Statistics of shallow convection on Mars based on large-eddy simulations. Part 1: shearless conditions

Results of large-eddy simulations of shallow, quasi-steady, shear-less convection in the Martian boundary layer are presented and discussed. In the considered three cases, turbulence is forced by the radiative flux divergence, prescribed as given functions of height, and the strength of the surface heat flux. It is constrained by the temperature inversion at the boundary-layer top. The resulting convective boundary layer exhibits horizontal cellular structures. The presence of radiative heating causes dimensionless statistics of turbulence to depend on the parameter F, defined in terms of the integrated radiative and turbulent heating rates in the boundary layer.     

Statistics of Scalar Fields in the Atmospheric Boundary Layer Based on Large-eddy Simulations. Part 1: Free Convection

Convection in a quasi-steady, cloud-free, shear-free atmospheric boundary layer is investigated based on a large-eddy simulation model. The performed tests indicate that the characteristic (peak) values of statistical moments at the top of the mixed layer are proportional to the interfacial scales (from gradients of scalars in the interfacial layer). Based on this finding a parameterization is proposed for profiles of scalar variances. The parameterization employs two, semi-empirical similarity functions F_m(z/z_i) andF_i(z/z_i), multiplied by a combination of the mixed-layer scales and the interfacial scales.     

Study of near-surface models for large-eddy simulations of a neutrally stratified atmospheric boundary layer

In large-eddy simulations (LES) of the atmospheric boundary layer (ABL), near-surface models are often used to supplement subgrid-scale (SGS) turbulent stresses when a major fraction of the energetic scales within the surface layer cannot be resolved with the temporal and spatial resolution at hand. In this study, we investigate the performance of both dynamic and non-dynamic eddy viscosity models coupled with near-surface models in simulations of a neutrally stratified ABL. Two near-surface models that are commonly used in LES of the atmospheric boundary layer are considered. Additionally, a hybrid Reynolds- averaged/LES eddy viscosity model is presented, which uses Prandtl’s mixing length model in the vicinity of the surface, and blends in with the dynamic Smagorinsky model away from the surface. Present simulations show that significant portions of the modelled turbulent stresses are generated by the near-surface models, and they play a dominant role in capturing the expected logarithmic wind profile. Visualizations of the instantaneous vorticity field reveal that flow structures in the vicinity of the surface depend on the choice of the near-surface model. Among the three near-surface models studied, the hybrid eddy viscosity model gives the closest agreement with the logarithmic wind profile in the surface layer. It is also observed that high levels of resolved turbulence stresses can be maintained with the so-called canopy stress model while producing good agreement with the logarithmic wind profile.     

Parameterization of sheared entrainment in a well-developed CBL. Part I: Evaluation of the scheme through large-eddy simulations

The entrainment flux ratio A _e and the inversion layer (IL) thickness are two key parameters in a mixed layer model. A _e is defined as the ratio of the entrainment heat flux at the mixed layer top to the surface heat flux. The IL is the layer between the mixed layer and the free atmosphere. In this study, a parameterization of A _e is derived from the TKE budget in the firstorder model for a well-developed CBL under the condition of linearly sheared geostrophic velocity with a zero value at the surface. It is also appropriate for a CBL under the condition of geostrophic velocity remaining constant with height. LESs are conducted under the above two conditions to determine the coefficients in the parameterization scheme. Results suggest that about 43% of the shear-produced TKE in the IL is available for entrainment, while the shear-produced TKE in the mixed layer and surface layer have little effect on entrainment. Based on this scheme, a new scale of convective turbulence velocity is proposed and applied to parameterize the IL thickness. The LES outputs for the CBLs under the condition of linearly sheared geostrophic velocity with a non-zero surface value are used to verify the performance of the parameterization scheme. It is found that the parameterized A _e and IL thickness agree well with the LES outputs.     

Statistics of Scalar Fields in the Atmospheric Boundary Layer Based on Large-Eddy Simulations. Part II: Forced Convection

Forced convection in a quasi-steady atmospheric boundary layer is investigated based on a large-eddy simulation (LES) model. The performed simulations show that in the upper portion of the mixed layer the dimensionless (in terms of mixed layer scales) vertical gradients of temperature, humidity, and wind velocity depend on the dimensionless height z/z _i and the Reech number Rn. The peak values of variances and covariances at the top of the mixed layer, scaled in terms of the interfacial scales, are functions of the interfacial Richardson number Ri. As a result expressions for the entrainment rates, in the case when the interfacial layer has a finite depth, and a condition for the presence of moistening or drying regimes in the mixed layer, are derived. Profiles of dimensionless scalar moments in the mixed layer are proposed to be expressed in terms of two empirical similarity functions F _m and F _i , dependent on dimensionless height z/z _i , and the interfacial Richardson number Ri. The obtained similarity expressions adequately approximate the LES profiles of scalar statistics, and properly represent the impact of stability, shear, and entrainment. They are also consistent with the parameterization proposed for free convection in the first part of this paper.     

风切变对边界层对流影响的大涡模拟研究

利用"西北干旱区陆-气相互作用野外观测实验"加密观测期间在敦煌站的观测资料以及大涡模式,模拟了对流边界层的发展,以及示踪物从混合层向残留层传输的时空变化。模拟的对流边界层的结构及演变特征与实测结果基本一致。进一步通过有风切变和无风切变的敏感性数值试验,研究了风切变对垂直速度、位温和示踪物浓度的水平分布以及示踪物传输高度的影响。研究结果表明,在有风切变的试验中(甚至风切变仅存在于近地层中),对流边界层的增长加强,而且示踪物被传输的高度也较高。与浮力驱动的对流边界层相比,由浮力和风切变共同驱动的边界层中上升气流较弱而下沉气流较强,但前者的上升气流与下沉气流的分布在垂直方向上更为倾斜。由于夹卷作用的增强,浮力和风切变共同驱动的对流边界层较浮力驱动的对流边界层暖。在夹卷层,浮力和风切变共同驱动的边界层对流的上升气流和下沉气流都比浮力驱动的边界层对流中的强,而且垂直速度的概率密度函数分布也较对称,其位温和示踪物浓度的概率密度函数分布也比浮力驱动的边界层中的平直。对湍流动能收支的分析也表明风切变对湍流动能有重要影响,尤其对夹卷层中的湍流动能切变产生项影响较大。示踪物浓度的概率密度函数垂直分布显示,浮力驱动的边界层中示踪物浓度随高度变化较小,而浮力和风切变共同驱动的边界层中示踪物浓度随高度递减,但是示踪物传输的高度比较高。     

Large-Eddy Simulation of air Pollution Dispersion in the Nocturnal Cloud-Topped Atmospheric Boundary Layer

Effects of stratocumulus clouds on the dispersion of contaminants are studied in the nocturnal atmospheric boundary layer. The study is based on a large-eddy simulation (LES) model with a bulk parametrization of clouds. Computations include Lagrangian calculations of atmospheric dispersion of a passive tracer released from point sources at various heights above the ground. The results obtained show that the vertical diffusion is non-Gaussian and depends on the location of a source in the boundary layer.     

Spatial representativeness of single tower measurements and the imbalance problem with eddy-covariance fluxes: results of a large-eddy simulation study

A large-eddy simulation (LES) study is presented that investigates the spatial variability of temporal eddy covariance fluxes and the systematic underestimation of representative fluxes linked to them. It extends a prior numerical study by performing high resolution simulations that allow for virtual measurements down to 20 m in a convective boundary layer, so that conditions for small tower measurement sites can be analysed. It accounts for different convective regimes as the wind speed and the near-surface heat flux are varied. Moreover, it is the first LES imbalance study that extends to the stable boundary layer. It reveals shortcomings of single site measurements and the necessity of using horizontally-distributed observation networks. The imbalances in the convective case are attributed to a locally non-vanishing mean vertical advection due to turbulent organised structures (TOS). The strength of the TOS and thus the imbalance magnitude depends on height, the horizontal mean wind and the convection type. Contrary to the results of a prior study, TOS cannot generally be responsible for large energy imbalances: at low observation heights (corresponding to small towers and near-surface energy balance stations) the TOS related imbalances are generally about one order of magnitude smaller than those in field experiments. However, TOS may cause large imbalances at large towers not only in the case of cellular convection and low wind speeds, as found in the previous study, but also in the case of roll convection at large wind speeds. In the stably stratified boundary layer for all observation heights neither TOS nor significant imbalances are observed. Attempting to reduce imbalances in convective situations by applying the conventional linear detrending method increases the systematic flux underestimation. Thus, a new filter method is proposed.     

Simulation of the Askervein flow. Part 2: Large-eddy simulations

Large-eddy simulations of the neutrally stratified flow over the Askervein Hill were performed, to improve the knowledge of the flow obtained from field measurements and numerical simulations with Reynolds averaged Navier-Stokes (RANS) methods. A Lagrangian dynamic subgrid model was used but, to avoid the underdissipative character near the ground, it was merged with a damped Smagorinsky model. Simulations of a flat boundary-layer flow with this subgrid model showed that the turbulent vertical motions and shear stress were better resolved using grids with a stream to spanwise aspect ratio Δx / Δy = 2 than with an aspect ratio Δx / Δy = 1. Regarding the flow over the Askervein Hill, it was found that large-eddy simulations provide an acceptable solution for the mean-velocity field and better predictions of the turbulent kinetic energy in the upstream side of the hill than the model. However, as with the model, grid convergence was not achieved in the lee side and the size of the zone with reversed flow increased with the grid refinement. Nevertheless, the existence of the intermittent separation predicted with unsteady RANS in part one of this work seems unquestionable, due to the deceleration of the flow. In our opinion, a better modelling of the decelerating boundary layer in the lee side is required to improve the results obtained using equilibrium assumptions and achieve grid convergence.     

Upscale effects in simulations of tropical convection on an equatorial beta-plane

A cloud-resolving model is configured to span the full meridional extent of the tropical atmosphere and have sufficient zonal extent to permit the representation of tropical cloud super-clusters. This is made computationally feasible by the use of anisotropic horizontal grids where one horizontal coordinate direction has over an order of magnitude finer resolution than the other direction. Typically, the meridional direction is chosen to have the coarser resolution (40 km grid spacing) and the zonal direction has enough resolution to ‘permit’ crude convective squall line ascent (1 km grid spacing). The aim was to run in cloud-resolving model (CRM) mode yet still have sufficient meridional resolution and extent to capture the equatorial trapped waves and the Hadley circulation. The large-scale circulation is driven by imposed uniform tropospheric cooling in conjunction with a fixed sea surface temperature distribution. At quasi-equilibrium the flow is characterized by sub-tropical jetstreams, tropical squall line systems that form eastward-propagating super-clusters, tropical depressions and even hurricanes.Two scientific issues are briefly addressed by the simulations: what forces the Hadley circulation and the nature of stratospheric waves appearing in the simulation. It is found that the presence of a meridional sea surface temperature gradient is not sufficient on its own to force a realistic Hadley circulation even though convection communicates the underlying temperature gradient to the atmosphere. It is shown in a simulation that accounts for the observed time and zonal-mean momentum forcing effect of large-scale eddies (originating in middle latitudes) that the heaviest precipitation is concentrated near the equator in association with moisture flux convergence driven by the Trade winds.A spectral analysis of the stratospheric waves found on the equator using the dispersion relation for equatorially-trapped waves provides strong evidence for the existence of a domain-scale Kelvin wave together with eastward and westward propagating inertia-gravity waves. The eastward-propagating stratospheric waves appear to be part of a convectively coupled wave system travelling at about 15 ms⁻¹.     

The Influence of Thermally-Induced Mesoscale Circulations on Turbulence Statistics Over an Idealized Urban Area Under a Zero Background Wind

The influence of mesoscale circulations induced by urban-rural differential surface sensible heat flux and roughness on convective boundary-layer (CBL) flow statistics over an isolated urban area has been examined using large-eddy simulation (LES). Results are analyzed when the circulations influence the entire urban area under a zero background wind. For comparison, the CBL flow over an infinite urban area with identical urban surface characteristics under the same background meteorological conditions is generated as a control case (without circulations). The turbulent flow over the isolated urban area exhibits a mix of streaky structure and cellular pattern, while the cellular pattern dominates in the control case. The mixed-layer height varies significantly over the isolated urban area, and can be lower near the edge of the urban area than over the rural area. The vertical profiles of turbulence statistics over the isolated urban area vary horizontally and are dramatically different from the control case. The turbulent kinetic energy (TKE) sources include wind shear, convergence, and buoyancy productions, compared to only buoyancy production in the control case. The normalized vertical velocity variance is reduced compared to the control case except in the central urban area where it is little affected. The low-level flow convergence is mainly responsible for the enhanced horizontal velocity variance in the central urban area, while wind shear is responsible for the additional local maximum of the horizontal velocity variance near the middle of the CBL outside the central area. Parameterizations in the prognostic equation for TKE used in mesoscale models are evaluated against the LES results over the isolated urban area. We also discuss conditions under which the urban-induced circulations occur and when they may affect the entire urban area. Given that urban-induced circulations can influence the entire urban area within hours for an urban area of a realistic size, it is inappropriate to directly apply empirical relations of turbulence statistics derived under horizontally-homogenous flow conditions to an urban area.     

Large-Eddy Simulations of the Stable Boundary Layer Using the Standard Kolmogorov Theory: Range of Applicability

Large-eddy simulations (LES) of the Stable Atmospheric Boundary Layer (SBL) are difficult because the turbulence is not isotropic for strong stratification and the Kolmogorov theory might be no longer valid. This fact compells us to work on modifications to the subgrid turbulence schemes, although there is not any widely accepted theory on anisotropic turbulence. In this work, a LES model is used to see what range of stable stratification can still be simulated with a subgrid turbulence scheme using the Kolmogorov theory for the dissipation. Twenty simulations of increasing stability have been performed using a horizontal resolution of 5 m. The model is able to simulate weakly and moderately stable conditions and experiences runaway cooling for strong stability. The goodness of the successful simulations is inspected through comparison to observations from the experimental campaigns SABLES-98 and CASES-99. Other supplementary tests have been performed on the resolution and the surface boundary condition.     

Parameterization of Sheared Entrainment in a Well-developed CBL.Part Ⅱ:A Simple Model for Predicting the Growth Rate of the CBL

Following the parameterization of sheared entrainment obtained in the companion paper, Liu et al. (2016), the present study aims to further investigate the characteristics of entrainment, and develop a simple model for predicting the growth rate of a well-developed and sheared CBL. The relative stratification, defined as the ratio of the stratification in the free atmosphere to that in the entrainment zone, is found to be a function of entrainment flux ratio (A _e). This leads to a simple expression of the entrainment rate, in which A _e needs to be parameterized. According to the results in Liu et al. (2016), A _e can be simply expressed as the ratio of the convective velocity scale in the sheared CBL to that in the shear-free CBL. The parameterization of the convective velocity scale in the sheared CBL is obtained by analytically solving the bulk model with several assumptions and approximations. Results indicate that the entrainment process is influenced by the dynamic effect, the interaction between mean shear and environmental stratification, and one other term that includes the Coriolis effect. These three parameterizations constitute a simple model for predicting the growth rate of a well-developed and sheared CBL. This model is validated by outputs of LESs, and the results show that it performs satisfactorily. Compared with bulk models, this model does not need to solve a set of equations for the CBL. It is more convenient to apply in numerical models.     

基于不同时间尺度风切变指数推算风资源的对比分析

利用2014—2018年辽宁省探空资料分析了水平风速的垂直风廓线分布特征。用2座代表性测风塔逐时梯度风观测分析了采用不同高度组合方案计算出风切变指数的月、日变化特征, 分别用月、小时、年风切变指数推算高层风速和风功率密度, 并与实测对比。结果表明: 沈阳相较于大连地区风速随高度增加较快, 180 m高度以上风速基本保持不变, 而大连因其纬度低且靠近海洋, 300 m以下风速均匀上升。在非复杂地形情况下, 距地面10 m高度以上间隔一定高度设立4层风观测, 基本可以满足近地层风资源评估需求。受太阳辐射、下垫面、海陆热力性质差异等影响, 辽宁省风切变指数日变化特征比月变化更显著。利用小时风切变指数推算高层风速和风功率密度的方案优于采用月、年风切变指数方案。风切变指数日变化越显著, 采用逐时风切变指数推算方案越优于其他计算方案。     

Large-eddy Simulation of Turbulent Flow Across a Forest Edge. Part I: Flow Statistics

The statistics of turbulent flow across a forest edge have been examined using large-eddy simulation, and results compared with field and wind-tunnel observations. The moorland-to-forest transition is characterized by flow deceleration in the streamwise direction, upward distortion of the mean flow, formation of a high pressure zone immediately in front of the edge, suppression of the standard deviations and covariance of velocity components, and enhancement of velocity skewnesses. For the selected forest density, it is observed that the maximum distortion angle is about 8 degrees from the horizontal. Instead of approaching a downwind equilibrium state in a monotonic manner, turbulence (standard deviations and covariances of velocity components) and mean streamwise velocity undershoot in the transition zone behind the edge. Evolution of flow statistics clearly reveals the growth of an internal boundary layer, and the establishment of an equilibrium layer downwind of the edge. It is evident that lower-order moments generally adjust more quickly over the new rough surface than do higher-order moments. We also show that the streamwise velocity standard deviation at canopy height starts its recovery over the rough surface sooner than does the vertical velocity standard deviation, but completes full adjustment later than the latter. Despite the limited domain size upstream of the edge, large-eddy simulation has successfully reproduced turbulent statistics in good agreement with field and wind-tunnel measurements.     

Evaluating Models of The Neutral, Barotropic Planetary Boundary Layer using Integral Measures: Part I. Overview

Data for the cross-isobaric angle ₀, the geostrophic drag coefficient C_g, and the functions A and B of Rossby number similarity theory, obtained from meteorological field experiments, are used to evaluate a range of models of the neutral, barotropic planetary boundary layer. The data give well-defined relationships for ₀, C_g, and the integrated dissipation rate over the boundary layer, as a function of the surface Rossby number. Lettau's first-order closure mixing-length model gives an excellent fit to the data; other simple models give reasonable agreement. However more sophisticated models, e.g., higher-order closure, large-eddy simulation, direct numerical simulation and laboratory models, give poor fits to the data. The simplemodels have (at least) one free parameter in their turbulence closure that is matched toatmospheric observations; the more sophisticated models either base their closure onmore general flows or have no free closure parameters. It is suggested that all of theatmospheric experiments that we could locate violate the strict simplifying assumptionsof steady, homogeneous, neutral, barotropic flow required by the sophisticated models.The angle ₀ is more sensitive to violations of the assumptions than is C_g.The behaviour of the data varies in three latitude regimes. In middle and high latitudes the observed values of A and B exhibit little latitudinal dependence; the best estimates are A = 1.3 and B = 4.4. In lower latitudes the neutral, barotropic Rossby number theory breaks down. The value of B increases towards the Equator; the determination of A is ambiguous – the trend can increase or decrease towards the Equator. Between approximately 5° and 30° latitude, the scatter in the data is thought to be primarily due to the inherent presence of baroclinicity. The presence of the trade-wind inversion, thermal instability and the horizontal component of the Earth's rotation _H also contribute.Marked changes in the values of A and B occur in the region between the Equator andapproximately 5° latitude, as the Coriolis parameter |f| approaches zero. Although the variation of A and B with latitude suggests some similarity to the results obtained from the direct numerical simulations, the presence of additional complexities in the real atmosphere that are not included in the numerical model, precludes a meaningful direct comparison.     

基于多普勒测风激光雷达的低空急流观测研究

基于相干多普勒测风激光雷达于2018年8月在山东德州获取的为期一个月的风廓线观测数据,进行了低空急流的判定、识别与统计分析。参考BONNER对低空急流的判定标准,对1 500 m高度以下的每10 min平均风廓线数据进行低空急流识别与统计,急流发生频率仅为3.6%。参考张世丰对低空急流的判定标准,统计了350 m高度以下10 min平均风廓线的低空急流风速、高度、风向及风切变等结构特征。急流发生频率为24.9%,急流速度主要介于6～10 m·s-1之间,急流高度出现3个峰值,分别位于110 m、160 m和220 m左右,急流风向主要为偏东风和偏南风。结果表明,多普勒激光雷达可以获取高时空分辨率的风廓线数据,进而可以有效检测低空急流结构的存在及其特征。     

基于风廓线雷达的对流边界层高度的确定

大气边界层高度对于天气、气候和大气污染研究是一个至关重要的参量。对流边界层(Convective Boundary Layer,CBL)顶部的夹卷过程造成温度和湿度垂直梯度增强,导致这一层的折射率结构常数C■变高。C■的这种垂直分布特征经常被用来定位出CBL高度Z_i。本文利用2010年7—8月天津大港的风廓线雷达数据推断出CBL高度Z_i,对于多重C■峰值或不明确的C■峰值,本文改进了对Z_i的测定,分别讨论了C■最大后向散射法与C■和垂直速度方差(σ■)相结合的新方法的适用性。研究显示:(1)C■廓线具有单峰时,最大后向散射强度法能正确估计CBL高度,这种情况往往对应的是晴天。CBL上存在的残留层或云层引起的温湿起伏变化导致C■廓线具有双峰甚至多峰时,最大后向散射强度法可能会错误估计CBL高度;(2)C■和σ■结合的方法不仅与晴天时C■最大后向散射法有较好的一致性,而且可以将CBL造成的C■峰值从云层造成的C■峰值中区分出来,从而正确估计CBL高度;(3)一般而言,对流边界层中存在有明显的、破碎或者分散不明显的云时,C■和σ■结合的方法都能较好地识别出CBL对应的C■峰值。但由于边界层中的情况极为复杂,C■和σ■结合法也会因不同的原因而错误估计CBL高度。     

The Effects of Canopy Leaf Area Index on Airflow Across Forest Edges: Large-eddy Simulation and Analytical Results

The structure of turbulent flows along a transition between tall-forested canopies and forest clearings continues to be an active research topic in canopy turbulence. The difficulties in describing the turbulent flow along these transitions stem from the fact that the vertical structure of the canopy and its leaf area distribution cannot be ignored or represented by an effective roughness length. Large-eddy simulation (LES) runs were performed to explore the effect of a homogeneous variation in the forest leaf area index (LAI) on the turbulent flow across forest edges. A nested grid numerical method was used to ensure the development of a deep boundary layer above the forest while maintaining a sufficiently high resolution in the region close to the ground. It was demonstrated that the LES here predicted first-order and second-order mean velocity statistics within the canopy that agree with reported Reynolds-Averaged Navier–Stokes (RANS) model results, field and laboratory experiments. In the simulations reported here, the LAI was varied between 2 and 8 spanning a broad range of observed LAI in terrestrial ecosystems. By increasing the forest LAI, the mean flow properties both within the forest and in the clearing near the forest edge were altered in two fundamental ways: near the forest edge and into the clearing, the flow statistical properties resembled the so-called back-facing step (BFS) flow with a mean recirculation zone near the edge. Another recirculation zone sets up downstream of the clearing as the flow enters the tall forest canopy. The genesis of this within-forest recirculation zone can be primarily described using the interplay between the mean pressure gradients (forcing the flow) and the drag force (opposing the flow). Using the LES results, a simplified analytical model was also proposed to explain the location of the recirculation zone inside the canopy and its dependence on the forest LAI. Furthermore, a simplified scaling argument that decomposes the mean velocity at the outflow edge into a superposition of ‘exit flow’ and BFS-like flow with their relative importance determined by LAI was explored.     

The Effects of Vegetation Density on Coherent Turbulent Structures within the Canopy Sublayer: A Large-Eddy Simulation Study

Large-eddy simulation has become an important tool for the study of the atmospheric boundary layer. However, since large-eddy simulation does not simulate small scales, which do interact to some degree with large scales, and does not explicitly resolve the viscous sublayer, it is reasonable to ask if these limitations affect significantly the ability of large-eddy simulation to simulate large-scale coherent structures. This issue is investigated here through the analysis of simulated coherent structures with the proper orthogonal decomposition technique. We compare large-eddy simulation of the atmospheric boundary layer with direct numerical simulation of channel flow. Despite the differences of the two flow types it is expected that the atmospheric boundary layer should exhibit similar structures as those in the channel flow, since these large-scale coherent structures arise from the same primary instability generated by the interaction of the mean flow with the wall surface in both flows. It is shown here that several important similarities are present in the two simulations: (i) coherent structures in the spanwise-vertical plane consist of a strong ejection between a pair of counter-rotating vortices; (ii) each vortex in the pair is inclined from the wall in the spanwise direction with a tilt angle of approximately 45°; (iii) the vortex pair curves up in the streamwise direction. Overall, this comparison adds further confidence in the ability of large-eddy simulation to produce large-scale structures even when wall models are used. Truncated reconstruction of instantaneous turbulent fields is carried out, testing the ability of the proper orthogonal decomposition technique to approximate the original turbulent field with only a few of the most important eigenmodes. It is observed that the proper orthogonal decomposition reconstructs the turbulent kinetic energy more efficiently than the vorticity.