, C. Boundary-Layer Meteorol (2012) 144: 199. doi:10.1007/s10546-012-9724-7


The limited-length-scale \({k-\varepsilon}\) model proposed by Apsley and Castro for the atmospheric boundary layer (Boundary-Layer Meteorol 83(1):75–98, 1997) is revisited with special attention given to its predictions in the constant-stress surface layer. The original model proposes a modification to the length-scale-governing \({\varepsilon}\) equation that ensures consistency with surface-layer scaling in the limit of small m/max (where m is the mixing length and max its maximum) and yet imposes a limit on m as m/max approaches one. However, within the equilibrium surface layer and for moderate values of z/max, the predicted profiles of velocity, mixing length, and dissipation rate using the Apsley and Castro model do not coincide with analytical solutions. In view of this, a general \({\varepsilon}\) transport equation is derived herein in terms of an arbitrary desired mixing-length expression that ensures exact agreement with corresponding analytical solutions for both neutral and stable stability. From this result, a new expression for \({C_{\varepsilon3}}\) can be inferred that shows this coefficient tends to a constant only for limiting values of z/L; and, furthermore, that the values of \({C_{\varepsilon3}}\) for z/L → 0 and z/L →∞ differ by a factor of exactly two.


\({k-\varepsilon}\) turbulence modelMixing lengthStable stratificationAtmospheric surface layer

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.École de Technologie SupérieureMontrealCanada