A laboratory analysis of free convection enhanced by a heat island in a calm and stratified environment

A free convection enhanced by a heating plate is studied in air-chambers under laminar conditions. Observations show the influence of the plate shape. Among the different convection patterns, a stationary cell is clearly identified. This bell-shaped convection typically represents the pollution domes observed over many cities. Convection begins immediately a horizontal temperature difference is created. From this point of view, a heat island situation appears quite different from a Rayleigh-Bénard one. Experiments reveal that the ambient stratification affects the Nusselt-Rayleigh relationship. The scale of the convection, the question of similarity and the limits of the experimental method are discussed. The results of experiments lead to the formulation of proposals concerning physical mechanisms which occur in the real atmosphere.     

Stability of Rayleigh-Benard convection rolls and bimodal flow at moderate Prandtl number

Experimental observations of cellular convection between two rigid, horizontal, conducting boundaries are reported for two different cases. First, the stability of two-dimensional roll convection of various wavenumbers and Rayleigh numbers is investigated in fluids of Prandtl numbers 16 and 2.7. The results qualitatively agree with earlier observations by Busse and Whitehead of fluid with Prandtl number 126 but they differ somewhat quantitatively. Second, the stability of the bimodal flow, consisting of two rolls of differing and perpendicular wavenumber, is observed to be stable for given bandwidths and ranges of Rayleigh numbers when the configuration of the bimodal flow, consisting of two sets of rolls at right angles, is flawless — without any disruptions in the periodic matrix. The stability range differs from earlier experiments and from our own experiments in which the bimodal planform is uncontrolled.     

A Case Study of Rayleigh-Bénard Convection with Clouds

A turbulence data set collected by the research aircraft Hercules and Falcon in the planetary boundary layer (PBL) over the North Sea during Rayleigh-Bénard convection (RBC) is analysed. Altogether nearly three hundred cell passages at different levels and in two different flight directions were sampled.The convective boundary-layer height (H) was about 1 km, and the RBC cells had a diameter D of roughly 2–3 km, resulting in an aspect ratio A = D/H 2–3. This value is also found in the case of RBC in laboratory-scale flows, whereas most of the recent PBL experimental work reports convection PBL rolls with A 3 and mesoscale cellular convection (MCC) with A 10–40 over the oceans.The large number of RBC cell passages made it possible to composite their average structure. Due to the more complex three-dimensional structure and the importance of thermals to the RBC dynamics, spectral, temporal and spatial decompositions and model calculations were necessary to illuminate structure, dynamics, energetics and organisation. The final impression is that the structure of RBC in the PBL is given by a honeycomb-like arrangement of short-lived mixed-layer thermals with more passive downward motions in between. The regularity of the Cu-cloud cover results partly from the more stationary flow in the cloud-free cell centres. On the other hand it is shown that active as well as inactive clouds contribute to the cloud cover. Thus, the PBL flow and the cloud cover are decoupled, at least temporarily and locally.Due to sparse observational and measured information about RBC occurrence and structure in the PBL, additional material was gathered, resulting in the impression that RBC is one additional realised mode of organised convection in the PBL, as has already been clarified for PBL rolls and MCC by recent investigations.     

A note on the multi-α solutions of the upper bounding problem for thermal convection

The transition to “multi-α” solutions of the upper bounding problem for thermal convection is discussed. For convection in a fluid contained between parallel stress-free perfectly conducting boundaries, the “single-α” solutions of Straus (1973) are used to determine the Rayleigh number R at which the first transition occurs. Two upper bounding problems are treated: one valid for all values of the Prandtl number and one valid only for large Prandtl numbers. A significant difference between the two problems is noted. The former has a transition at R ～ 28200; the latter has no transition within the range of Rayleigh numbers treated here: R ? 2.3 · 10⁵.     

Global stability for convection induced by absorption of radiation

We study the linear instability and nonlinear stability of a model, for convection induced by selective absorption of radiation, due to Krishnamurti. The nonlinear analysis yields critical Rayleigh numbers very close to the critical ones of linear instability theory and this demonstrates that linear theory effectively captures the physics of the onset of convection. Realistic boundary conditions appropriate to fixed surfaces are analysed and these reflect the experiments performed by Krishnamurti. The results obtained here lend much credence to use of the model of Krishnamurti for convection in a fluid layer stably stratified when the heat source depends on the concentration of the stratifying agent.     

Power laws of high Rayleigh number convection

Previous theoretical and observational investigations have shown that vertical plumes are formed in the high Rayleigh number convection field over heated horizontal surfaces and that these plumes become unsteady and turbulent when the Rayleigh number is higher than about 20 times its critical value R _c. Based on these results, we conclude that the dissipation of kinetic energy takes place mainly in the surface boundary layer in high Rayleigh number laminar convection and mainly in the vertical plumes in turbulent convection, while the conversion of eddy potential energy into kinetic energy is accomplished mainly in the well-mixed main body of the fluid. On making use of these rather general conclusions concerning the kinetic energy generation and dissipation processes in the energy integrals, we are able to derive the well known 5/4 and 4/3 power laws of upward heat transfer by laminar and turbulent convections theoretically.     

Turbulent flow over a wavy boundary

The linearized, two-dimensional flow of an incompressible fully turbulent fluid over a sinusoidal boundary is solved using the method of matched asymptotic expansions in the limit of vanishing skin-friction.A phenomenological turbulence model due to Saffman (1970, 1974) is utilized to incorporate the effects of the wavy boundary on the turbulence structure.Arbitrary lowest-order wave speed is allowed in order to consider both the stationary wavy wall, and the water wave moving with arbitrary positive or negative velocity.Good agreement is found with measured tangential velocity profiles and surface normal stress coefficients. The phase shift of the surface normal stress exhibits correct qualitative behavior with both positive and negative wave speeds, although predicted values are low.     

分层气流条件下地形降水的二维理想数值试验

利用WRF v3.5中尺度数值模式,在条件不稳定层结下,针对分层气流(基本气流风速和大气湿浮力频率呈二层均匀分布)过山时,地形对降水的影响进行了多组二维理想数值试验,以研究不同高度、尺度山脉和不同方向基本气流对降水形态和分布的影响。模拟结果表明,地形重力波触发对流是地形降水的主要机制之一,地形波的特征(波长、振幅)和传播均受到地形和基本气流的影响,其中,强基本气流流经高而陡峭的山脉时,更容易在其背风坡捕捉到重力波,地形降水呈现多种模态,反之亦然;当改变基本气流与山脉交角时,主要通过影响地形强迫抬升速度、基流对波动稳定性发展来进一步影响地形降水的强度和分布。     

The transition of a multi-dimensional lorenz system

A multi-dimensional Lorenz system, which includes thirty-three amplitude equations describing time evolu-tion of convection, is derived from two-dimensional Boussinesq equations by using the Galerkin method. Its transition is studied by numerical solution. It is found that, with Rayleigh number increasing from zero to one hundred, five different types of motion appear one after another as follows: stationary motion, periodic motion, quasiperiodic motion with two-fundamental frequencies, quasi-periodic motion with three fundamental frequencies, and chaotic motion. By comparing with the Lorenz model and Curry's fourteen-dimensional model, it is shown that as retained modes increase, the critical values of transition become larger and the types of bi-furcation change. The results of dynamic behavior happen to be in agreement with the IIIa route of the Gollub and Benson experiments.     

边界层对流对示踪物抬升和传输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"加密观测期间敦煌站的实测资料以及大涡模式, 通过一系列改变地表热通量和风切变的敏感性数值试验, 分析了地表热通量和风切变对边界层对流的强度、形式, 以及对对流边界层结构和发展的影响。模拟结果显示风切变一定, 增大地表热通量时, 由于近地层湍流运动增强, 向上输送的热量也较多, 使对流边界层变暖增厚, 而且边界层对流的强度明显增强, 对流泡发展的高度也较高。当地表热通量一定, 增大风切变时, 由于风切变使夹卷作用增强, 将逆温层中的暖空气向下卷入混合层中, 使对流边界层增暖增厚, 但是对流泡容易破碎, 对流的强度也较弱。另外通过在模式近地层释放绝对浓度为100的被动示踪物方法, 用最小二乘法定量地分析了地表热通量和风切变分别与示踪物抬升效率和传输高度的关系。分析结果表明, 风切变小于10.5×10-3 s-1时, 增大地表热通量加强了上层动量的下传, 使示踪物的抬升效率也线性增大;地表热通量小于462.5 W m-2时, 增大风切变减弱了边界层对流的强度, 从而使示踪物的抬升效率减弱。当风切变一定时, 示踪物的平均传输高度随地表热通量增加而增大, 而地表热通量一定, 只有风切变大于临界值时, 示踪物平均传输高度才随风切变的增加而增大, 而临界风速的大小由地表热通量决定。     

引入考虑凝结作用的连续性方程与积云对流参数化方案修正

文章研究了在热带海洋面上的水蒸发，发现水蒸发进入大气层将改变地面气压场，且蒸发潜热分为内潜热(水汽内能)和外潜热(水汽压力能)，蒸发内潜热立即成为大气热能的一部分，而蒸发外潜热直接对大气层作功，使得大气位能增加；研究了大气中的大尺度凝结降水和积云对流凝结降水对于环境气压场与位势高度场的直接影响。用郭晓岚积云对流参数化方案(已考虑凝结内潜热对大气的加热作用)，加入了考虑因大尺度凝结降水和积云对流参数化凝结降水造成地面气压场及高空位势高度场的变化，后者应是凝结外潜热过程作用的结果。在上述研究过程中，必须引入考虑凝结作用的连续性方程，且最终可以改变有积云对流凝结降水发生的数值预报模式动力框架。     

Local Log-Law-of-the-Wall in Neutrally-Stratified Boundary-Layer Flows

It is well known that in a neutrally-stratified turbulent flow in a deep constant-stress layer above a flat surface,the horizontal mean velocity varies logarithmically with height (the so-called `log-law-of-the-wall').More recently, the same logarithmic law has also been foundin the presence of non-flat surfaces, where it governs thedynamics of the areally-averagedvelocity and involves renormalized effective parameters.Here, we analyze wind profiles over two-dimensional sinusoidal hillsobtained both from numerical simulations performed with a primitiveequation model and from wind-tunnel measurements. We showthat also the local velocity profiles behave to a verygood approximation logarithmically, for a distance from the surface of the order of the maximum hill height almost to the top of the boundary layer. Such alocal log-law-of-the-wall involves effective parameters smoothly depending on theposition along the underlying topography.This dependence looks very similar to the topography itself.     

Development and structure of a maritime continent thunderstorm

Summary The evaluation of a maritime continent thunderstorm complex (Hector) occurring over Bathurst and Melville Islands north of Darwin, Australia (12° S, 131° E) is investigated primarily using Doppler radar data. Thunderstorm formation follows the development of sea breeze circulations and a period of shallow non-precipitating convection. Evidence exists for initiation of long-lived and organised convection on the sea breeze fronts, although short-lived, scattered convection is apparent earlier in the day. Merging of the convective systems is observed in regions of enhanced low-level convergence related to sea breeze circulations. The merged convective complex is initially aligned in an almost east-west direction consistent with the low-level forcing. The merged complex results in rapid vertical development with updraughts reaching 40 m s^– and echo tops reaching 20 km height. Maximum precipitation production occurs during this merger phase. On the perimeter of the merged convective complex, evidence exists for front-to-rear updraughts sloped over lower-level downdraughts with rear-to-front relative flow and forward propagating cold pools. The mature phase is dominated by this convection and the complex re-orientates in the prevailing easterly vertical shear to an approximate north-south direction, then moves westward off the islands with the classic multicellular squall-like structure.The one-dimensional cloud model of Ferrier and Houze (1989) used with a four class ice formulation reproduced the cloud top height, updraught structure and echo profile very well. To test the importance of ice physics upon thunderstorm development, several sensitivity tests were made removing the effects of the ice phase. All of these model clouds reached nearly 20 km, although simulations without the effects of ice had updraughts reduced from about 40 m s^–1 to 30 m s^–1. The simulated convection was more sensitive to changes in environmental conditions and parameterised cloud dynamics. The strong intensity of the convection was largely accounted for by increasing equivalent potential temperatures due to diurnal heating of the surface layer. The vertical velocity and radar structure of the island thunderstorm has more similarity with continental rather than oceanic convection. Maximum vertical velocities, in particular are almost an order of magnitude greater than typical of oceanic convection. With the intense updraughts, even in the low shear environment, there is evidence for mesoscale circulations within the convection.With 17 Figures     

Planetary boundary layer of equatorial waves and critical latitude

The boundary-layer solutions for oscillatory interior flow in a neutral fluid show that, away from the critical latitude, the planetary boundary-layer flow is composed of two vertically propagating waves; one is of shorter vertical wavelength and attenuates faster with height while the other is of longer wavelength and attenuates slowly with height. At the critical latitude, the longer wave is of the nature of an inertial oscillation and penetrates the entire depth of the fluid and gives rise to a rather stronger (but finite) vertical motion than in the surroundings at great height, but below 2 km this difference is not very great. In general, the vertical velocity of the boundary-layer flow depends on both the vorticity and the divergence of the interior flow, and the influence of the former is to intensify while that of the latter is to diminish the existing vertical motion. The influence of the stable stratification above a mixed, neutral surface layer on the boundary-layer flow of the equatorial waves is analyzed in detail. It is shown that the boundary-layer flow is greatly impeded by the stable layer and the horizontal velocities of the boundary-layer flows are made to change their directions in the upper part of the mixed layer and above, so that the vertical velocity is greatly reduced. The effect of the critical latitude is almost absent in the antisymmetric Rossby waves under stable stratification.     

On the Nature of the Transition Between Roll and Cellular Organization in the Convective Boundary Layer

Both observational and numerical studies of the convective boundary layer (CBL) have demonstrated that when surface heat fluxes are small and mean wind shear is strong, convective updrafts tend to organize into horizontal rolls aligned within 10–20\(^\circ \) of the geostrophic wind direction. However, under large surface heat fluxes and weak to negligible shear, convection tends to organize into open cells, similar to turbulent Rayleigh-Bénard convection. Using a suite of 14 large-eddy simulations (LES) spanning a range of \(-z_i/L\) between zero (neutral) and 1041 (highly convective), where \(z_i\) is the CBL depth and L is the Obukhov length, the transition between roll- and cellular-type convection is investigated systematically for the first time using LES. Mean vertical profiles including velocity variances and turbulent transport efficiencies, as well the “roll factor,” which characterizes the rotational symmetry of the vertical velocity field, indicate the transition occurs gradually over a range of \(-z_i/L\); however, the most significant changes in vertical profiles and CBL organization occur from near-neutral conditions up to about \(-z_i/L \approx \) 15–20. Turbulent transport efficiencies and quadrant analysis are used to characterize the turbulent transport of momentum and heat with increasing \(-z_i/L\). It is found that turbulence transports heat efficiently from weakly to highly convective conditions; however, turbulent momentum transport becomes increasingly inefficient as \(-z_i/L\) increases.     

Nonlinear generation of harmonics through the interaction of an internal wave beam with a model oceanic pycnocline

The interaction of an internal wave beam (IWB) with an idealized oceanic pycnocline is examined using two-dimensional fully nonlinear direct numerical simulations based on a spectral multidomain penalty method in the vertical direction. The phenomenon of focus is the nonlinear generation of harmonics. A total of 24 simulations have been performed, varying the normalized pycnocline thickness and the ratio of peak pycnocline Brunt-Väisälä frequency to that of the stratified lower layer. Harmonics at the point of IWB entry into the pycnocline increase in amplitude and number with a measure of the maximum gradient of the Brunt-Väisälä frequency, suggesting refraction as an important factor in harmonic generation. Among the simulations performed, two distinct limits of pycnocline thickness are identified. For thin pynoclines, whose thickness is 10% of the incident IWB's horizontal wavelength, harmonics trapped within the pycnocline have maximum amplitude when their frequency and wavenumber match those of the natural pycnocline interfacial wave mode. Results in this case are compared with weakly nonlinear theory for harmonic generation by plane wave refraction. For thicker pycnoclines, whose thickness is equal the incident IWB's horizontal wavelength, IWB refraction results in harmonic generation at multiple locations in addition to pycnocline entry, giving rise to complex flow structure inside the pycnocline.     

Numerical simulation of scattered light polarization in a developing convective cloud for millimeter wavelengths

The optical characteristics of scattered light polarization in a developing convective cloud for millimeter wavelengths are numerically studied using the convection jet model and Stokes parameters. The analysis revealed that the value of all polarization forms does not depend on the cloud droplet spectrum and wavelength in the lower layers of a convective cloud. As the cloud droplet size increases and the wavelength decreases, the polarizations of all forms vary greatly and may have several maxima. It is also demonstrated that the degree of partial polarization may make no sense in the Rayleigh region at the certain values of polarization parameters.     

大气凝结水汽汇、凝结潜热作用与积云对流参数化

从引入包含质量(水汽)源、汇的连续方程出发,重新推导出大尺度凝结降水和积云对流凝结降水之水汽汇起作用的热力学方程,从而重新给出气压、气温预报方程及地面气压与高空位势高度预报方程。发现,在此基础上,才能实现凝结3个作用:气块水汽质量流失与气压降低;气块虚温降低;加热气块;和通过大气运动方程,实现大气凝结潜热“热机”作功。这时,对于预报气压、气温场,积云对流参数化方案中的参数在凝结3个作用中保持一致。否则,通过积云对流参数化方案,虽可以近似实现对于预报气压和气温场的凝结3个作用,但不可能调好参数的降水物理特性及其时空分布特征。且对于静力模式预报地面气压和高空位势高度场,不可能实现上述的第一凝结作用。最后表明,当模式分辨率提高到只用降水显式方案、不再用积云对流参数化方案后,则必须引入包含水汽源、汇的连续方程。因在热带海洋面上的水蒸发过程,水汽进入大气将改变地面气压场,且蒸发潜热可分为内潜热(水汽内能)和外潜热(水汽压力能),内潜热立即成为大气热能的一部分,而外潜热直接对大气层作功,使得大气位能增加。文中研究了大气中的大尺度凝结降水和积云对流凝结降水对气压场与位势高度场的影响。一般积云对流参数化方案都已考虑内潜热对大气的加热作用,但还须考虑因凝结与降水造成地面气压场及高空位势高度场的变化,后者应是外潜热作用的结果。在上述研究过程中,必须引入考虑凝结作用的连续方程,且最终可以改变有降水(包括大尺度凝结降水和积云对流凝结降水)发生时的数值预报模式动力框架。     

Temporal Oscillations in the Convective Boundary Layer Forced by Mesoscale Surface Heat-Flux Variations

A theoretical approach suggests that the surface heterogeneity on a scale of tens of kilometres can generate mesoscale motions that are not in a quasi-stationary state. The starting point of the theoretical approach is the equations of horizontal velocity and potential temperature that are low-pass filtered with a mesoscale cut-off wavelength. The transition of the generated mesoscale motions from a quasi-stationary state to a non-stationary state occurs when horizontal advection is strong enough to level out the potential temperature gradient on the surface heterogeneity scale. Large-eddy simulations (LES) suggest that the convective boundary layer (CBL) changes to a non-stationary state when forced by a surface heat-flux variation of amplitude of 100W m⁻² or higher and a wavelength of the order of 10 km. Spectral analysis of the LES reveals that when the mesoscale motions are in a quasi-stationary state, the energy provided by the surface heat-flux variation remains in organized mesoscale motions on the scale of the surface variation itself. However, in a non-stationary state, the energy cascades to smaller scales, with the cascade extending down into the turbulence scale when the wavelength of the surface heat-flux variation is on a scale smaller than 100 times the CBL height. The energy transfer from the generated mesoscale motions to the CBL turbulence results in the absence of a spectral gap between the two scales. The absence of an obvious spectral gap between the generated mesoscale motions and the turbulence raises questions about the applicability of mesoscale models for studies on the effect of high-amplitude surface heterogeneity on a scale of tens of kilometres. The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Simulating the diurnal cycle of rainfall in global climate models: resolution versus parameterization

The effects of horizontal resolution and the treatment of convection on simulation of the diurnal cycle of precipitation during boreal summer are analyzed in several innovative weather and climate model integrations. The simulations include: season-long integrations of the Non-hydrostatic Icosahedral Atmospheric Model (NICAM) with explicit clouds and convection; year-long integrations of the operational Integrated Forecast System (IFS) from the European Centre for Medium-range Weather Forecasts at three resolutions (125, 39 and 16 km); seasonal simulations of the same model at 10 km resolution; and seasonal simulations of the National Center for Atmospheric Research (NCAR) low-resolution climate model with and without an embedded two-dimensional cloud-resolving model in each grid box. NICAM with explicit convection simulates best the phase of the diurnal cycle, as well as many regional features such as rainfall triggered by advancing sea breezes or high topography. However, NICAM greatly overestimates mean rainfall and the magnitude of the diurnal cycle. Introduction of an embedded cloud model within the NCAR model significantly improves global statistics of the seasonal mean and diurnal cycle of rainfall, as well as many regional features. However, errors often remain larger than for the other higher-resolution models. Increasing resolution alone has little impact on the timing of daily rainfall in IFS with parameterized convection, yet the amplitude of the diurnal cycle does improve along with the representation of mean rainfall. Variations during the day in atmospheric prognostic fields appear quite similar among models, suggesting that the distinctive treatments of model physics account for the differences in representing the diurnal cycle of precipitation.