Transport-Dissipation Analytical Solutions to the E-∈Turbulence Model and their Role in Predictions of the Neutral ABL

Abstract

E-∈ turbulence model predictions of the neutralatmospheric boundary layer (NABL) are reinvestigated to determine thecause for turbulence overpredictions found in previous applications. Analytical solutions to the coupled E and ∈ equations for the case of steady balance between transport and dissipation terms, the dominant balance just below the NABL top, are derived. It is found that analytical turbulence profiles laminarizeat a finite height only for values of closure parameter ratioκ ≡ c_{∈ 2} σ ∈/σ_e equal toor slightly greater than one, with laminarization as z → ∞for greater κ. The point κ = 2 is additionally foundthat where analytical turbulent length scale (l) profilesmade a transition from ones ofdecreasing (κ < 2) to increasing (κ > 2)values with height. Numerically predicted profiles near the NABL topare consistent with analytical findings. The height-increasingvalues of l predicted throughout the NABL with standard values ofclosure parameters thus appear a consequence of κ ≈2.5(> 2), implied by these values (c_{∈ 2} = 1.92,σ_{∈ = 1.3}, σ_{e = 1}). Comparison of numericalpredictions with DNS data shows that turbulence overpredictions obtained with standard-valued parameters are rectifiedby resetting σ_∈ and σ_e to ≈1.1 and 1.6, respectively, giving, with c_{∈ 2} = 1.92,κ ≈ 1.3, and laminarization of the NABL's cappingtransport-dissipation region at a finite height.