Mixing efficiency in decaying stably stratified turbulence

Mixing efficiency in stratified flows is a measure of the proportion of turbulent kinetic energy that goes into increasing the potential energy of the fluid by irreversible mixing. In this research direct numerical simulations (DNS) and rapid distortion theory (RDT) calculations of transient turbulent mixing events are carried out in order to study this aspect of mixing. In particular, DNS and RDT of decaying, homogeneous, stably-stratified turbulence are used to determine the mixing efficiency as a function of the initial turbulence Richardson number R_it0=(N_L0/_u0)²$R{i}_{t0}={(N{L}_0/u_0)}^2$, where N   is the buoyancy frequency and _L0$L_0$ and _u0$u_0$ are initial length and velocity scales of the turbulence. The results show that the mixing efficiency increases with increasing R_it0$R{i}_{t0}$ for small R_it0$R{i}_{t0}$, but for larger R_it0$R{i}_{t0}$ the mixing efficiency becomes approximately constant. These results are compared with data from towed grid experiments. There is qualitative agreement between the DNS results and the available experimental data, but significant quantitative discrepancies. The grid turbulence experiments suggest a maximum mixing efficiency (at large R_it0$R{i}_{t0}$) of about 6%, while the DNS and RDT results give about 30%. We consider two possible reasons for this discrepancy: Prandtl number effects and non-matching initial conditions. We conclude that the main source of the disagreement probably is due to inaccuracy in determining the initial turbulence energy input in the case of the grid turbulence experiments.     

Vertical eddy diffusivity estimations in Swan river estuary

A field experiment is described in which diapycnal diffusivity is estimated by direct and indirect methods in Swan river estuary, Perth, Western Australia. The microstructure profiles were collected in a narrow and straight part of this estuary using a portable flux profiler (PFP). The profiles were segmented into stationary parts and the rate of vertical eddy diffusivity was estimated for the segments within the pycnocline. The direct measurement showed that instantaneous flux could be positive or negative with a low net rate of vertical eddy diffusivity for mass of about 6.5 × 10⁻⁸ m² s⁻¹. All the indirect methods overestimated this rate. However, within the indirect methods, the method of Osborn yielded the poorest estimate while the method of Osborn and Cox gave the closest estimate.     

Rapid distortion theory for mixing efficiency of a flow stratified by one or two scalars

The mixing efficiency of unsheared homogeneous turbulence in flows stratified by one or two active scalars was calculated with rapid distortion theory (RDT). For the case with one scalar the mixing efficiency η depends on the Schmidt number Sc = ν/D and the Grashof number Gr = NL²/ν, where ν is the kinematic viscosity, D is the molecular diffusivity, N is the buoyancy frequency, and L is a length scale representative of the large eddies. For the case with two scalars the efficiency also depends on the density ratio R_ρ, which compares the density difference caused by temperature and the density difference caused by salt. In the one scalar case when Gr is large, η decreases as Sc increases. The mixing efficiency increases with Gr up to a maximum value, as in numerical simulations and experiments. The maximum mixing efficiency of approximately 30% for low Sc is consistent with simulations, while the maximum efficiency of 6% for heated water is consistent with laboratory measurements. However, RDT underpredicts the maximum efficiency for saltwater and also the value of Gr at which the efficiency becomes constant. The predicted behavior of the mixing efficiency for two active scalars is similar to that for one scalar, and the efficiency decreases as R_ρ decreases, as in experiments and semi-empirical models. These calculations show that results from simulations with low Sc likely overestimate the efficiency of turbulence in strongly stratified flows in lakes and oceans.     

A Simple Mixing Length Formulation for the Eddy-Diffusivity Parameterization of Dry Convection

In this paper a simple mixing length formulation for the eddy-diffusivityparameterization of dry convection is suggested. The new formulation relates the mixinglength to the square root of the turbulent kinetic energy (e) and a time scale ( ):l = e. To close the parameterization the time scale is calculated as a functionof the boundary-layer height (h) and the convective velocity scale (w_*), h/w_*. Thesimpler approach of a constant time scale is also studied. The simulation of a case of dry atmosphericconvection with a one-dimensional boundary-layer model shows that the model with the new formulationreproduces quite well the main properties of the convective boundary layer. In particular,the entrainment is realistically represented by the new mixing length, which has the advantage of naturallydecreasing with the turbulent kinetic energy. Sensitivity studies to the surface flux and the lapserate, in the context of a simplified situation, show the robustness of the new formulation.     

Evaluation of turbulent Prandtl (Schmidt) number parameterizations for stably stratified environmental flows

In this study, we evaluate four different parameterizations of the turbulent Prandtl (Schmidt) number Pr_t = ν_t/Γ_t where ν_t is the eddy viscosity and Γ_t is the scalar eddy diffusivity, for stably stratified flows. All four formulations of Pr_t are strictly functions of the gradient Richardson number Ri, which provides a measure of the strength of the stratification. A zero-equation (i.e. no extra transport equations are required) turbulence model for ν_t in a one-dimensional, turbulent channel flow is considered to evaluate the behavior of the different formulations of Pr_t. Both uni-directional and oscillatory flows are considered to simulate conditions representative of practical flow problems such as atmospheric boundary layer flows and tidally driven estuarine flows, to quantify the behavior of each of the four formulations of Pr_t. We perform model-to-model comparisons to highlight which of the models of Pr_t allow for a higher rate of turbulent mixing and which models significantly inhibit turbulent mixing in the presence of buoyancy forces resulting from linear (continuous) stratification as well as two-layer stratification. The basis underlying the formulation of each model in conjunction with the simulation results are used to emphasize the considerable variability in the different formulations and the importance of choosing an appropriate parameterization of Pr_t given a model for ν_t in stably stratified flows.     

对流层物质垂直交换模式中的参数化处理

为了研究对流层(TL)中垂直涡旋扩散系数(K_z)随高度变化的参数化形式对物质垂直交换的贡献,用“高分辨TL物质交换模式”(EM3)对5种不同K_z型进行了数值对比模拟,结果表明:KK_z型较好地描述了行星边界层(PBL)内受下垫面影响的高频湍流和PBL以上TL由各种动力学和热力学过程产生的切变湍流;垂直运动和K_z对PBL下层的物质输送到TL上层和从源高度向下输送到PBL低层两者均有重要作用;垂直运动的作用具有间隙性,而K_z是连续的.     

A model for eddy diffusivity in a stable boundary layer

Expressions for the vertical and the lateral diffusivity coefficients were derived from the Local Similarity Theory and the Statistical Diffusion Theory. For such, the spectral density energies for the turbulent velocities were used. The expressions here derived are compared with the diffusivity coefficients for momentum and heat suggested by Sorbjan (from the Minnesota experiments) and Nieuwstadt (from the Cabauw experiments). This comparison allows us to conclude that turbulence is equally efficient in transporting momentum, heat and contaminants in an ideally stable boundary layer.     

A turbulent energy model for geophysical flows

A simple turbulent flow model for geophysical flows is presented, which is based on the transport equation for turbulent energy and on algebraic expressions relating the Reynolds stress and turbulent heat flux to the velocity and temperature gradients. The model, which is similar to the 2.5 level closure model of Mellor and Yamada, includes constraints based on the realizability conditions as well as expressions for the length scale which account for the influence of stratification and the Coriolis acceleration. The model is shown to reproduce satisfactorily the main features of existing laboratory measurements of stress-induced and convective turbulent entrainment in stratified flows.     

Influence of Vertical Eddy Diffusivity Parameterization on Daily and Monthly Mean Concentrations of O3 and NOy

Two parameterization schemes for vertical eddy diffusivity were utilized to investigate their impacts on both the daily and monthly mean concentrations of ozone and NOy, which are the major fractions of the sum of all reactive nitrogen species, i.e., NOy=NO＋NO2＋HNO3＋PAN. Simulations indicate that great changes in the vertical diffusivity usually occur within the planetary boundary layer （PBL）. Daily and monthly mean concentrations of NOy are much more sensitive to changes in the vertical diffusivity than those of ozone and ozone and NOy levels only at or in （relatively） clean sites and areas, where long-range transport plays a crucial role, display roughly equivalent sensitivity. The results strongly suggest that a widely-accepted parameterization scheme be selected and the refinement of the model＇s vertical resolution in the PBL be required, even for regional and long-term studies, and ozone only being examined in an effort to judge the model＇s performance be unreliable, and NOy be included for model evaluations.     

中国地区对流参数化加热廓线的分析研究和数值试验

为了使MM4模式在我国范围内得到很好的应用,需用我国的气候资料对MM4模式中的对流加热参数进行统计分析,以适应我国各地区气候状态。为此,本文选取了1990～1993年6～8月的常规探空资料,采用郭氏的对流参数化方案,放宽假设后直接计算求得各站点各时次的对流加热率参数,再按气象站的站区分区进行统计。结果表明：黄河以南地区,对流云上、下部的垂直加热率比较均匀,加热廓线峰值偏低,为σ=0.65～0.80,对流云顶也比较高。黄河以北地区,对流云中的垂直加热率分布不均,加热集中在某一层上,加热廓线峰值出现在σ=0.     

A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows

A long-standing problem in large-eddy simulations (LES) of the planetary boundary layer (PBL) is that the mean wind and temperature profiles differ from the Monin-Obukhov similarity forms in the surface layer. This shortcoming of LES has been attributed to poor grid resolution and inadequate sub-grid-scale (SGS) modeling. We study this deficiency in PBL LES solutions calculated over a range of shear and buoyancy forcing conditions. The discrepancy from similarity forms becomes larger with increasing shear and smaller buoyancy forcing, and persists even with substantial horizontal grid refinement. With strong buoyancy forcing, however, the error is negligible.In order to achieve better agreement between LES and similarity forms in the surface layer, a two-part SGS eddy-viscosity model is proposed. The model preserves the usual SGS turbulent kinetic energy formulation for the SGS eddy viscosity, but it explicitly includes a contribution from the mean flow and a reduction of the contributions from the turbulent fluctuations near the surface. Solutions with the new model yield increased fluctuation amplitudes near the surface and better correspondence with similarity forms out to a distance of 0.1–0.2 times the PBL depth, i.e., a typical surface-layer depth. These results are also found to be independent of grid anisotropy. The new model is simple to implement and computationally inexpensive.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Tilting separation flows: a mechanism for intense vertical mixing in the coastal ocean

Observations of a front associated with boundary layer separation from a headland illustrate a mechanism by which horizontal density gradients create intense turbulence and vertical mixing, thus, contributing to water property modification in the coastal zone. Tidal current past an island separates from the coast, creating a shear zone between the primary flow and the slowly moving water in the lee of the island. The density structure on either side of the front may differ due to different origins or degrees of prior mixing. Consequently, there can be horizontal density gradients across the front. Boundary layer separation from the headland begins as a vertical vortex sheet on which instabilities grow to form a sequence of eddies. The presence of horizontal density gradients causes the shear layer to tilt. Tilting and stretching of the sheared flow generates intense circulation. Whirlpools and boils appear at the surface accompanied by vertical motions in which broad areas of upwelling alternate with narrow areas of downwelling. These mix the water throughout its depth; bubbles entrained at the surface reach depths of over 120 m. Such violent mixing weakens stratification associated with the estuarine circulation and aerates water masses passing through the area.     

Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Part I: steady-state,homogeneous regimes

We propose a new turbulence closure model based on the budget equations for the key second moments: turbulent kinetic and potential energies: TKE and TPE (comprising the turbulent total energy: TTE = TKE + TPE) and vertical turbulent fluxes of momentum and buoyancy (proportional to potential temperature). Besides the concept of TTE, we take into account the non-gradient correction to the traditional buoyancy flux formulation. The proposed model permits the existence of turbulence at any gradient Richardson number, Ri. Instead of the critical value of Richardson number separating—as is usually assumed—the turbulent and the laminar regimes, the suggested model reveals a transitional interval, , which separates two regimes of essentially different nature but both turbulent: strong turbulence at ; and weak turbulence, capable of transporting momentum but much less efficient in transporting heat, at . Predictions from this model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulation and large-eddy simulation.     

A parameterized yet accurate model of ozone and water vapor transmittance in the solar-to-near-infrared spectrum

A parameterized transmittance model(PTR) for ozone and water vapor monochromatic transmittance calculation in the solar-to-near-infrared spectrum 0.3-4 μm with a spectral resolution of 5 cm-1 was developed based on the transmittance data calculated by Moderate-resolution Transmittance model(MODTRAN).Polynomial equations were derived to represent the transmittance as functions of path length and airmass for every wavelength based on the least-squares method.Comparisons between the transmittances calculated using PTR and MODTRAN were made,using the results of MODTRAN as a reference.Relative root-mean-square error(RMSre) was 0.823% for ozone transmittance.RMSre values were 8.84% and 3.48% for water vapor transmittance ranges of 1-1×10 18 and 1-1×10 3,respectively.In addition,the Stratospheric Aerosol and Gas Experiment II(SAGEII) ozone profiles and University of Wyoming(UWYO) water vapor profiles were applied to validate the applicability of PTR model.RMSre was 0.437% for ozone transmittance.RMSre values were 8.89% and 2.43% for water vapor transmittance ranges of 1-1×10 18 and 1-1×10 6,respectively.Furthermore,the optical depth profiles calculated using the PTR model were compared to the results of MODTRAN.Absolute RMS errors(RMSab) for ozone optical depths were within 0.0055 and 0.0523 for water vapor at all of the tested altitudes.Finally,the comparison between the solar heating rate calculated from the transmittance of PTR and Line-by-Line radiative transfer model(LBLRTM) was performed,showing a maximum deviation of 0.238 K d-1(6% of the corresponding solar heating rate calculated using LBLRTM).In the troposphere all of the deviations were within 0.08 K d-1.The computational speed of PTR model is nearly two orders of magnitude faster than that of MODTRAN.     

A semi-analytical model of barotropic and baroclinic flows for an open Panama Gateway

A semi-analytical model of the Panama throughflow is presented. The model expresses the throughflow transport as a function of deep water formation in the North Pacific and in the North Atlantic, and of the Panama Gateway depth. The model is derived from the integral of the momentum equation along a circumpolar path, and can be interpreted from the point of view of the vorticity balance. The important conditions are whether the deep water, whose location is considered to be above the bottom water formed around Antarctica, originates from the North Atlantic or from the North Pacific, and whether the Panama Gateway is shallower than the lower boundary of the deep water. The present model indicates that the barotropic transport through the Panama Gateway is eastward, except for the case where the deep water is formed in the North Pacific and the sill of the Panama Gateway is shallow. The baroclinic structure of the Panama throughflow depends on whether the deep water is formed in the North Pacific or in the North Atlantic. These qualitative implications of the model are consistent with recent numerical studies and proxy-based paleoceanographic studies. Numerical experiments performed in the present study reinforce confidence in the semi-analytical model.     

一个对流边界层中的随机扩散模式

通过对对流边界层(CBL)湍流结构的分析,首次提出用两种不同尺度的湍流模拟CBL中的铅直扩散.在此基础上发展了一个随机扩散模式,并用它模拟了典型对流条件下两种高架连续点源的扩散.与Willis水槽模拟和Lamb等人数值模拟以及CONDORS计划外场试验的结果的比较表明,本模式能成功地模拟CBL中的横向积分浓度.与其它数值模式相比,还具有输入参数少、计算量极小和更加简单实用的优点.     

适用于大中尺度污染物输送模式的粒子干沉降参数化方案

用“二层”模式给出一个适用于污染物输送模式的粒子干沉降参数化方案,它比较详细地考虑了近地面层的气象条件,地表特性和气溶胶粒子的物理、化学特性等。从计算值与观测值的比较来看,计算值的离散范围能涵盖所有的观测结果,因而从总体上看此参数化方案是合理的,能够描述粒子总污染物干沉降的主要物理过程及机制。       

WRF模式中微物理和积云参数化方案的对比试验

基于中尺度大气数值模式WRF,检验分析YSU和MYJ两种边界层参数化方案和分辨率分别为1 km（称为USGS）和500 m（称为MODIS）的两类下垫面资料对2014年5月9—12日青岛一次暴雨过程模拟的影响。分析表明, YSU和MYJ方案都能模拟出强降雨带的位置和强度,MYJ试验对大雨TS评分高达0.88,YSU对暴雨TS评分为0.65;和USGS试验相比,MODIS试验提高了暴雨的TS评分,提高率为6.2%,但对大雨仍易空报。YSU、MYJ和MODIS试验较好地模拟了2 m气温、10 m风向。YSU模拟的2 m气温准确率是降雨前优于降雨开始后,MYJ则相反;MODIS试验预报沿海地区气温偏高。和USGS相比,MODIS提高了近地面风速和风向的模拟精度。总体上,所有试验方案对所考虑气象要素的模拟,基本上是内陆站准确率高于沿海站,YSU优于MYJ,MODIS优于USGS。