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.     

The Scaling Behaviour of a Turbulent Kinetic Energy Closure Model for Stably Stratified Conditions

We investigate the scaling behaviour of a turbulent kinetic energy (TKE) closure model for stably stratified conditions. The mixing length scale for stable stratification is proportional to the ratio of the square root of the TKE and the local Brunt–Väisälä frequency, which is a commonly applied formulation. We analyze the scaling behaviour of our model in terms of traditional Monin–Obukov Similarity Theory and local scaling. From the model equations, we derive expressions for the stable limit behaviour of the flux–gradient relations and other scaling quantities. It turns out that the scaling behaviour depends on only a few model parameters and that the results obey local scaling theory. The analytical findings are illustrated with model simulations for the second GABLS intercomparison study. We also investigate solutions for the case in which an empirical correction function is used to express the eddy diffusivity for momentum as a function of the Richardson number (i.e. an increasing turbulent Prandtl number with stability). In this case, it seems that for certain parameter combinations the model cannot generate a steady-state solution. At the same time, its scaling behaviour becomes unrealistic. This shows that the inclusion of empirical correction functions may have large and undesired consequences for the model behaviour.     

A numerical study of the marine stratocumulus cloud layer

A one-dimensional grid-level model including longwave radiative transfer and a level-4 second-order turbulent transfer closure which contains prognostic equations for turbulent quantities, is used to study the physics and dynamics of inversion-capped marine stratocumulus clouds.A set of numerical experiments had been performed to examined the role of sea surface temperature, large-scale vertical velocity, wind speed, and vertical wind shear in the formation and the structure of low-level clouds. For a given sea surface and geostrophic wind speed, stratocumulus clouds can grow higher with smaller large-scale subsidence as less dry air entrains into the cloud. Clouds grow higher with higher sea surface temperature for a given geostrophic wind speed and large-scale subsidence as a result of enhanced moist convection. In high wind speeds, the entire cloud deck is lifted up because of larger surface energy flux. In the budget studies of the turbulent kinetic energy (TKE), the buoyancy term is a major source term when the wind speed and the vertical shear are small across the inversion top. When the wind speed and the vertical wind shear across the inversion top become large, the mixed layer is decoupled into a cloud and a subcloud layer. In the TKE budget studies, the shear generation term becomes an important term in the budgets of the TKE and the variance of vertical velocity.     

Generation of oceanic internal gravity waves by a cyclonic surface stress disturbance

Atmospheric cyclones with strong winds significantly impact ocean circulation, regional sea surface temperature, and deep water formation across the global oceans. Thus they are expected to play a key role in a variety of energy transport mechanisms. Even though wind-generated internal gravity waves are thought to contribute significantly to the energy balance of the deep ocean, their excitation mechanisms are only partly understood.The present study investigates the generation of internal gravity waves during a geostrophic adjustment process in a Boussinesq model with axisymmetric geometry. The atmospheric disturbance is set by an idealized pulse of cyclonic wind stress with a Rankine vortex structure. Strength, radius and duration of the forcing are varied. The effect upon wave generation of stratification with variable mixed-layer depth is also examined.Results indicate that internal gravity waves are generated after approximately one inertial period. The outward radial energy flux is dominated by waves having structure close to vertical mode-1 and with frequency close to the inertial frequency. Less energetic higher mode waves are observed to be generated close to the sea floor underneath the storm. The total radiated energy corresponds to approximately 0.02% of the wind input. Deeper mixed-layer conditions as well as weaker stratification reduce this fraction.The low energy transfer rates suggest that other processes that drive vertical motion like surface heat fluxes, turbulent motion, mixed region collapse and storm translation are essential for significant energy extraction by internal gravity waves to occur.     

Helicopter-Borne Flux Measurements in the Nocturnal Boundary Layer Over Land – a Case Study

This case study introduces measurements of turbulent fluxes in a nocturnal boundary layer in North Germany with the new helicopter-borne turbulence measurement system HELIPOD, a detailed data analysis and examination in regard of systematic errors of the instrument, and some comparison with local similarity theory and experiments of the past, in order to confirm the occurrence of small vertical turbulent fluxes. The examined nocturnal boundary layer offered excellent conditions to analyse the quality of the measurement system. In this connection, a detailed look at a strong ground-based inversion disclosed small turbulent fluxes with a spectral maximum at ten metres wavelength or less, embedded in intermittent turbulence. For verification of these fluxes, the measurements were compared with well established results from past experiments. Local similarity theory was applied to calculate dimensionless variances of the turbulent quantities, which were found in good agreement with other observations. Since shear and stratification varied significantly on the horizontal flight legs due to global intermittency, a method was developed to determine vertical gradients on a horizontal flight pattern, by use of small fluctuations of the measurement height. With these locally determined gradients, gradient transport theory became applicable and the turbulent diffusivities for heat and momentum, the Richardson number, and the flux Richardson number were estimated within isolated strong turbulent outbursts. Within these outbursts the flux Richardson number was found between 0.1 and 0.2. The functional relationship between the gradient Richardson number and the turbulent Prandtl number agreed well with observations in past experiments and large eddy simulation. The impact of the stratification on the vertical turbulent exchange, as already described for the surface layer using Monin–Obukhov similarity, was analogously observed in the very stably stratified bulk flow when local scaling was applied.     

Impact of the Nocturnal Low-Level Jet and Orographic Waves on Turbulent Motions and Energy Fluxes in the Lower Atmospheric Boundary Layer

The nocturnal low-level jet (LLJ) and orographic (gravity) waves play an important role in the generation of turbulence and pollutant dispersion and can affect the energy production by wind turbines. Additionally, gravity waves have an influence on the local mixing and turbulence within the surface layer and the vertical flux of mass into the lower atmosphere. On 25 September 2017, during a field campaign, a persistent easterly LLJ and gravity waves were observed simultaneously in a coastal area in the north of France. We explore the variability of the wind speed, turbulent eddies, and turbulence kinetic energy in the time–frequency and space domain using an ultrasonic anemometer and a scanning wind lidar. The results reveal a significant enhancement of the turbulence-kinetic-energy dissipation (by?50%) due to gravity waves in the LLJ shear layer (below the jet core) during the period of wave propagation. Large magnitudes of zonal and vertical components of the shear stress (approximately 0.4 and 1.5 m² s^?2, respectively) are found during that period. Large eddies (scales of 110 to 280 m) matching the high-wind-speed regime are found to propagate the momentum downwards, which enhances the mass transport from the LLJ shear layer to the roughness layer. Furthermore, these large-scale eddies are associated with the crests while comparatively small-scale eddies are associated with the troughs of the gravity wave.

     

Large-eddy Simulation of Turbulent Flow across a Forest Edge. Part II: Momentum and Turbulent Kinetic Energy Budgets

Momentum and turbulent kinetic energy (TKE) budgets across a forest edge have been investigated using large-eddy simulation (LES). Edge effects are observed in the rapid variation of a number of budget terms across this vegetation transition. The enhanced drag force at the forest edge is largely balanced by the pressure gradient force and by streamwise advection of upstream momentum, while vertical turbulent diffusion is relatively insignificant. For variance and TKE budgets, the most important processes at the forest edge are production due to the convergence (or divergence) of the mean flow, streamwise advection, pressure diffusion and enhanced dissipation by canopy drag. Turbulent diffusion, pressure redistribution and vertical shear production, which are characteristic processes in homogeneous canopy flow, are less important at the forest transition. We demonstrate that, in the equilibrated canopy flow, a substantial amount of TKE produced in the streamwise direction by the vertical shear of the mean flow is redistributed in the vertical direction by pressure fluctuations. This redistribution process occurs in the upper canopy layers. Part of the TKE in the vertical velocity component is transferred by turbulent and pressure diffusion to the lower canopy levels, where pressure redistribution takes place again and feeds TKE back to the streamwise direction. In this TKE cycle, the primary source terms are vertical shear production for streamwise velocity variance and pressure redistribution for vertical velocity variance. The evolution of these primary source terms downwind of the forest edge largely controls the adjustment rates of velocity variances.     

Morning Boundary-Layer Turbulent Kinetic Energy by Theoretical Models

A major factor that influences the diurnal variation of turbulent kinetic energy (TKE) is the sensible heat flux at the surface. Here, the TKE variations are analysed during the morning transition phase because subsequent to the neutral or stable stratification during the night, peaks of concentration of scalars develop. The characteristics of the TKE during the growth phase of convection are analysed with the help of two analytical models. For this purpose, a three-dimensional spectral model of the growth of convection, starting from a neutral layer, and other formulations of micrometeorological parameters such as the convective and neutral spectra, velocity variance and dissipation rates are utilised. The peak values in the TKE spectra in the lower, middle and upper levels of the convective boundary layer showed a migration to higher wavelengths as the convection increased with time. The TKE evolutions generated by the analytical models agree fairly well with the results of large-eddy simulation for three vertical levels.     

A Study On Atmospheric Boundary-Layer Characteristics At Anand, India Using Lsp Experimental Data Sets

An attempt is made to study the planetary boundary layer (PBL) characteristics during the winter period at Anand (22.4°N, 72.6°E), a semi-arid region, which is located in the western part of India. A one-dimensional turbulent kinetic energy (TKE) closure model is used for the study. The structure of the PBL,which consists of profiles of zonal and meridional components of wind,potential temperature and specific humidity, is simulated. A one-dimensional soil heat and moisture transport parameterization scheme is incorporated for the accurate representation of the energy exchange processes at the soil-atmosphere interface. The diurnal variation of fluxes of sensible heat, latent heat, shortwave radiation, net radiation and soil flux, soil temperature at different depths, Richardson number and TKE at the height of the constant flux layer is studied. The model predictions are compared with the available observations obtained from a special Land Surface Processes (LSP) experiment.     

南极瑞穗站辐射平衡及湍流通量特征

本文利用南极瑞穗站１９７９—１９８０年近地面层微气象及辐射平衡等观测资料，分析了春、夏、秋和冬季辐射平衡分量的日、年变化特征，采用空气动力学方法和廓线梯度迭代法计算了不同季节的动量通量、感热通量和由能量平衡方程得到的潜热通量的日变化特征，并对计算结果进行了比较。文中还对湍流热量交换系数、湍流动量交换系数与理查孙数的日变化关系进行了讨论。     

MM5模式中城市冠层参数化方案的设计及其数值试验

文中在综合国外一些较先进的中尺度模式城市作用参数化方案的基础上 ,从城市下垫面结构对城市边界层大气作用的物理机制及实际应用两方面出发 ,对城市下垫面结构和人为活动等因素对边界层结构的影响及中尺度模式中城市化作用的合理体现等问题进行了较全面的考虑 ,改进和设计出能够较全面、细致地描述城市结构对大气边界层动力、热力结构的影响 ,且适合中尺度模式结构特点的城市冠层参数化方案 (UCP) ,并实现了其与MM5模式的耦合。进行了耦合后的UCP方案及采用原城市作用方案的MM5模式对BECAPEX试验期间北京地区气象条件多重嵌套细尺度进行了模拟试验 ,并与观测结果对比 ,结果表明 :相比于MM 5模式中原有表示城市作用的参数化方案来讲 ,设计的UCP方案在很大程度上提高了MM 5模式对城市边界层热力和动力结构的模拟能力。     

A unified linear theory of wavelike perturbations under general ocean conditions

A linearized instability analysis model with five unknowns was proposed to describe disturbance motions under general oceanic background conditions, including large-scale current shear, density stratification, frontal zone, and arbitrary topography. A unified linear theory of wavelike perturbations for surface gravity waves, internal gravity waves and inertial gravity waves was derived for the adiabatic case, and the solution was then found using Fourier integrals. In this theory, we discarded the assumptions widely accepted in the literature concerning derivations of wave motions such as the irrotationality assumption for surface gravity waves, the rigid-lid approximation for internal gravity waves, and the long-wave approximation for inertial gravity waves. Analytical solutions based on this theory indicate that the complex dispersion relationships between frequency and wave-number describing the propagation and development of the three types of wavelike perturbation motions include three components: complex dispersion relationships at the sea surface; vertical invariance of the complex frequency; and expressions of the vertical wave-number (phase). Classical results of both surface waves and internal waves were reproduced from the unified theory under idealized conditions. The unified wave theory can be applied in the dynamical explanation of the generation and propagation properties of internal waves that are visible in the satellite SAR images in the southern part of the China Seas. It can also serve as the theoretical basis for both a numerical internal-wave model and analytical estimation of the ocean fluxes transported by wavelike perturbations.     

不同边界层参数化方案对一次梅雨锋暴雨过程湍流交换特征模拟的影响

利用WRF模式结合不同的边界层参数化方案,对2007年7月3—5日发生在江淮流域的一次梅雨锋暴雨过程进行多组数值模拟试验。结果发现,边界层方案的选取对于降水的落区和强度模拟会产生较显著的影响;在降水率及地面要素的模拟上,各方案在降水中后期的模拟差异明显大于降水发生阶段;不同边界层方案的选取对于降水时段内的水平风场、垂直运动和假相当位温的垂直分布都产生影响,直接影响降水时空分布的模拟;不同方案都模拟出了在降水发生之后不同于晴空日变化的湍流动能垂直分布,经分析发现与局地较强的垂直风切变和近地面强湍流气团被抬升有关,而浮力项起着耗散作用;各方案的湍流交换特征与湍流动能特征基本吻合,相比于其他方案,MYJ方案在降水区域的湍流动能及湍流交换强度明显偏弱,对热通量的输送也偏弱;GBM方案在边界层内的湍流混合偏弱而在边界层以上湍流混合显著偏强,热通量输送在边界层以上的高度上误差明显,影响了对降水区域气象要素的模拟能力,仍需要进一步改进。      

A Simple Model for the Afternoon and Early Evening Decay of Convective Turbulence Over Different Land Surfaces

A simple model to study the decay of turbulent kinetic energy (TKE) in the convective surface layer is presented. In this model, the TKE is dependent upon two terms, the turbulent dissipation rate and the surface buoyancy fluctuations. The time evolution of the surface sensible heat flux is modelled based on fitting functions of actual measurements from the LITFASS-2003 field campaign. These fitting functions carry an amplitude and a time scale. With this approach, the sensible heat flux can be estimated without having to solve the entire surface energy balance. The period of interest covers two characteristic transition sub-periods involved in the decay of convective boundary-layer turbulence. The first sub-period is the afternoon transition, when the sensible heat flux starts to decrease in response to the reduction in solar radiation. It is typically associated with a decay rate of TKE of approximately t ⁻² (t is time following the start of the decay) after several convective eddy turnover times. The early evening transition is the second sub-period, typically just before sunset when the surface sensible heat flux becomes negative. This sub-period is characterized by an abrupt decay in TKE associated with the rapid collapse of turbulence. Overall, the results presented show a significant improvement of the modelled TKE decay when compared to the often applied assumption of a sensible heat flux decreasing instantaneously or with a very short forcing time scale. In addition, for atmospheric modelling studies, it is suggested that the afternoon and early evening decay of sensible heat flux be modelled as a complementary error function.     

Wave and turbulence structure in a disturbed nocturnal inversion

Acoustic sounder and tower data obtained at the Boulder Atmospheric Observatory (BAO) are used to examine several features of the wave and turbulence structure associated with a disturbed nocturnal inversion. General features, including mean fields and Richardson number, for the case selected for this study are presented. Spectral analysis of the tower data reveals a separation of energy into wavelike and turbulent fluctuations. Analysis of the heat flux, however, shows upward counter-gradient fluxes in the vicinity of a low-level jet and near the top of the inversion. Cospectral analysis shows that the major contribution to the upward heat flux occurs at frequencies that would normally be considered characteristic of waves. In some cases, the upward flux is associated with a phase shift between vertical velocity w and fluctuating temperature θ different from the quadrature relation that would be expected of internal waves. Time series analysis reveals that these unexpected positive fluxes occur in relatively short bursts. Analysis of time series of θ and w in other cases, as well as inspection of acoustic sounder records, shows that sometimes such upward fluxes can result from a combination of wave motion and horizontal temperature advection. In this case the advection is associated with a shallow cold front.     

Turbulence in stably stratified fluids: A review of laboratory experiments

This is a review of laboratory studies of mixing in stably stratified fluids away from the direct intluence of boundary layers, and was written to introduce the session on laboratory experiments at the IUCRM Colloquium.Internal waves (Section 2) can lead to turbulence by creating regions of unstable density gradients through their mutual interactions, by individually breaking by forming rotors, and by reducing the local Richardson number until Kelvin-Helmholtz instability results. They may be important in radiating energy from turbulent or spreading regions. Critical-layer absorption of internal waves is not found to be a direct cause of turbulence in experiments with 15 Richardson number 5, although the modification of the vertical density profile may be significant.Turbulent-laminar interfaces without mean shear (Section 3) and with mean shear (Section 4) are described. The source of turbulence in these experiments is partly external, either generated by an oscillating grid or by a (relatively) moving boundary. The development of turbulence generated entirelywithin a stratified layer by Kelvin-Helmholtz instability, is described in detail in Section 5, and the results are compared with measurements in the ocean and in the atmosphere.     

RADIATION BALANCE AND TURBULENT FLUX CHARACTERISTICS OVER MIZUHO STATION IN ANTARCTICA

In this paper,by using measurements in micrometeorology and radiation balance in the surface layer(Yamanouchiet al.,1981;Wada et al.,1981;Ishikawa et al.,1982;Ohata et al.,1983),we have analyzed the diurnal and annual varia-tion characteristics of radiation balance in spring,summer,autumn and winter,and calculated the momentum flux andsensible heat flux with the aerodynamic method and profile gradient alternate method in different seasons.We have alsoobtained the diurnal variation characters of the latent heat flux from the equation for energy balance.The results fromthe calculation are compared.Finally,the relationship between the turbulent heat and momentum exchange coefficientand the diurnal variation of the Richardson number is discussed.     

Sea breeze activity at an inland station Kharagpur (India) — A case study

Surfaces fluxes, turbulent kinetic energy and Flux Richardson number are calculated for three typical sea breeze days characterizing three types of sea breeze onset at an inland station Kharagpur (22°21 N, 87°19 E), 80 km inland, one of the sites for MONTBLEX (MONsoon Trough Boundary Layer EXperiment), in India. The sea breeze onset is associated with a decrease in momentum and heat fluxes and an increase in moisture flux. The turbulent kinetic energy shows quite a significant value even in the late afternoon. The surface layer becomes nearly stable even before sunset, due to the passage of the sea breeze.     

Boundary layer structure over an inhomogeneous surface: Simulation with a non-hydrostatic mesoscale model

A three-dimensional, non-hydrostatic mesoscale model is used to study boundary-layer structure over an area characterized by the city of Copenhagen, the Øresund strait, and adjacent coastal farmland. Simulations are compared with data obtained on June 5, 1984 during the Øresund experiment.Under moderately strong wind conditions, a stable internal boundary layer (IBL) developed over the Øresund strait during the day. Near-surface winds decelerate over water due to diminished vertical momentum transfer.The turbulent kinetic energy field closely reflects the surface roughness distribution due to the imposed relatively strong wind forcing. TKE budgets over water, farmland and a city area are discussed by inspection of vertical profiles of the individual terms. The buoyancy term is used to indicate IBL heights because it changes sign at the boundary between different stability regimes. Measured and simulated dissipation rates show a decrease in the transition zone as the air travels over water and an abrupt increase when the IBL over a downwind city area is intersected. The top of the stable IBL is characterized by a minimum in the vertical TKE profile.     

Effect of wind shear on atmospheric wave instabilities revealed by FM/CW radar observations

An FM/CW radar sounding system designed and built by one of us (Richter, 1969) reveals atmospheric wave structure in unparalleled detail.The most outstanding features evident in the record are; internal gravity waves; features resembling Kelvin/Helmholtz instability structures; and multiple layering, often with lamina only a few meters thick.This paper shows a variety of atmospheric structural patterns and compares them with several hypothetical models of internal waves to obtain more insight into the atmospheric processes at work. Special attention is given to the distribution of the Richardson number in trapped and untrapped gravity waves. It is proposed that the multiple layers result from untrapped internal gravity waves whose propagation vector is directed nearly vertically within very stable height regions. It is argued that the layers are caused by dynamic instability resulting from reduction in the Richardson number due to wave induced shear and to some background wind shear when the amplitude-to-wavelength ratio grows during propagation into thermally stable height regions of the atmosphere.