Turbulent mixing in a rotating,stratified fluid

Abstract

An experimental study was carried out to investigate the effect of rotation on turbulent mixing in a stratified fluid when the turbulence in the mixed layer is generated by an oscillating grid. Two types of experiments were carried out: one of them is concerned with the deepening of the upper mixed layer in a stable, two-fluid system, and the other deals with the interaction between a stabilizing buoyancy flux and turbulence.

In the first type of experiments, it was found that rotation suppresses entrainment at larger Rossby numbers. As the Rossby number becomes smaller (Ro 0.1), the entrainment rate increases with rotation—the onset of this phenomenon, however, was found to coincide with the appearance of coherent vortices within the mixed layer. The radiation of energy from the mixed layer to the lower non-turbulent layer was found to occur and the magnitude of the energy flux was found to be increased with the rotational frequency. It was also observed that vortices are generated, rather abruptly, in the lower layer as the mixed layer deepens.

In the second set of experiments a quasi-steady mixed layer was found to develop of which the thickness varies with rotation in a fashion that is consistent with the result of the first experiment. Also the rotation was found to delay the formation of a pycnocline.     

The structure of separated flow past a circular cylinder in a rotating frame

Abstract

This paper examines the detailed E ^1/4-layer structure of separated flow past a circular cylinder in a low-Rossby-number rotating fluid as the Ekman number E tends to zero. This structure is based on an initial proposal by Page (1987) but with some modifications in response to further evidence, outlined both in this paper and elsewhere, on the behaviour of E ^1/4-layer flows in this context. Numerical calculations for flow in an E ^1/4 shear layer along the separated free streamline are described and the mass flux from this layer is then used to calculate the higher-order flow within the separation bubble. The flow structure is found to have two forms, depending on the value of the O(1) parameter λ, and these are compared with results from published “Navier-Stokes” type calculations for the flow at small but finite values of E.     

Correlation between plate age and layer separation of double seismic zones

Global seismicity catalogs are sufficient for characterizing double seismic zones (DSZs) in subducting slab and facilitate to estimate layer separation without inconsistent uncertainties as local catalogs. Previous studies have shown the correlation between DSZs layer separation and plate age while correlation for those younger than ~60 Ma is suspicious. The lacking of DSZs with layer separation less than 10 km further makes it difficult to precisely estimate such correlation. Thus, we incorporate eight DSZs data determined through local seismicity into globally-determined dataset and reexamine such correlation. The best fitting results show that both a linear model and a square root of plate age can mathematically fit the layer separation well. However, it is difficult to distinguish these two models when plate age is greater than ~20 Ma since their difference is less than 2 km. However, if extrapolation is possible, both models should provide physical information that DSZs will not form if there is no subducting lithosphere. As a result, the DSZs cannot be produced until the oceanic lithospheric age becomes greater than 0.9 Ma in the square root model while the linear model gives a misleading result. As such the square root model demonstrates the relationship physically better than the linear one, it still needs further test in the future with more available data, nevertheless, our study might also provide evidence for the suggestion that the plate age is a primary control factor of the DSZs geometry as well as the subducting process which disregards any local tectonic stresses.     

大气边界层研究进展

大气边界层对云和对流的发展、演变有重要作用.本文回顾了在大气边界层高度计算方法,边界层的时空分布特征、结构和发展机理,以及边界层参数化方案等方面的主要研究进展.大气边界层高度计算方法主要分为基于大气廓线观测数据计算和基于模式参数化方案计算两大类;大气边界层高度频率分布形态具有明显的日变化特征,并且稳定、中性和对流边界层高度的频率分布呈现出不同的Gamma分布特征;地面湿度状况对边界层发展影响明显,对于不同的下垫面热力性质和地形状况,大气边界层高度呈现出明显的空间差异,青藏高原边界层高度明显高于一般平原地区;在强烈的地面加热驱动下,对流边界层与残余层通过正反馈机制循环增长可以形成4000 m以上的超高大气边界层;研制大气边界层、浅对流以及云物理方案的统一参数化框架是未来数值预报模式的发展趋势.

     

The Influence of a Homogeneous Magnetic Field on the Ekman and Stewartson Layers

This contribution is aimed at a comparison of two different methods of how to deal with the solid inner core in geodynamo models. The first method, based on a direct application of the non-slip boundary conditions, was frequently used in the past. The second one, developed by the authors of the present paper, is based on an advanced analytical solution within the boundary layers and consequent formulation of new boundary conditions on the flow in the volume of the outer core. As an example we have used the results obtained by Hollerbach (1997) in the study of the influence of an imposed axial magnetic field on the fluid flow in a differentially rotating spherical shell. In the case of a weak imposed magnetic field, our solutions are very similar to those of Hollerbach. This non-trivial correspondence confirms the correctness of both methods, which are different not only in the formulation of boundary conditions, but also in the numerical methods: whereas Hollerbach used spectral methods, our computer code is based on finite differences. The influence of the conductivity of the inner core on the fluid flow was also studied.     

The onset of magnetoconvection at large Prandtl number in a rotating layer II. Small magnetic diffusion

Abstract

This paper develops further a convection model that has been studied several times previously as a very crude idealization of planetary core dynamics. A plane layer of electrically-conducting fluid rotates about the vertical in the presence of a magnetic field. Such a field can be created spontaneously, as in the Childress-Soward dynamo, but here it is uniform, horizontal and externally-applied. The Prandtl number of the fluid is large, but the Ekman, Elsasser and Rayleigh numbers are of unit order. In Part I of this series, it was also supposed that the ratio thermal diffusivity diffusivity/magnetic diffusivity is O(1), but here we suppose that this ratio is large. The character of the solution is changed in this limit. In the case of main interest, when the layer is confined between electrically-insulating no-slip walls, the solution is significantly different from the solution when the mathematically simpler, illustrative boundary conditions also considered in Part I are employed. As in Part I, attention is focussed on the onset of convection as the temperature difference applied across the layer is increased, and on the preferred mode, i.e., the planform and time-dependence of small amplitude convection.     

The origin of the crustal conductive layer and the conductivity of supercritical brine (II)

This paper is the second one of a series of three papers on fluid evolution of the crust-upper mantle and the causes of earthquakes. Based on the first paper, two conductive mechanisms of the crustal conductive layer (CCL), graphite and supercritical saline aqueous fluids, are discussed. As there are difficulties for graphite model, the supercritical fluids are investigated in this paper concerning the phases, the electrically conductive behaviors, the evolution and the sealing mechanisms of the fluids. It is obvious that this model is reasonable to explain the geophysical and geochemical characteristics of the CCL presented in the first paper.     

The onset of magnetoconvection at large Prandtl number in a rotating layer I. Finite magnetic diffusion

Abstract

This paper develops further a convection model that has been studied several times previously as a very crude idealization of planetary core dynamics. A plane layer of electrically-conducting fluid rotates about the vertical in the presence of a magnetic field. Such a field can be created spontaneously, as in the Childress—Soward dynamo, but here it is uniform, horizontal and externally-applied. The Prandtl number of the fluid is large, but the Ekman, Elsasser and Rayleigh numbers are of order unity, as is the ratio of thermal to magnetic diffusivity. Attention is focused on the onset of convection as the temperature difference applied across the layer is increased, and on the preferred mode, i.e., the planform and time-dependence of small amplitude convection. The case of main interest is the layer confined between electrically-insulating no-slip walls, but the analysis is guided by a parallel study based on illustrative boundary conditions that are mathematically simpler.     

民航气象观测的中国中东部大气边界层廓线数据的评估与应用

本文从民航气象报告(AMDAR)数据库中提取了2008—2019年期间我国中东部18个机场飞机起飞和降落期间的大气边界层(ABL)廓线数据,并利用常规探空数据评估了不同季节和高度范围的AMDAR数据准确性及其随探空站与机场距离和飞行状态的变化.与常规探空数据相比,低层(P>850 hPa)的AMDAR温度和风分量的均方根误差(RMSE)均比较高层(850~500 hPa)小,且各高度层上的温度和风分量的RMSE都随间隔距离的增加而增大.相对而言,飞行状态对AMDAR数据准确性的影响很小.在间隔距离小于50 km且P>850 hPa高度层范围内,温度、纬向风和经向风的平均RMSE分别为0.68~0.83 K、1.48~1.62 m·s^-1和1.73~1.81 m·s^-1.相比于RMSE,对应的平均偏差都显著更小,且随间隔距离无明显变化.数据应用示例表明,AMDAR廓线数据由于其较高的时间分辨率,不仅可以反映ABL结构的日变化特征,还可用于研究ABL局地环流特征.基于18个机场AMDAR廓线数据分析发现,我国远内陆、干燥地区大气边界层高度(ABLH)具有较强的日变化,尤其是在春夏两季,而沿海和近内陆地区ABLH的日变化强度和季节差异都较小.

     

Wake effects on turbulent transport in the convective boundary layer

The effect of the downstream propagation of a wake on the transport of momentum, energy and scalars (such as humidity) in the convective boundary layer (CBL) is studied using a direct numerical simulation. The incompressible Navier–Stokes and energy equations are integrated under neutral and unstable thermal stratification conditions in a rotating coordinate frame with the Ekman layer approximation. Wake effects are introduced by modifying the mean velocity field as an initial condition on a converged turbulent Ekman layer flow. With this initial velocity distribution, the governing equations are integrated in time to determine how turbulent transport in the CBL is affected by the wake. Through the use of Taylor’s hypothesis, temporal evolution of the flow field in a doubly periodic computational domain is transformed into a spatial evolution. The results clearly indicate an increase in the scalar flux at the surface for the neutrally stratified case. An increase in wall scalar and heat flux is also noted for the CBL under unstable stratification, though the effects are diminished given the enhanced buoyant mixing associated with the hot wall.     

Linear theory of rotating fluids using spherical harmonics part I: Steady flows

Abstract

It is shown that a systematic development of physical quantities using spherical harmonics provides analytical solutions to a whole class of linear problems of rotating fluids.

These solutions are regular throughout the whole domain of the fluid and are not much affected by the equatorial singularity of steady boundary layers in spherical geometries.

A comparison between this method and the one based on boundary layer theory is carried out in the case of the steady spin-up of a fluid inside a sphere.     

Some effects of intra-red radiation on the dynamics of the atmospheric boundary layer

An approximate infra-red radiation scheme, employing essentially the cooling to space approximation, is included in a one-dimensional model of the atmospheric boundary layer. The approximate scheme is found not to produce significant errors in the behaviour of the dynamical model when integrated over a few hours. Radiative cooling is shown to be important in the development of a clear well-mixed layer which is capped by an essentially dry region; in particular, convetive instability is induced and this enhances the rate of entrainment of dry air. The development of fog is found to require sound models of both radiative transfer and turbulent diffusion.     

Hard state of the urban canopy layer turbulence and its self-similar multiplicative cascade models

It is found by experiment that under the thermal convection condition, the temperature fluctuation in the urban canopy layer turbulence has the hard state character, and the temperature difference between two points has the exponential probability density function distribution. At the same time, the turbulent energy dissipation rate fits the log-normal distribution, and is in accord with the hypothesis proposed by Kolmogorov in 1962 and lots of reported experimental results. In this paper, the scaling law of hard state temperature n order structure function is educed by the self-similar multiplicative cascade models. The theory formula is Sn = n/3μ{n(n+6)/72+[2lnn!-nln2]/2ln6}, and μ Is intermittent exponent. The formula can fit the experimental results up to order 8 exponents, is superior to the predictions by the Kolmogorov theory, the β And log-normal model.     

黏性声波方程数值正演中的匹配Z变换完全匹配层吸收边界

本文将非分裂场形式的匹配Z变换PML引入黏声波方程数值正演中,用时域有限差分模拟检验了其在黏声波方程模拟中的效果.数值正演结果表明,在大角度入射时匹配Z变换完全匹配层比传统PML表现更佳,消除了大角度入射产生的低频虚假反射.长时间能量衰减计算证明匹配Z变换完全匹配层在黏声波方程模拟中具有105时间步的稳定性.     

Vertical distribution of ozone in the planetary boundary layer at the Ming Tombs, Beijing

Surface ozone (O3) and vertical O3 distribution in the planetary boundary layer (PBL) at the Ming Tombs (40°17′15″N, 116°12′51″E), Beijing during September 7―12, 2001 were measured by ground based measurements and an in-situ tethersonde system. The results indicated that O3 concentration measured at surface level agreed well with that measured by tethersonde system in daytime when active thermal mixing was dominated. Ozone showed the lowest concentration before the sunrise and then gradually increased in the morning and reached the maximum in the afternoon 14:00―17:00 (lst). After sunset, O3 gradually decreased and resulted in low value below 200―300 m due to surface loss processes and chemical destruction in stable boundary layer characterized by temperature inversions. High O3 was observed whenever there was pollutants transport from the metropolitan areas of Beijing. Our analysis suggested the complex terrain of the Ming Tombs region caused pollutants transported from Beijing to accumulate in the PBL, and resulted in severe O3 pollution, with a maximum over 160×10-9, when the synoptic conditions was favorable for photochemical O3 production.     

Flow of a double-diffusive stratified fluid in a differentially-rotating cylinder

Abstract

A study has been made of a basic state of axisymmetric flow, at large rotational Reynolds numbers, in a double-diffusive stratified fluid contained in a vertically-mounted, differentially-rotating cylindrical cavity. The aim is to describe the qualitative characteristics of the flow of a fluid, the density of which is stratified by two diffusive effects, i.e., temperature and salinity gradients. Attention is confined to situations in which the temperature and salinity gradients make opposing contributions to the overall density profile, the undisturbed stratification being gravitationally stable. Finite difference numerical solutions of the governing Navier-Stokes equations have been obtained using the Boussinesq approximation. The results are presented in a way that illustrates the explicit effects of double-diffusivity when the cavity aspect ratio, height/radius, is O(1). The principal non-dimensional parameters characterizing the flow field are identified. In the interior core, the primary dynamic balance is between the horizontal density gradient and the vertical shear of the prevailing azimuthal velocity. The effective stratification is seen to decrease as the double-diffusivity increases, even if the overall stratification parameter, St, is held constant. The solute field contains a very thin boundary layer structure at large Lewis numbers. The effective stratification increases with the Prandtl number. Results have been derived for extreme values of the cavity aspect ratio. For small cavity aspect ratios, the dominant dynamic ingredients are viscous diffusion and rotation. For large aspect ratios, the bulk of the flow field is determined by the rotating sidewall. In this case, the direct influence of the double-diffusivity is minor.     

Long waves due to a symmetrical wind stress on the surface of a rotating ocean

Abstract

The problem of unsteady long waves generated by any horizontal and symmetrically distributed, time-periodic surface wind on a rotating ocean is analysed for large times and distances. Uniform asymptotic estimates of the surface displacement in the unsteady state are obtained. The steady-state wave and velocity fields at any distance are also determined. Some characteristics of the unsteady and steady motions are described. Also noted are the features that distinguish the motion from its one-dimensional analogue for which a non-uniform analysis in the unsteady state along with a large-distance form of the surface elevation are already known.     

Gradient-based similarity in the atmospheric boundary layer

The “flux-based” and “gradient-based” similarity in the stable boundary layer and also in the interfacial part of the convective boundary layer is discussed. The stable case is examined on the basis of data collected during the CASES-99 experiment. Its interfacial counterpart is considered in both the quasi-steady (mid-day) and non-steady states, utilizing the results of large-eddy simulations. In the stable regime, the “gradient-based” approach is not unique and can be based on various master length scales. Three local master length scales are considered: the local Monin-Obukhov scale, the buoyancy scale, and the Ellison scale. In the convective “quasi-steady” (mid-day) case, the “mixed layer” scaling is shown to be valid in the mixed layer and invalid in the interfacial layer. The temperature variance profile in non-steady conditions can be expressed in terms of the convective temperature scale in the mixed layer. The analogous prediction for velocity variances is not valid under non-steady conditions.