The coalescence of water drops II. The coalescence problem and coalescence efficiency

By the use of the model of approaching drops (Arbel and Levin, 1977) the coalescence efficiencies of drops are computed. It is found that for interactions of drops at their terminal velocities the coalescence depends both on the size of the large drop and on the size ratio of the interacting drops in agreement with the experimental results of Whelpdale and List (1971) and Levin and Machnes (1977).The results were found to be sensitive to the assumption of the drops deformation and to the critical separation distance. This distance is defined as the distance at which the drops begin to merge. The variations of the coalescence efficiency with these parameters is discussed.Appendix: List of symbols D distance between the deformed surfaces of the drops - D _o initial value ofD - D _s stop distance, the distance at which the impact velocity vanishes - D _c critical coalescence distance - E collection efficiency - E ₁ collision efficiency - E ₂ coalescence efficiency - E _2R coalescence efficiency for collisions with stationary targets - F _c centrifugal force - p ratio of the radii of the interacting drops - r _o initial distance between drops' centers - R _L radius of larger drop - R _s radius of smaller drop - R _D radius of deformation - v approach velocity of two deformed surfaces - v _o initial value ofv - V _i impact velocity (given negative sign when drops approach each other) - V _c critical impact velocity - W _i velocity of the smaller drop at infinity for it to reachD _o with velocityv _o - x _i impact distance, the distance between the trajectories of the two drops - x _c critical impact distance for coalescence -  average critical impact distance for coalescence - X _c critical impact distance for collisions - coefficient of deformation given in equation 1 - _i impact angle defined byWhelpdale andList (1971) given also inArbel andLevin (1977) - coefficient of deformation given in equation 2 - viscosity of air - _i impact angle used inArbel andLevin (1977) and here - _c critical angle for coalescence - average critical angle for coalescence On sabbatical leave (1976–77) from the Department of Geophysics and Planetary Sciences, Tel Aviv University, Ramat Aviv, Israel.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The coalescence of water drops I. A theoretical model of approaching drops

The approach of two water drops in the absence of air flow around them is theoretically investigated. By assuming deformation criteria it is possible to solve the equation of motion of the drops under the influence of a variety of forces. These forces include the viscous force exerted by the air between the two deformed surfaces, the London-Van Der Waals forces and the force of gravity. It is found that the viscous forces dominate over the whole distance of the interaction. The equations have analytical solutions when a head-on approach is considered and when the deformation of the drops is assumed constant during the interaction. The equations were solved numerically for other deformation criteria and for non head-on approaches.The results of the present model are used in the following paper to compute the coalescence efficiencies of water drops. The model is primarily applicable to situations in which the large drop is stationary and the small one approaches it from below. However, it could also be used for interaction between freely falling drops as long as their relative velocities exceed about 13 cm/sec.Appendix: List of symbols C constant of the motion - D distance between the deformed surfaces of the drops - D _o initial value ofD - D _m the value at which the viscous force is maximum - D _N normalized distance - D _s the distance at which the velocity of approach vanishes - F _c centrifugal force - F _g force due to gravity - F _N normalized viscous force - F _LV force due to London-Van der Waals effect - F _R radial component of the force - F _V viscous force - F _t tangential component of the force - g acceleration due to gravity - M _L mass of large drop - m _s mass of small drop - p ratio of radii of interacting drops - R radius of an arbitrary drop - r distance between the centers of mass of the two drops - R _D radius of deformation - R _L radius of larger drop - R _s radius of smaller drop - t time - u defined in equation 20 — has the meaning of kinetic energy - v relative velocity of the deformed surfaces - v ₀ initial value ofv - V ₀ initial relative velocity of the centers of the drops - V _c critical impact velocity - V _i impact velocity - V _N ,v _n normalized velocity - V _t tangential component of the velocity - W _i velocity of the small drop at infinity for it to reach the pointD ₀ at velocityV ₀ - x instantaneous impact distance -  average critical impact distance for coalescence - x ₀ initial value of the impact distance - x _c critical impact distance for coalescence - coefficient of deformation - _i impact angle according toWhelpdale andList (1971) - coefficient of deformation - viscosity - surface tension - F _s sum of forces acting on the small drop - F _L sum of forces acting on the large drop - time constant - _R Rayleigh's oscillation period On sabbatical leave (1976–77) from the Department of Geophysics and Planetary Sciences, Tel Aviv University, Ramat Aviv, Israel.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On the hydrodynamic behavior of supercooled water drops interacting with columnar ice crystals

A numerical evaluation of the complete Navier-Stokes equations of motion for steady-state, incompressible flow past an infinite circular cylinder is given in terms of the stream function, vorticity, and pressure distribution past such bodies. A method is described which allows use of these flow characteristics: (1) to approximate the characteristics of air flow past hexagonal columnar ice crystals falling under gravity at terminal velocity in air, (2) to compute the trajectory of supercooled cloud drops relative to such ice crystals, and (3) to determine the efficiency with which short columnar ice crystals and needle shaped ice crystals collide with supercooled cloud drops. It is found that for all columnar type ice crystals riming is negligible if the cloud drop size is less than 5 m, and that for riming to commence short columnar crystals must have diameters larger than 50 m, while needle crystals must have diameters larger than 40 m. It is further shown that the collision efficiency cut-offs at the small drop radius and at the large drop radius end of the collision efficiency diagram can be explained on the basis of the cloud drop trajectories for these drop size ranges.     

磁岛合并研究

本文采用二维全粒子模拟来研究无碰撞等离子体中的磁岛合并过程.结果表明,磁岛合并分为两个阶段,在第一个阶段,两个磁岛因同向电流丝之间的吸引力而缓慢地相互靠近,在这个过程中,合并线附近的电子被面外电场加速,形成薄电流片,同时电流片两侧形成磁场堆积.第二个阶段为快速重联阶段,合并线附近的电磁场结构和以Harris电流片为初态的重联扩散区的电磁场结构很相似,其中最显著的特点为面外磁场的四极型结构.     

Oil slicks on water surface: Breakup,coalescence, and droplet formation under breaking waves

The ability to calculate the oil droplet size distribution (DSD) and its dynamic behavior in the water column is important in oil spill modeling. Breaking waves disperse oil from a surface slick into the water column as droplets of varying sizes. Oil droplets undergo further breakup and coalescence in the water column due to the turbulence. Available models simulate oil DSD based on empirical/equilibrium equations. However, the oil DSD evolution due to subsequent droplet breakup and coalescence in the water column can be best represented by a dynamic population model. This paper develops a phenomenological model to calculate the oil DSD in wave breaking conditions and ocean turbulence and is based on droplet breakup and coalescence. Its results are compared with data from laboratory experiments that include different oil types, different weathering times, and different breaking wave heights. The model comparisons showed a good agreement with experimental data.     

Study on determination of stress level by seismic stress drops and the stress axis deflections before and after large earthquakes

Introduction The study of tectonic stress field, a major branch of the Earth science, plays an important role in geodynamics. The world stress map plan started from 1980s and was leaded by Zoback. Lots of scientists from many countries participated this plan. The plan collected global tectonic stress measurements and research results and established global stress database. The world stress map was edited based on the global stress database. The world stress map reflected feature of global li…     

维西—乔后断裂带上连续地震的应力降和两种不同的孕震机制

2021年5月21日云南省维西—乔后断裂带上发生M_S6.4漾濞地震,造成了大量的人员伤亡和财产损失.该断裂带上还曾先后发生过2013年M_W5.3和2017年M_W4.91两次洱源地震.本文反演了维西—乔后断裂中南段2013年、2017年与2021年三次地震震群的震源机制解,使用谱比法计算了主震和较大的前震、余震共17个事件的拐角频率与应力降.结果表明：2013年M_W5.3主震与M_W4.96余震均为正断层事件,随后的地震序列皆为右旋走滑事件,2017年M_W4.91主震与M_W4.89前震均为右旋走滑事件.发生在东南侧15 km左右的2021年漾濞M_W6.2主震也为右旋走滑事件,但前震和余震震群中包括约70%的走滑事件和30%的正断层事件,推测发震断层为维西—乔后断裂带的次级断裂;2013年M_W5.3主震的拐角频率为0.68±0.03 Hz,应力降为11.98-1.52/+1.66 MPa,2017年M_W4.91主震的拐角频率为1.59±0.05 Hz,应力降为39.84-3.64/+3.88 MPa,2021年M_W6.2主震的拐角频率为0.415±0.01 Hz,应力降为65.35-4.61/+4.84 MPa;17个地震应力降反映出走滑事件的自相似性,而正断层事件同震断层面上可能的流体扩散引起了自相似性破缺.两种地震事件在拐角频率与应力降方面存在明显差异,可能源于断层受构造形变、结构和岩性的差异的影响,在横向与纵向上的摩擦系数、破裂尺度、裂隙流体等特性存在较大差异,因而可能存在两种不同的孕震机制.从潜在的地震风险来说,走滑的孕震过程可能触发更大的破裂,具有更大的潜在破坏性.

     

The effect of a simple shear flow upon the coalescence rate of water droplets

There is some experimental evidence by Schotland (1957) and by Telford and Cottis (1964) that there is an interaction region associated with the wake of a small droplet such that other droplets inside this region eventually collide with that droplet. It is shown that the existence of such a region produces a significant collision rate between droplets of comparable size in a vertical shear flow. The general features of the collision process are in agreement with the experimental results of Jonas and Goldsmith (1972).     

The dynamical and liquid water structure of the small cumulus as determined from its environment

This paper examines the evidence for the model of a small cumulus cloud represented as a quasi static but turbulent entity, growing on the upshear side and decaying on the downshear side. While the air just outside the cloudy outline is, on average, stationary relative to the embedding airmass, there is a slight flow, upwards and forward as though the updraft has induced upward motion in the clear air outside the cloud, on the growing side. On the decaying side the motion is downwards and away from the cloud.This is a flow pattern which is not consistent with the air flowing around the cloud as it moves forward but it agrees well with the picture given. Decayed remnants of cloud are found throughout the air previously occupied by the cloud. The cloud outline moves through the embedding air at a velocity which is almost as large as the relative motion of the subcloud feeding airflow (which is almost free from internal wind shear in strong convection).The mixing of dry air from above the inversion yields the observed diluted liquid water content in small cumuli, if such mixing is allowed to proceed until the cloud density equals that of the surrounding air. Quantitative conditions relating the liquid water to inversion temperature and moisture changes, and to the stability of the environment are presented. The strong vertical mixing from the top of the cloud downwards is important to microphysical processes.     

Effects of organic aerosol constituents on extinction and absorption coefficients and liquid water contents of fogs and clouds

We have speculated on the influence of organic material on extinction and absorption coefficients and liquid water content of fogs and of clouds immediately after their condensational stage. It results therefore, that the reduction of the speed of growth from fog to cloud droplets due to the presence of organic films largely reduces the properties mentioned. Compared to that their increase coming from the surface tension reduction due to organic material being dissolved or building up films is expected to be less effective.     

On the quasi-steady approximation for evaporating and condensing water drops in air

Summary The quasi-steady approximation, commonly used to calculate the rate of evaporation or condensation of water drops, is shown formally to be valid provided that the vapour of the condensate is very dilute. A uniformly valid asymptotic expansion is found for the full set of equations under isothermal conditions. The leading terms of the expansion correspond to the quasi-steady approximation.     

On the growth of ice crystals in supercooled water and aqueous solution drops

Summary The results of a recent investigation on the free growth rate and the growth forms of ice in supercooled water and aqueous solutions are presented. The results are used to discuss the structure of frozen drops, the structure of hailstones, the mechanisms which are responsible for the glaciation of atmospheric clouds and the mechanisms which cause cloud electrification. It was found that the presence of dissolved salts and dust particles in cloud drops favor the formation of spongy and polycristalline ice, that it is unlikely for frozen cloud drops to develop into hexagonal shaped ice single-crystals, and that it is also unlikely that in atmospheric clouds freezing drops shatter and splinter. The latter result casts serious doubts on the splintering mechanism to contribute to thunderstorm electrification and to promote glaciation of clouds.This work was supported by the National Science Foundation under Grant No. GP 2922.     

Observations of condensation growth determined by entity type mixing

It has been speculated for many years that the development of the droplet spectra in cloud is probably influenced by mixing processes. Various theoretical attempts to broaden the droplet spectra by mixing parcels with different velocity histories has shown that that particular effect is small. Similarly, very simpleuniform entrainment procedures did not lead to cloud drop size spectra which were broad enough, although by producing cloud drop size distributions with a double mode these models did substantially improve the drop size spectra of earlier adiabatic models which only exhibited a single mode.Recently a model based on entraining entities representing moving parcels of cloud air within the cloud was detailed byTelford andChai (1980). This study showed that the mixing in of dry air at cumulus turrets could lead to vertical cycling of diluted parcels, and that this cycling, with continual entrainment across the parcel boundaries, will produce much larger drops, as well as smaller drops of all sizes, in the droplet spectra. The entity entrainment concept studied there appears to apply to the observations of stratus cloud discussed in this paper.This paper presents data taken in marine stratus off the California coast which give a particularly clear example of how such droplet spectra modification occurs in practice. Both large drops, and the spread of the spectra to smaller sizes, occur in relation to other variables in such a way as to be consistent with an entity entrainment explanation, with no other obvious possibility.In a marine stratus cloud just over 200 m thick and many tens of miles in extent we find clear evidence that dry air is mixing in at cloud tops. Strong vertical motion is to be found in the cloud, large sized drops are found in cloud parcels where the mixing gives lower droplet concentrations, and there is evidence that newly formed cloud parcels are warmer and contain many more smaller droplets.The observations show that immediately following entrainment of dry air drop diameters are not reduced appreciably, but, in the same parcels, drop concentrations have been reduced by a factor of ten or more. Further down in the cloud big drops, able to start growth by coalescence, are found associated with low total droplet concentrations.Overall, it seems likely from the consideration of these observations that the formation of the large drops which lead to precipitation processes in clouds depends critically on the mixing in of dry air at cloud tops, and very little on the size of the small drops resulting from the condensation nucleus counts. As a conclusion it appears reasonable to state that if entrainment occurs at cloud tops, then big drops will be formed!     

2021年5月21日青海玛多MW7.4地震及余震序列应力降时空分布与孕震环境

2021年5月21日发生在青藏高原巴颜喀拉块体内部的玛多M_W7.4地震是继2008年M_W7.9汶川地震之后在中国陆区发生的最大地震.由于玛多地震发生在板块内部滑移速率较缓慢的次级断裂上,该地震成为研究巴颜喀拉块体内部地震危险性的典型震例.通过计算2021年玛多地震序列中震级大于2.5的地震应力降,我们调查了该地震序列应力释放的时空演化规律.首先,利用已有的青藏高原及其周边地区宽频带Lg波衰减模型,对玛多地震序列产生的地震Lg波观测数据进行了传播路径衰减校正,获得119个地震事件的Lg波震源谱;然后,通过将理论震源函数与观测数据拟合,获得对Lg波标量地震矩、拐角频率和高频下降率的估计;最后,根据标量地震矩和拐角频率计算了2021年玛多地震序列的应力降.结果表明,2021年5月21日玛多地震主震应力降为22 MPa,余震序列的应力降分布范围为0.08~7.5 MPa、中位数为0.39 MPa,平均值为0.88 MPa.应力降与震级具有较强的正相关关系,说明该地区的地震活动可能并不遵从地震自相似理论.换言之,大小地震具有不同的破裂动力学性质.玛多地震序列应力降变化反映了断层面上的应力释放过程具有强烈的非均质性.主震发生之后余震应力降显著降低,但其间仍夹杂着少数具有较高应力降的事件.这些高应力降事件所在区域与主震后破裂面上的闭锁和应力集中区域相对应.

     

Remotely sensed estimation of water discharge into the rapidly dwindling Dead Sea

Abstract

The Dead Sea is shrinking as its water level drops at the alarming rate of about 1 m year^-1. The Dead Sea is important to the economies of Israel and Jordan due to the extracted minerals (primarily potassium, also magnesium and bromide). It is also central to regional tourism. It is the lowest place on Earth and its endorheic, saline basin attracts international research in various disciplines. Additional to the Lower Jordan River, the discharge of which has been decreased to a small fraction of its original value, fresh to brackish springs are the main source of water to the rapidly dwindling Dead Sea. Although the existence of these springs has been known for decades, until recently estimates of spring water discharge into the Dead Sea were scarce. In this study, we developed a methodology of water discharge estimation for channels incising into a lacustrine bed using remotely sensed data and a single hydraulic geometry variable, water-surface width. Based on calibration of over 400 in situ measurements and simultaneous hydrometric data from aerial images, width–discharge rating curves were established, tested, and found suitable (r² = 0.92, p = 0.001) for the estimation of water discharge, with ±5% uncertainty. Furthermore, we used these relationships to estimate retrospectively the temporal changes in water discharge of seven main channels traceable in historical aerial images. The reconstructed trend reveals a major (63%) reduction in average freshwater inflow between 1990 and 2006. Our results maximize the use of water-surface width information from aerial imagery, and suggest applicability to areas experiencing rapid exposure of sea/lake bed and consequent access difficulties in in situ discharge monitoring.

Editor Z.W. Kundzewicz     

On the coalescence of twisted flux tubes

Abstract

We study the problem of the coalescence of twisted flux tubes by assuming that the azimuthal field lines reconnect at a current sheet during the coalescence process and everywhere else the magnetic field is frozen in the fluid. We derive relations connecting the topology of the coalesced flux tube with the topologies of the initial flux tubes, and then obtain a structure equation for calculating the field configuration of the coalesced flux tube from the given topology. Some solutions for the two extreme cases of low-β plasma and high-β plasma are discussed. The coalesced flux tube has less twist than the initial flux tube. Magnetic helicity is found to be exactly conserved during the coalescence, but the assumptions in the model put a constraint on the energy dissipation so that we do not get a relaxation to the minimum-energy Taylor state in the low-β case. It is pointed out that the structure equation connecting the topology and the equilibrium configuration is quite general and can be of use in many two-dimensional flux tube problems.     

Characteristics of cloud drop spectra in tropical warm clouds

Characteristics of cloud drop spectra were studied using 400 samples obtained from 120 warm cumulus clouds formed during the summer monsoon season.The total concentration of cloud drops (N _T) varied from 384 to 884 cm^–3 and the maximum concentration was observed in the layer below the cloud-top. The width of the drop spectrum was broader in the cloud-base region and in the region below the cloud-top. The spectrum was multimodal at all levels except in the cloud-top region where it was unimodal. The concentration of drops with diameter greater than 50 m (N _L) varied from 0.0 to 0.674 cm^–3.N _L was larger in the cloud-base region.N _L decreased with height up to the middle level and thereafter showed an increase. In the cloud-top region no large drops were present. The computed values of the liquid water varied between 0.132 and 0.536 g m^–3 and the mean volume diameter (MVD) varied between 8.1 and 12.0 m. The LWC and MVD showed a decrease with height except in the middle region of the cloud where the values were higher than the adjacent levels. The dispersion of the cloud drops was lower (0.65) in the cloud-top region and higher (1.01) in the cloud-base region.The observed cloud microphysical characteristics were attributed to vertical mixing in clouds induced by the cloud-top gravity oscillations (buoyancy oscillations) generated by the intensification of turbulent eddies due to the buoyant production of energy by the microscale-fractional-condensation (MFC) in turbulent eddies.     

Some Thoughts on the Earthquake Science Experimental Site——The Underground Cloud Map

The Western Yunnan Earthquake Predication Test Site set up jointly by the China Earthquake Administration, the National Science Foundation Commission of America, and United States Geological Survey has played an important role in development of early earthquake research work in China. Due to various objective reasons, most of the predicted targets in the earthquake prediction test site have not been achieved, and the development has been hindered. In recent years, the experiment site has been reconsidered, and renamed the “Earthquake Science Experimental Site”. Combined with the current development of seismology and the practical needs of disaster prevention and mitigation, we propose adding the “Underground Cloud Map” as the new direction of the experimental site. Using highly repeatable, environmentally friendly and safe airgun sources, we could send constant seismic signals, which realizes continuous monitoring of subsurface velocity changes. Utilizing the high-resolution 3-D crustal structure from ambient noise tomography, we could obtain 4-D (3-D space + 1-D time) images of subsurface structures, which we termed the “Underground Cloud Map”. The “Underground Cloud Map” can reflect underground velocity and stress changes, providing new means for the earthquake monitoring forecast nationwide, which promotes the conversion of experience-based earthquake prediction to physics-based prediction.     

DEVEX-disdrometer evaluation experiment: Basic results and implications for hydrologic studies

Increasing our understanding of the small scale variability of drop size distributions (DSD), and therefore of several bulk characteristics of rainfall processes, has major implications for our interpretation of the remote sensing based estimates of precipitation and its uncertainty. During the spring and summer of 2002 the authors conducted the DEVEX experiment (disdrometer evaluation experiment) to compare measurements of natural rain made with three different types of disdrometers collocated at the Iowa City Municipal Airport in Iowa City, Iowa in the Midwestern United States. This paper focuses on the evaluation of the instruments rather than analysis of the hydrometeorological aspects of the observed events. The comparison demonstrates discrepancies between instruments. The authors discuss the systematic and random effects in terms of rainfall quantities, drop size distribution properties, and the observed drop size vs. velocity relationships. Since the instruments were collocated, the effects of the natural variability of rain are reduced some with time integration, isolating the instrumental differences. The authors discuss the status of DSD measurement technologies and the implications for a range of hydrologic applications from remote sensing of rainfall to atmospheric deposition to soil erosion and sediment transport in the environment. The data set collected during the DEVEX experiment is made available to the research community.