The Apsley and Castro limited-length-scale k-ζ model revisited for improved performance in the atmospheric surface layer

• Published in: Boundary-layer meteorology 2012-08, Vol.144 (2), p.199
• Main Authors: Sumner, Jonathon, Masson, Christian
• Format: Article
• Language: English
• Subjects: Planetary boundary layer
• ISSN: 0006-8314
• DOI: 10.1007/s10546-012-9724-7

The limited-length-scale k - ζ 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 ζequation that ensures consistency with surface-layer scaling in the limit of small [l.sub.m]/[l.sub.max] (where [l.sub.m] is the mixing length and [l.sub.max] its maximum) and yet imposes a limit on [l.sub.m] as [l.sub.m]/[l.sub.max] approaches one. However, within the equilibrium surface layer and for moderate values of z/[l.sub.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 ζ 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.sub.ζ3] 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.sub.ζ3] for z/L[right arrow]∞and z/L→∞ differ by a factor of exactly two. Keywords k - ζ turbulence model * Mixing length * Stable stratification * Atmospheric surface layer