Modeling non-equilibrium atmospheric turbulence.

摘要

Reynolds-averaged turbulence modeling in meteorology is advanced by developing a new model, better suited than traditional ones for non-equilibrium atmospheric turbulent flows. Traditional models are based on equilibrium, most notably the local equilibrium assumption on the turbulent kinetic energy ( E) equation and/or algebraic equations for turbulence length scale, l, designed for classical quasi-steady, one-dimensional atmospheric boundary layers (1D-ABLs). The validity of these models is therefore questionable for non-equilibrium flows.; The new model is of E-ϵ type, computing eddy viscosities as K_α = c_α E2/ϵ (α an arbitrary quantity) with transport equations for E and its dissipation rate, ϵ. The model thus prognostically calculates l ∼ E 3/2/ϵ, allowing sensitivity to non-equilibrium. Stability functions, c_α, derived from second-order closure equations, are functions of static stability and the deviation of E from its local equilibrium value. The novel element is a modified ϵ-equation, of standard form but with coefficients altered or functions for them introduced to correct predictive failures of the standard equation for neutral and stable 1D-ABLs. The modifications result from mathematical analyses to enforce equation consistency with 1D-ABL theory.; The modified E-ϵ model is applied to the one-dimensional neutral-to-stable transitional ABL to assess its predictive improvements over traditional models for three non-equilibrium flows: the evening transition, residual layer and “very stable” ABL. The new model accurately predicts ABL bulk quantities and turbulence profiles for these cases, outperforming traditional models. This is attributed to its prediction of growing l with time in decaying, stably-stratified turbulence. Although counterintuitive, since l is generally thought limited in strong stability, growth is appropriate for shifting the dominant sink terms in the second-order closure equations basing the model from dissipation and slow pressure redistribution to buoyancy destruction as EN/ϵ approaches infinity in decaying turbulence (N being the Brunt-Vaisala frequency). Traditional models are either inconsistent with decaying turbulence or limit l in stable stratification regardless of turbulence state, leading to their reduced accuracy.; The success of the new model is promising for research on non-equilibrium atmospheric turbulent flows of decaying, stably-stratified turbulence through three-dimensional Reynolds-averaged computation. Investigation of non-equilibrium flows of growing turbulence and incorporation into weather and climate codes necessitate model extension to buoyantly driven flows, a future research task.