A benchmark comparison of numerical methods for infinite Prandtl number thermal convection in two-dimensional Cartesian geometry

Abstract

A comparison is made between seven different numerical methods for calculating two-dimensional thermal convection in an infinite Prandtl number fluid. Among the seven methods are finite difference and finite element techniques that have been used to model thermal convection in the Earth's mantle. We evaluate the performance of each method using a suite of four benchmark problems, ranging from steady-state convection to intrinsically time-dependent convection with recurring thermal boundary layer instabilities. These results can be used to determine the accuracy of other computational methods, and to assist in the development of new ones.     

Deep‐water dunes on drowned isolated carbonate terraces (Mozambique Channel,south‐west Indian Ocean)

Subaqueous sand dunes are common bedforms on continental shelves dominated by tidal and geostrophic currents. However, much less is known about sand dunes in deep‐marine settings that are affected by strong bottom currents. In this study, dune fields were identified on drowned isolated carbonate platforms in the Mozambique Channel (south‐west Indian Ocean). The acquired data include multibeam bathymetry, multi‐channel high‐resolution seismic reflection data, sea floor imagery, a sediment sample and current measurements from a moored current meter and hull‐mounted acoustic Doppler current profiler. The dunes are located at water depths ranging from 200 to 600 m on the slope terraces of a modern atoll (Bassas da India Atoll) and within small depressions formed during tectonic deformation of drowned carbonate platforms (Sakalaves Seamount and Jaguar Bank). Dunes are composed of bioclastic medium size sand, and are large to very large, with wavelengths of 40 to 350 m and heights of 0·9 to 9·0 m. Dune migration seems to be unidirectional in each dune field, suggesting a continuous import and export of bioclastic sand, with little sand being recycled. Oceanic currents are very intense in the Mozambique Channel and may be able to erode submerged carbonates, generating carbonate sand at great depths. A mooring located at 463 m water depth on the Hall Bank (30 km west of the Jaguar Bank) showed vigorous bottom currents, with mean speeds of 14 cm sec^?1 and maximum speeds of 57 cm sec^?1, compatible with sand dune formation. The intensity of currents is highly variable and is related to tidal processes (high‐frequency variability) and to anticyclonic eddies near the seamounts (low‐frequency variability). This study contributes to a better understanding of the formation of dunes in deep‐marine settings and provides valuable information about carbonate preservation after drowning, and the impact of bottom currents on sediment distribution and sea floor morphology.     

南极近地层大气的热量逆梯度输送现象

根据南极中山站观测结果 ,分析了南极地区近地层热量逆梯度输送的现象。结果表明南极地区在近地层逆温较明显时 ,常会出现热量逆梯度输送的现象 ;同时也探讨了近地层在稳定层结条件下 ,热量逆梯度输送通量的多尺度计算方法。计算结果表明 ,逆梯度输送的感热通量主要是由浮力湍涡的穿越能力决定的 ,而经典的梯度输送公式在该场合下无法使用。     

Evapotranspiration of a Populuseuphratica Oliv. forest and its controlling factors in the lowerHeihe RiverBasin, Northwest China

Evapotranspiration (ET) within an ecosystem is crucial for the water-limited environment that currently lacks adequate quantification in the arid region of Northwest China, mainly covered by phreatophytes, such as the Populus euphratica Oliv. tree and the Tamarix ramosissima Ledeb. shrub species. Accordingly, ET was measured for an entire year using eddy covariance (EC) in P. euphratica stands in the lower Heihe River Basin, Northwest China. During the growing season, the total ET was 850 mm, with a mean of 4.0 mm/d, which is obviously more than that observed at tree-level and standlevel scales, which was likely due to the different level of soil evaporation induced by irrigation via water conveyance. Factors associated with ET fall into either environmental or plant eco-physiological categories. Environmental factors account for at least 79% variation of ET, and the linear relationship between ET and the groundwater table (GWT) revealed the potential water use of P. euphratica forests under the non-water stress condition with the GWT less than 3 m deep. Plant eco-physiological parameters, specifically the leaf area index (LAI), have direct impact on the seasonal pattern of ET, which provides a valuable reference to the wide-area estimates of ET for riparian forests by using LAI. In conclusion, P.euphratica forests have high water use after water conveyance, which may be the result of long-term adapting to local climates and limited water availability.     

湍流混合动力学机理研究

在分析传统混合动力学机理基础上,通过宏观混合与微观混合时间量级的对比,提出了湍流条件下,涡流扩散主导宏观混合,分子扩散主导微观混合,而混合过程由宏观混合主导,欧拉数Eu可作为混合效果的控制指标,并通过3种不同容积反应器的混合搅拌试验,进一步证实了该指标的实用性。     

Effects of different gap filling methods and land surface energy balance closure on annual net ecosystem exchange in a semiarid area of China

Based on eddy covariance measurements over two kinds of land surfaces(a degraded grassland and a maize cropland)in a semiarid area of China in 2005 and 2008,the effects of different gap filling methods,energy balance closure and friction velocity threshold(u*)on annual net ecosystem exchange(NEE)were analyzed.Six gap filling methods,including mean diurnal variation(MDV),marginal distribution sampling(MDS),and nonlinear regressions method,were investigated by generating secondary datasets with four different artificial gap lengths(ranging in length from single half-hours to 12 consecutive days).The MDS generally showed a good overall performance especially for long gaps,with an annual sum bias error less than 5 g C m-2 yr-1.There was a large positive annual sum bias error for nonlinear regressions,indicating an overestimate on net ecosystem respiration.The offset in the annual sum NEE for four nonlinear regressions was from 8.0 to 30.8 g C m-2 yr-1.As soil water content was a limiting factor in the semiarid area,the nonlinear regressions considering both soil temperature and soil water content as controlling variables had a better performance than others.The performance of MDV was better in daytime than in nighttime,with an annual sum bias error falling between-2.6 and-13.4 g C m-2 yr-1.Overall,the accuracy of the gap filling method was dependent on the type of the land surface,gap length,and the time of day when the data gap occurred.The energy balance ratio for the two ecosystems was nearly 80%.Turbulent intensity had a large impact on energy balance ratio.Low energy balance ratio was observed under low friction velocity during the night.When there was a large fetch distance in a wind direction,a low energy balance ratio was caused by mismatch of the footprints between the available energy and turbulent fluxes.The effect of energy balance correction on CO2 flux was evaluated by assuming the imbalance caused by the underestimation of sensible heat flux and latent heat flux.The results showed an average increase of 10 g C m-2 yr-1 for annual NEE in both ecosystems with an energy balance correction.On the other hand,the u*threshold also have a large impact on annual sum NEE.Net carbon emission increased 37.5 g C m-2 yr-1 as u*threshold increased from 0.1 to 0.2 m s-1,indicating a large impact of imposing u*threshold on net ecosystem carbon exchange.     

Upper-Tropospheric Environment–Tropical Cyclone Interactions over the Western North Pacific: A Statistical Study

Based on 25-year(1987–2011) tropical cyclone(TC) best track data, a statistical study was carried out to investigate the basic features of upper-tropospheric TC–environment interactions over the western North Pacific. Interaction was defined as the absolute value of eddy momentum flux convergence(EFC) exceeding 10 m s~(-1)d~(-1). Based on this definition, it was found that 18% of all six-hourly TC samples experienced interaction. Extreme interaction cases showed that EFC can reach~120 m s~(-1)d~(-1) during the extratropical-cyclone(EC) stage, an order of magnitude larger than reported in previous studies.Composite analysis showed that positive interactions are characterized by a double-jet flow pattern, rather than the traditional trough pattern, because it is the jets that bring in large EFC from the upper-level environment to the TC center. The role of the outflow jet is also enhanced by relatively low inertial stability, as compared to the inflow jet. Among several environmental factors, it was found that extremely large EFC is usually accompanied by high inertial stability, low SST and strong vertical wind shear(VWS). Thus, the positive effect of EFC is cancelled by their negative effects. Only those samples during the EC stage, whose intensities were less dependent on VWS and the underlying SST, could survive in extremely large EFC environments, or even re-intensify. For classical TCs(not in the EC stage), it was found that environments with a moderate EFC value generally below ~25 m s~(-1)d~(-1) are more favorable for a TC's intensification than those with extremely large EFC.     

全球资料同化中误差协方差三维结构的准确估计与应用Ⅰ:观测空间协方差的准确估计

观测误差与背景误差协方差在四维资料同化和业务资料分析系统中起到决定性作用,它决定着观测信息与背景初猜值信息的相对重要性以及这些信息在空间及不同变量间的扩展方式.由于实际大气的真值并不知道,需要发展不同的技巧来估计观测误差与背景误差协方差,其中在观测空间利用观测与背景初猜值之差来分离观测误差与背景误差协方差的方法估计出的结果较为准确,其估计出的观测误差可直接用于资料分析系统中,背景误差可作为标尺来度量其他方法估计结果的可靠性.文章采用国家气象中心T213L31全球中期分析预报系统的6 h预报作为背景初猜场及同时段冬夏两个季节的北半球探空,利用贝塞尔函数拟合方法来分离观测误差与背景误差协方差,并比较了东亚区、北美区、欧洲区3个探空资料均匀密集区的区域与季节变化结果.结果表明,观测空间拟合方法所要求的水平均质、各向同性在欧洲区和北美区成立程度较好,在东亚区略差,使用时需要斟酌.此外均方差区域间差别较大,在冬季明显大于夏季,温度场偏大0.2 K,风场偏大0.9 m/s.温度场在400 hPa以下与150 hPa以上,背景误差略小于观测误差,而在200-300 hPa,背景误差略大一些.风场的特点与温度场比较一致.温度与风场背景误差主要集中在前40波,并在20波左右达到最大,水平相关季节区域差别不大,而温度垂直相关比风场窄,两者相关范围比较大的波数主要集中在前20波.此外利用贝塞尔函数拟合方法获得结果的分析表明,在质量场中不同区域季节间温度误差的稳定性要明显好于高度场,涡度散度的稳定性要明显好于流函数和势函数,特别是对于特征长度更为明显.这表明利用贝塞尔函数拟合方法获得的结果对校准在全球资料同化中采用温度、涡度散度作为资料同化的分析变量具有一定的优势.     

The phase difference effects on 3-D structure of wave pressure acting on a composite breakwater

In designing the coastal structures, the accurate estimation of the wave forces on them is of great importance. In this paper, the influences of the phase difference on wave pressure acting on a composite breakwater installed in the three-dimensional (3-D) wave field are studied numerically. We extend the earlier model [Hur, D.S., Mizutani, N., 2003. Coastal Engineering 47, 329–345] to simulate 3-D wave fields by introducing 3-D Navier–Stokes solver with the Smagorinsky's sub-grid scale (SGS) model. For the validation of the model, the wave field around a 3-D asymmetrical structure installed on a submerged breakwater, in which the complex wave deformations generate, is simulated, and the numerical solutions are compared to the experimental data reported by Hur, Mizutani, Kim [2004. Coastal Engineering (51, 407–420)]. The model is then adopted to investigate 3-D characteristics of wave pressure and force on a caisson of composite breakwater, and the numerical solutions were discussed with respect to the phase difference between harbor and seaward sides induced by the transmitted wave through the rubble mound or the diffraction. The numerical results reveal that wave forces acting on the composite breakwater are significantly different at each cross-section under influence of wave diffraction that is important parameter on 3-D wave interaction with coastal structures.     

极化分析研究及其在波场分离中的应用

不同的波在空间的质点运动轨迹和极化方向是不同的，利用三分量或二分量记录，在特定的以ｔ０为中心，长为Ｎ△ｔ的滑动时窗中计算出描述波的质点运动轨迹和极化方向的特征参数。利用这些参数可以设计出合适的极化滤波函数，保留那些满足特定要求的质点运动，而衰减那些不满足设计要求的质点运动，利用某些算子可以把弹性波分解成Ｐ波和ＳＶ波，而且衰减面波；利用另外一些算子可以把Ｐ波和ＳＶ波衰减而使面波增强。这些算子甚至可以在嗓音和信号具有相同频率的情况下，成功地提高信嗓比。