The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameteri...The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.展开更多
Cloud microphysical properties are significantly affected by entrainment and mixing processes.However,it is unclear how the entrainment rate affects the relative dispersion of cloud droplet size distribution.Previousl...Cloud microphysical properties are significantly affected by entrainment and mixing processes.However,it is unclear how the entrainment rate affects the relative dispersion of cloud droplet size distribution.Previously,the relationship between relative dispersion and entrainment rate was found to be positive or negative.To reconcile the contrasting relationships,the Explicit Mixing Parcel Model is used to determine the underlying mechanisms.When evaporation is dominated by small droplets,and the entrained environmental air is further saturated during mixing,the relationship is negative.However,when the evaporation of big droplets is dominant,the relationship is positive.Whether or not the cloud condensation nuclei are considered in the entrained environmental air is a key factor as condensation on the entrained condensation nuclei is the main source of small droplets.However,if cloud condensation nuclei are not entrained,the relationship is positive.If cloud condensation nuclei are entrained,the relationship is dependent on many other factors.High values of vertical velocity,relative humidity of environmental air,and liquid water content,and low values of droplet number concentration,are more likely to cause the negative relationship since new saturation is easier to achieve by evaporation of small droplets.Further,the signs of the relationship are not strongly affected by the turbulence dissipation rate,but the higher dissipation rate causes the positive relationship to be more significant for a larger entrainment rate.A conceptual model is proposed to reconcile the contrasting relationships.This work enhances the understanding of relative dispersion and lays a foundation for the quantification of entrainment-mixing mechanisms.展开更多
Following the parameterization of sheared entrainment obtained in the companion paper, Liu et al. (2016), the present study aims to further investigate the characteristics of entrainment, and develop a simple model ...Following the parameterization of sheared entrainment obtained in the companion paper, Liu et al. (2016), the present study aims to further investigate the characteristics of entrainment, and develop a simple model for predicting the growth rate of a well-developed and sheared CBL. The relative stratification, defined as the ratio of the stratification in the free atmosphere to that in the entrainment zone, is found to be a function of entrainment flux ratio (Ae). This leads to a simple expression of the entrainment rate, in which Ae needs to be parameterized. According to the results in Liu et al. (2016), Ae can be simply expressed as the ratio of the convective velocity scale in the sheared CBL to that in the shear-free CBL. The parameterization of the convective velocity scale in the sheared CBL is obtained by analytically solving the bulk model with several assumptions and approximations. Results indicate that the entrainment process is influenced by the dynamic effect, the interaction between mean shear and environmental stratification, and one other term that includes the Coriolis effect. These three parameterizations constitute a simple model for predicting the growth rate of a well-developed and sheared CBL. This model is validated by outputs of LESs, and the results show that it performs satisfactorily. Compared with bulk models, this model does not need to solve a set of equations for the CBL. It is more convenient to apply in numerical models.展开更多
The volume fraction of the solid and liquid phase of debris flows, which evolves simultaneously across terrains, largely determines the dynamic property of debris flows. The entrainment process significantly influence...The volume fraction of the solid and liquid phase of debris flows, which evolves simultaneously across terrains, largely determines the dynamic property of debris flows. The entrainment process significantly influences the amplitude of the volume fraction. In this paper, we present a depth-averaged two-phase debris-flow model describing the simultaneous evolution of the phase velocity and depth, the solid and fluid volume fractions and the bed morphological evolution. The model employs the Mohr–Coulomb plasticity for the solid stress, and the fluid stress is modeled as a Newtonian viscous stress. The interfacial momentum transfer includes viscous drag and buoyancy. A new extended entrainment rate formula that satisfies the boundary momentum jump condition (Iverson and Ouyang, 2015) is presented. In this formula, the basal traction stress is a function of the solid volume fraction and can take advantage of both the Coulomb and velocity-dependent friction models. A finite volume method using Roe’s Riemann approximation is suggested to solve the equations. Three computational cases are conducted and compared with experiments or previous results. The results show that the current computational model and framework are robust and suitable for capturing the characteristics of debris flows.展开更多
In the present study the data of wind and temperature profiles and sensible heat flux observed in Beijing in July and December of 1986,together with the results of water tank experiments for comparison,are used to tes...In the present study the data of wind and temperature profiles and sensible heat flux observed in Beijing in July and December of 1986,together with the results of water tank experiments for comparison,are used to test the prediction models of the atmospheric mixed layer with zero order and first order assumption,respectively. The results show that the entrainment rates in summer and winter used in the zero order model are 0.15 and 0.10,respectively,while its value in the first order model ranges between 0.15 and 0.19 with a lower rate at the initial stage of mixed layer development. Emphasis in the study is also placed on the relationship between the entrainmert rate and the development of the mixed layer.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.42175099,42027804,42075073)the Innovative Project of Postgraduates in Jiangsu Province in 2023(Grant No.KYCX23_1319)+3 种基金supported by the National Natural Science Foundation of China(Grant No.42205080)the Natural Science Foundation of Sichuan(Grant No.2023YFS0442)the Research Fund of Civil Aviation Flight University of China(Grant No.J2022-037)supported by the National Key Scientific and Technological Infrastructure project“Earth System Science Numerical Simulator Facility”(Earth Lab)。
文摘The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41822504, 42175099, 42027804, 42075073 and 42075077)the National Center of Meteorology, Abu Dhabi, UAE under the UAE Research Program for Rain Enhancement Science+4 种基金LIU is supported by the U.S. Department of Energy Atmospheric System Research (ASR) Program (DE-SC00112704)Solar Energy Technologies Office (SETO) under Award 33504LUO is supported by Research Fund of Civil Aviation Flight University of China (J2022-037)LI is supported by Research Fund of Civil Aviation Flight University of China (09005001)WU is supported by Research on Key of Manmachine Ring in Plateau Flight (FZ2020ZZ03)
文摘Cloud microphysical properties are significantly affected by entrainment and mixing processes.However,it is unclear how the entrainment rate affects the relative dispersion of cloud droplet size distribution.Previously,the relationship between relative dispersion and entrainment rate was found to be positive or negative.To reconcile the contrasting relationships,the Explicit Mixing Parcel Model is used to determine the underlying mechanisms.When evaporation is dominated by small droplets,and the entrained environmental air is further saturated during mixing,the relationship is negative.However,when the evaporation of big droplets is dominant,the relationship is positive.Whether or not the cloud condensation nuclei are considered in the entrained environmental air is a key factor as condensation on the entrained condensation nuclei is the main source of small droplets.However,if cloud condensation nuclei are not entrained,the relationship is positive.If cloud condensation nuclei are entrained,the relationship is dependent on many other factors.High values of vertical velocity,relative humidity of environmental air,and liquid water content,and low values of droplet number concentration,are more likely to cause the negative relationship since new saturation is easier to achieve by evaporation of small droplets.Further,the signs of the relationship are not strongly affected by the turbulence dissipation rate,but the higher dissipation rate causes the positive relationship to be more significant for a larger entrainment rate.A conceptual model is proposed to reconcile the contrasting relationships.This work enhances the understanding of relative dispersion and lays a foundation for the quantification of entrainment-mixing mechanisms.
基金sponsored by the National Natural Science Foundation of China(Grant No.40975004)the State Key Basic Program(973)(Grant No.2013CB430100)
文摘Following the parameterization of sheared entrainment obtained in the companion paper, Liu et al. (2016), the present study aims to further investigate the characteristics of entrainment, and develop a simple model for predicting the growth rate of a well-developed and sheared CBL. The relative stratification, defined as the ratio of the stratification in the free atmosphere to that in the entrainment zone, is found to be a function of entrainment flux ratio (Ae). This leads to a simple expression of the entrainment rate, in which Ae needs to be parameterized. According to the results in Liu et al. (2016), Ae can be simply expressed as the ratio of the convective velocity scale in the sheared CBL to that in the shear-free CBL. The parameterization of the convective velocity scale in the sheared CBL is obtained by analytically solving the bulk model with several assumptions and approximations. Results indicate that the entrainment process is influenced by the dynamic effect, the interaction between mean shear and environmental stratification, and one other term that includes the Coriolis effect. These three parameterizations constitute a simple model for predicting the growth rate of a well-developed and sheared CBL. This model is validated by outputs of LESs, and the results show that it performs satisfactorily. Compared with bulk models, this model does not need to solve a set of equations for the CBL. It is more convenient to apply in numerical models.
基金Financial support from NSFC(Grant No.41572303,4151001059,41101008)Key Projects in the National Science & Technology Pillar Program(2014BAL05B01)CAS "Light of West China" Program
文摘The volume fraction of the solid and liquid phase of debris flows, which evolves simultaneously across terrains, largely determines the dynamic property of debris flows. The entrainment process significantly influences the amplitude of the volume fraction. In this paper, we present a depth-averaged two-phase debris-flow model describing the simultaneous evolution of the phase velocity and depth, the solid and fluid volume fractions and the bed morphological evolution. The model employs the Mohr–Coulomb plasticity for the solid stress, and the fluid stress is modeled as a Newtonian viscous stress. The interfacial momentum transfer includes viscous drag and buoyancy. A new extended entrainment rate formula that satisfies the boundary momentum jump condition (Iverson and Ouyang, 2015) is presented. In this formula, the basal traction stress is a function of the solid volume fraction and can take advantage of both the Coulomb and velocity-dependent friction models. A finite volume method using Roe’s Riemann approximation is suggested to solve the equations. Three computational cases are conducted and compared with experiments or previous results. The results show that the current computational model and framework are robust and suitable for capturing the characteristics of debris flows.
文摘In the present study the data of wind and temperature profiles and sensible heat flux observed in Beijing in July and December of 1986,together with the results of water tank experiments for comparison,are used to test the prediction models of the atmospheric mixed layer with zero order and first order assumption,respectively. The results show that the entrainment rates in summer and winter used in the zero order model are 0.15 and 0.10,respectively,while its value in the first order model ranges between 0.15 and 0.19 with a lower rate at the initial stage of mixed layer development. Emphasis in the study is also placed on the relationship between the entrainmert rate and the development of the mixed layer.