Laminar-Turbulent Bifurcation Scenario in 3D Rayleigh-Benard Convection Problem

We are considering two initial-boundary value problems for Rayleigh-Benard convection in Oberbeck-Boussinesq approximation for incompressible fluid in 3D-rectangular domain with 4:4:1 geometric ratio with periodicity in two directions and cubic domain with 1:1:1 ratio and zero velocity and temperature gradient boundary conditions. For this purpose, we use two numerical method: one is a Pseudo-Spectral-Galerkin method with trigonometric-Chebyshev polynomials and the other is finite element/volume method with WENO interpolation for advection term. Numerical methods are presented shortly and are benchmarked against known DNS data and against one another (for quasi-periodic domain problem). Then we perform stability analysis using analytical expression for main stationary solutions and eigenvalue numerical analysis by applying Implicitly Restarted Arnoldi (IRA) method. The IRA is used to perform linear stability analysis, find bifurcations of stationary points and analyze eigenvalues of monodromy matrices. Thus characteristic exponents of the system for time periodic solutions (limited cycles of various periods and resonance invariant tori) are computed. We show, numerically, the existence of multistable rotes to chaos through chaotic fractal attractors, full Feigenbaum-Sharkovski cascades and multidimensional torus attractors (Landau-Hopf scenario). The existence of these attractors is shown through analysis of phase subspaces projections, Poincare sections and eigenvalue analysis of numerically computed DNS data. These attractors burst into chaos with the increase of Rayleigh number either through resonance and phase-locking or through emergence of singular chaotic attractors.

Analysis of a Large-scale Hail Process in Ulanqab City

Based on the weather monitoring data,NCEP/NCAR reanalysis data and Doppler weather radar data,the circulation background,atmospheric stability and changing characteristics of radar echoes of a large-scale hail weather process in Ulanqab City on July 5,2021 were analyzed.The results show that this hail weather process occurred in the summer afternoon of the hail-prone period in Ulanqab City,and was formed under the influence of upper trough and the circulation background of"two troughs and one ridge",which was conducive to the occurrence of strong convection weather.The low-level shear line provided the dynamic and water vapor conditions for the occurrence of the hail.In strong convection weather,water vapor was transported mainly from the Bay of Bengal,India and Nepal over the Himalayas.Before the occurrence of strong convection weather,water vapor transport increased significantly,and the low-level water vapor concentrated below 400 hPa,with obvious convergence and vertical transport.The characteristic parameters of radar echoes,such as combined reflectivity,vertically integrated liquid,and echo top height,increased significantly before and during the occurrence of hail,which had good indicative significance for the prediction and early warning of hail.

Analysis of Physical Quantities and Radar Parameters about Hail Shooting and Heavy Convective Rainfall

[Objective] The paper is to analyze physical quantities and radar parameter of hail shooting and heavy convective rainfall weather. [Method] Using radar data of Jinan station during 2002 and 2008, combined with sounding data, the physical quantities and radar parameter of hail shooting and heavy convective rainfall weather are compared and analyzed. [Result] The smaller Sl is conducive to the generation of hail weather. When K〉 35 ~C, the probability for occurrence of heavy rainfall weather is significantly increased; when K〈20 ^（3, the probability for occurrence of heavy rainfall weather is significantly decreased. When CAPE value is greater than 1 500 J/KG, the probability for occurrence of hail weather is significantly decreased, while the probability for occurrence of heavy rainfall weather is significantly in- creased. The possibility for occurrence of hail monomer is small when the wind shear is less than 5 m/s; and it is large while wind shear is greater than 20 m/s. The radar forecasting indexes of hail monomer is as follows： VIL value reaches 35 kg/m2 （May）, 43 kg/m2 （June and July）, the monomer height is greater than 9 km, the maximum reflectivity factor is larger than 60 dBz, strong center height reaches 3.3 km （May）, 4.3 km （June） and 5.5 km （July）; VlL value of heavy rainfall monomer generally is below 25 kg/m2. [Conclusion] The paper provides basis form prediction of hail and heavy rainfall.

Multi-scale Analysis of a Hailstorm and Short-time Heavy Rainfall Process in Hohhot City

Based on the conventional observation data,satellite,radar,automatic observation and other refined monitoring data,the severe hail weather in Hohhot City on July 29,2015 was analyzed at multiple scales.The results showed that from the perspective of synoptic-scale system,high-altitude cold air invaded Mongol shortwave trough,and the North China small high pressure and the subtropical high formed a warm shear line;the surface convergence line triggered severe convection weather.Unstable vertical structure,continuous increase of low-level humidity,more drier of high altitudes and the wind direction shear at 180° triggered hailstorm and lightning weather in Hohhot.α-scale convective cloud clusters were maintained in Hohhot,and the ground "herringbone" shear line oscillated violently between the north and the south.Strong lightning and big hails appeared on the ground.The "herringbone" shear line lifted slowly to the north,and there was short-time heavy precipitation on the ground.Radar products showed "bow echo",and the echo had a hanging structure;a mesoscale cyclone was formed 3 km away from the ground.On the radar wind profile,it can be seen that low-layer warm advection and strong wind shear triggered strong hailstorm in Hohhot.The disappearance of low- level warm advection and the maintenance of strong vertical shear of wind produced short-time heavy precipitation.There was a small difference between short-time heavy precipitation and hail in echo top height,but the coverage was significantly reduced.In Hohhot City,vertically integrated liquid water content quickly increased during the hail,and decreased during the short-time heavy precipitation.

Analysis on the Meso-scale Characteristics of a Hail Process in Linyi Area

[Objective] The research aimed to study the meso-scale characteristics of a hail process in Linyi area. [Method] By comprehensively using MICAPS conventional observation data, automatic encryption ground station, MM5 model product and Doppler weather radar data, a strong convective hail weather process which happened in Shandong Peninsula and southeast of Shandong on May 30, 2010 was analyzed. The circulation background and physical mechanism of strong convection weather occurrence, the features of meso- and micro-scale systems were discussed. Some occurrence and development rules of such weather were found. [Result] The strong convective weather was mainly affected by the cold vortex and translot. The high-altitude northwest airflow, low-level southwest airflow, dry and cold air at the high layer, warm and wet air at the low layer, forward-tilting trough caused the strong convective weather. The radar echo analysis showed that the radar echo in the process belonged to the typical multi-monomer windstorm echo, and the strong echo zone was in the forefront of echo. When the convection development was the strongest, the echo intensity reached 65 dBz, and the echo top height surpassed 11 km. As the development of windstorm monomer, the big-value zone of vertical liquid water content product had the jumping formation and disappearance. Moreover, there was obvious weak echo zone. The windstorm monomer moved to the southeast direction as the precipitation system. In the right front of monomer moving direction, there was hook echo feature. The evolution characteristics of radial speed field at the different elevation angles before and after the hail weather occurrence were analyzed. It was found that the radial speed field had some premonitory variations before the hail weather occurrence. Doppler radar product was used to improve the initial field of MM5 model, which could improve the forecast effect in the certain degree and the accuracy of short-time forecast and nowcasting. [Conclusion] The research accumulated the experience for the short-term forecast and nowcasting work of strong convective weather in future.

Analysis on a Gale Hail Strong Convective Weather in Weifang Region of Shandong

To better study occurrence and development mechanism and characteris-tics of strong convective weather in Weifang, reduce the harm brought by disastrous weather, such as gale and hail, extract available forecast index for future strong convective weather forecast work in spring and summer, and improve forecast ac-curacy, diagnostic analysis of the strong convective weather process was conducted. By using conventional weather data for profile and sounding analysis, and combining short-term numerical forecast products for cause analysis, such as radar and satel-lite cloud chart, occurrence characteristics and type of such strong convective weather were obtained. Results showed that the important reason of the strong convective weather occurrence was high-altitude trough split out in eastward move-ment process of northeast cold vortex. In the afternoon of 2nd when hail occurred, temperature rise was obvious at low layer, and energy was sufficient. High-altitude trough with forward tilting structure made that dry cold air at high layer overlapped on warm wet air at lower layer, thereby causing stable stratification formation and triggering the occurrence of strong convective weather.

THE 2－D NUMERICAL STUDY ON THE PRINCIPLES OF RAIN－ENHANCEMENT AND HAIL－SUPPRESSIONIN CONVECTIVE CLOUDS

ＴＨＥ２－ＤＮＵＭＥＲＩＣＡＬＳＴＵＤＹＯＮＴＨＥＰＲＩＮＣＩＰＬＥＳＯＦＲＡＩＮ－ＥＮＨＡＮＣＥＭＥＮＴＡＮＤＨＡＩＬ－ＳＵＰＰＲＥＳＳＩＯＮＩＮＣＯＮＶＥＣＴＩＶＥＣＬＯＵＤＳＭａｏＹｕｈｕａ（毛玉华）ａｎｄＨｕＺｈｉｊｉｎ（胡志晋）ＴＨＥ２－Ｄ...

NUMERICAL SIMULATION OF BENARD CONVECTION IN A CLOSED RECTANGLE (Ⅱ)——THREE-DIMENSIONAL CASE

In the paper, numerical simulation is performed for Benard convection in a closed three-dimensional rectangle with non-slippery bound. Numerical results show that when Rayleigh number Ra<3.6×104, Benard convection is steady, and when Ra≥3.6×104 it is unsteady and irregular. The cross sections and correlation coefficients of various fields are studied, and it is found that the external correlation scales of flow decrease as Ra increases when Ra≥ 7.5×104. Moreover, statistical analyses show that the Taylor inner scales (λv,λθv and so on) also decrease as Ra increases, and that the changing rates of λv and λθv with height are very different to each other in the vicinity of upper and lower bounds. Furthermore, statistical analyses show that the computed Nusselt number Nu is close to the lower limit of many experimental values, and in the transient region of flow pattern d1gNu/d1gRa is relatively greater than that in other region. In addition, other statistical quantities of the fields of temperature, velocity and vorticity are also computed and discussed.

NUMERICAL SIMULATION OF BENARD CONVECTION IN A CLOSED RECTANGLE (Ⅰ)——TWO-DIMENSIONAL CASE

In the paper, a finite differential numerical model is proposed for Benard convection ina non-slippery closed rectangle. By this model, we have discussed the bifurcation character-istics of two-dimensional Benard convection when Prandtl number is 1. The computed re-sults show that if the Rayleigh number Ra≥1.75×10~5, the Benard convection is unsteady andirregular, and that in the transient region of flow pattern, the changing rate of the Nusseltnumber Nu to Ra, dlgNu/dlgRa, is rather smaller than that in the non-transient region.Moreover, in the paper, we have analysed the relation between the shrinking rate of thephase flow and each term in the governing equations of Benard convection. And further,we have developed a new method to calculate the pressure gradient.

Absolute scaling law for temperature data in Rayleigh-Benard convection

In addition to the hierarchical-structure (H-S) model, this paper further explores the most intensive intermittent structure of Rayleigh-Bénard convection at the high Ra numbers proportional to temperature. With respect to the discovery and by means of the scale, both of Bolgiano, there are two regions of the structure holding the absolute scaling law given by Ching’s paper. Through theoretic analysis of data, this paper indicates that the regions act as two local intensive intermittent structures, by which the statistical absolute scaling performance of region is induced, rather than the statistical result of the entire time series in belief since 1941. In terms of statistical theory, the local structure in fluid, therefore, is the essence governing the absolute scaling performance of region, especially in high intensity.

Understanding the factors influencing cloud-core vertical accelerations during deep convection formation in the WRF model

本文将扰动气压利用一个线性诊断关系代替,重新推导了WRF模式框架地形追随坐标系下的垂直动量方程,建立了垂直加速与对流触发(DCI)影响因子(如温度,水汽等)的直接联系.研究发现,DCI过程与对流核垂直加速相关,三维副散,扰动位势在垂直方向的二阶非均匀性,扰动位温垂直梯度,比湿及其垂直梯度,水凝物拖曳,均是能够直接影响垂直加速和对流触发的物理因子,这些量与模式基本预报量相关,通过解析基本预报量对对流发展的直接影响,可能有助于理解模式对DCI过程预测失败的原因.

Rayleigh-Benard对流及其在工程中的应用

Rayleigh-Benard对流是日常生活中常见的一种热对流现象。本文在介绍Rayleigh-Benard对流的基础上讨论了工程中存在的一些Rayleigh-Benard对流以及Rayleigh-Benard对流原理在工程中的应用。

轴向通流旋转盘腔内类Rayleigh-Benard对流稳定性研究

利用数值模拟的方法对冷气轴向通流旋转盘腔的流动过程进行了研究。研究发现 ,对应一进口冷气的雷诺数 ,存在一临界瑞利数 ( Rac) ,高于该瑞利数 ( Ra) ,流动出现不稳定现象 ,且 Ra越大 ,不稳定行为越严重。对于特例 ,盘腔内的流动可以看成是由类 Rayleigh-Benard对流和强迫对流两个区域构成 ,两个区域通过能量和质量交换相互影响 ,流动随着 Ra的增加从稳态发展为非稳态 ;采用频谱图分析的方法对数值解的不稳定性进行定性分析 ,结果显示随着 Ra的增大 ,数值解经历了从稳定解到分贫的周期性不稳定和准周期不稳定的发展过程。离心浮升力引起的类 Rayleigh-Benard对流是造成流动从稳定到不稳定发展的重要原因 。

矩形腔体中Rayleigh-Benard对流结构的分析

通过对二维流体力学基本方程的数值摸拟,讨论了在二维矩形腔体中,不同条件与Rayleigh-Benard(RB)对流耦合作用的结构图案和特性。在分析了RB对流结构的基础上,分别对比分析了水平流及脉冲流与RB对流耦合作用的结构,并得出了其规律。RB对流系统为定常流动,对流轨道具有空间周期性。当RB对流与水平来流耦合作用时,系统为非定常流动,对流结构既表现空间周期性,同时也表现时间周期性。当外加来流的大小呈周期性变化时,此时系统流动的形式与外加来流的周期密切相关。

混合流体Rayleigh-Benard对流的多重稳定性现象

通过流体力学基本方程组的数值模拟,初步探讨了矩形腔体内具有Soret效应的混合流体Rayleigh-Benard对流系统中斑图(Pattern)选择的多重稳定性(Multistability)现象.包括有间歇性缺陷的行波和缺陷源水平运动的对传波(Counterpropagating wave)的多重稳定性现象,不同波数的摆动(Undulation)行波的多重稳定性现象,行波和摆动行波的多重稳定性现象等.对由沿着r增加或r减小方向计算引起的斑图转化过程的滞后(Hysteresis)现象也进行了分析.结果说明混合流体Rayleigh-Benard对流系统中的滞后现象和多重稳定性现象是存在的.

周期加热的Rayleigh-Benard对流时空结构

通过二维流体力学基本方程组的数值模拟,研究了普朗特数Pr=6.99时矩形渠槽周期加热对Rayleigh-Benard对流时空结构的影响.当水平流动强度Re=0时,发现稳定的由周期加热引起的局部定常对流.当Re比较小时,对流滚动抑制水平流动,获得了由周期加热引起的局部行波对流.当水平流动强度比较大时,由于周期加热与水平流动相互作用,水平流动抑制部分对流滚动,导致对流区域上游附近出现传导区域,对流区域减小,从而形成一种新的局部行波对流结构.并进一步讨论了Rayleigh-Benard对流时空结构的动力学特性.

二成分混合流体Rayleigh-Benard对流

Rayleigh-Benard(RB)对流是研究非平衡对流的稳定性、非线性动力学特性及湍流形成机理的典型模型之一。在介绍RB对流研究方法的基础上,论述了其最新研究进展:混合流体RB对流运动的稳定性及其非线性动力特性;RB对流与水平流动相耦合时的非线性动力特性。最后提出了有待进一步研究和探讨的问题。

水平流动作用下的纯流体Rayleigh-Benard对流时空结构

通过二维流体力学基本方程组的数值模拟,研究了普朗特数Pr=1.0时矩形渠槽中水平流动作用下的纯流体Rayleigh-Benard对流时空结构的影响,并与Pr=6.99时的结果进行了比较。结果表明:当水平流动雷诺数Re=0时,定常对流的波数随着瑞利数的增加而变大;对于相对瑞利数r=3.0的情况,当Re<40时,获得了行波对流结构,当40≤Re≤75时,出现了局部行波对流结构;在局部行波对流存在的范围内,随着雷诺数的增加或瑞利数的减小,局部行波对流的存在宽度减小;当Pr从6.99减小到1.0时,局部行波对流的Re依赖范围将由9≤Re≤18变成40≤Re≤75。

双流体Rayleigh-Benard对流中的局部行波

Rayleigh-Benard对流是研究非平衡对流的斑图(Pattern)及非线性动力学特性的典型模型之一。据此,通过流体力学基本方程组的数值模拟,探讨了分离比ψ=-0.4时双流体局部行波的形成过程;讨论了双流体局部行波流速场、温度场、浓度场、平均浓度流的结构和特性,分析了局部行波被局部化的原因。研究结果表明:局部行波始终在背离端壁方向传播并被限定在此端,它存在于腔体左端还是右端取决于经过过渡后对传波中最终控制腔体的一支行波的传播方向;在局部行波的存在范围内(1.519≤r≤1.604),随相对瑞利数增加,衡量对流振幅的最大垂直流速、特征通过流体层的垂直热流量的努塞尔数、局部行波宽度等都在增加,但反映浓度特性的混合参数减小。

具有不同来流形式的Rayleigh-Benard对流特性

主要研究了在二维矩形腔体中,不同条件对Rayleigh-Benard对流时空结构影响。首先分析了没有水平流速作用下,Rayleigh-Benard对流的对流特性;其次,分析了具有水平流速作用下的Rayleigh-Benard对流的特性;最后,分析了在变调流速作用下,Rayleigh-Benard对流的特性。总结得出对流结构的动力学特性和时空结构。