Due to the long-term plate tectonic movements in southwestern China,the in-situ stress field in deep formations is complex.When passing through deep soft-rock mass under non-hydrostatic high in-situ stress field,tunne...Due to the long-term plate tectonic movements in southwestern China,the in-situ stress field in deep formations is complex.When passing through deep soft-rock mass under non-hydrostatic high in-situ stress field,tunnels will suffer serious asymmetric deformation.There is no available support design method for tunnels under such a situation in existing studies to clarify the support time and support stiffness.This study first analyzed the mechanical behavior of tunnels in non-hydrostatic in-situ stress field and derived the theoretical equations of the ground squeezing curve(GSC)and ground loosening curve(GLC).Then,based on the convergence confinement theory,the support design method of deep soft-rock tunnels under non-hydrostatic high in-situ stress field was established considering both squeezing and loosening pressures.In addition,this method can provide the clear support time and support stiffness of the second layer of initial support.The proposed design method was applied to the Wanhe tunnel of the China-Laos railway in China.Monitoring data indicated that the optimal support scheme had a good effect on controlling the tunnel deformation in non-hydrostatic high in-situ stress field.Field applications showed that the secondary lining could be constructed properly.展开更多
In relatively coarse-resolution atmospheric models,cumulus parameterization helps account for the effect of subgridscale convection,which produces supplemental rainfall to the grid-scale precipitation and impacts the ...In relatively coarse-resolution atmospheric models,cumulus parameterization helps account for the effect of subgridscale convection,which produces supplemental rainfall to the grid-scale precipitation and impacts the diurnal cycle of precipitation.In this study,the diurnal cycle of precipitation was studied using the new simplified Arakawa-Schubert scheme in a global non-hydrostatic atmospheric model,i.e.,the Yin-Yang-grid Unified Model for the Atmosphere.Two new diagnostic closures and a convective trigger function were suggested to emphasize the job of the cloud work function corresponding to the free tropospheric large-scale forcing.Numerical results of the 0.25-degree model in 3-month batched real-case simulations revealed an improvement in the diurnal precipitation variation by using a revised trigger function with an enhanced dynamical constraint on the convective initiation and a suitable threshold of the trigger.By reducing the occurrence of convection during peak solar radiation hours,the revised scheme was shown to be effective in delaying the appearance of early-afternoon rainfall peaks over most land areas and accentuating the nocturnal peaks that were wrongly concealed by the more substantial afternoon peak.In addition,the revised scheme enhanced the simulation capability of the precipitation probability density function,such as increasing the extremely low-and high-intensity precipitation events and decreasing small and moderate rainfall events,which contributed to the reduction of precipitation bias over mid-latitude and tropical land areas.展开更多
A numerical investigation on the effectiveness of the actuator disc method in producing the interactions of multiple tidal stream devices via the 3D-RANS finite element model Telemac3D is explored. The methodology for...A numerical investigation on the effectiveness of the actuator disc method in producing the interactions of multiple tidal stream devices via the 3D-RANS finite element model Telemac3D is explored. The methodology for the implementation of the source term to represent an array of 20 m rotor diameter turbines deployed in an idealized channel is reviewed and discussed in detail. Flow interactions between multiple turbines are investigated for a single row arrangement with only two turbines and a two row arrangement containing three turbines. The results demonstrate that the non-hydrostatic solver shows better agreement when validated against published experimental data. Notably,the mesh density at the device location can strongly influence the simulated thrust from the disc. Although the actuator disc model can generally replicate the wake interactions well, the results indicate that it cannot accurately characterize the flow for regions with high turbulences. While a model setup with the largest lateral spacing(1.5D) demonstrates excellent agreement with the experimental data, the 0.5D model(smallest gap) deviates by up to 25%. These findings demonstrate the effectiveness of the applied source term in reproducing the wake profile, which is comparable with the published data, and highlight the inherent nature of the RANS and actuator disc models.展开更多
Aerosol optical properties are simulated using the Spectral Radiation Transport Model I~）r Aerosol Species （SPRINTARS） coupled with the Non-hydrostatic ICosahedral Atmospheric Model （NICAM）. The 3-year global mea...Aerosol optical properties are simulated using the Spectral Radiation Transport Model I~）r Aerosol Species （SPRINTARS） coupled with the Non-hydrostatic ICosahedral Atmospheric Model （NICAM）. The 3-year global mean all-sky aerosol optical thickness （AOT） at 550 nm, theAngstr/Sm Exponent （AE） based on AOTs at 440 and 870 nm, and the single scattering albedo （SSA） at 550 nm are estimated at 0.123, 0.657 and 0.944, respectively. For each aerosol species, the mean AOT is within the range of the AeroCom models. Both the modeled all-sky and clear-sky results are compared with observations from the Moderate Resolution Imaging Spectroradiometer （MODIS） and the Aerosol Robotic Network （AERONET）. The simulated spatiotemporal distributions of all-sky AOTs can generally reproduce the MODIS retrievals, and the correlation and model skill can be slightly improved using the clear-sky results over most land regions. The differences between clear-sky and all-sky AOTs are larger over polluted regions. Compared with observations from AERONET, the modeled and observed all-sky AOTs and AEs are generally in reasonable agreement, whereas the SSA variation is not well captured. Although the spatiotemporal distributions of all-sky and clear-sky results are similar, the clear-sky results are generally better correlated with the observations. The clear-sky AOT and SSA are generally lower than the all-sky results, especially in those regions where the aerosol chemical composition is contributed to mostly by sulfate aerosol. The modeled clear-sky AE is larger than the all-sky AE over those regions dominated by hydrophilic aerosol, while the＇opposite is found over regions dominated by hydrophobic aerosol.展开更多
The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries...The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. Calculation shows the INHB equations are invariant under some Galilean transformations, scaling transformations, and space-time translations. The symmetry reduction equations and similar solutions of the INHB equations are proposed.展开更多
This paper discusses the calculation of plastic zone properties around circular tunnels to rock-masses that satisfy the Hoek–Brown failure criterion in non-hydrostatic condition,and reviews the calculation of plastic...This paper discusses the calculation of plastic zone properties around circular tunnels to rock-masses that satisfy the Hoek–Brown failure criterion in non-hydrostatic condition,and reviews the calculation of plastic zone and displacement,and the basis of the convergence–confinement method in hydrostatic condition.A two-dimensional numerical simulation model was developed to gain understanding of the plastic zone shape.Plastic zone radius in any angles around the tunnel is analyzed and measured,using different values of overburden(four states)and stress ratio(nine states).Plastic zone radius equations were obtained from fitting curve to data which are dependent on the values of stress ratio,angle and plastic zone radius in hydrostatic condition.Finally validation of this equation indicate that results predict the real plastic zone radius appropriately.展开更多
A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into...A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.展开更多
The wave-induced setup and circulation in a two dimensional horizontal(2DH)reef-lagoon-channel system is investigated by a non-hydrostatic model.The simulated results agree well with observations from the laboratory e...The wave-induced setup and circulation in a two dimensional horizontal(2DH)reef-lagoon-channel system is investigated by a non-hydrostatic model.The simulated results agree well with observations from the laboratory experiments,revealing that the model is valid in simulating wave transformation and currents over reefs.The effects of incident wave height,period,and reef flat water depth on the mean sea level and wave-driven currents are examined.Results show that the distributions of mean sea level and current velocities on the reef flat adjacent to the channel vary significantly from those in the area close to the side walls.From the wave averaged current field,an obvious alongshore flux flowing from the reef flat to the channel is captured.The flux from the reef flat composes the second source of the offshore rip current,while the first source is from the lagoon.A detailed momentum balance analysis shows that the alongshore current is mainly induced by the pressure gradient between the reef flat and the channel.In the lagoon,the momentum balances are between the pressure and radiation stress gradient,which drives flow towards the channel.Along the channel,the offshore current is mainly driven by the pressure gradient.展开更多
In order to accurately simulate strong three-dimensional （3-D） free surface flows and sediment transport, the fully 3- D non-hydrostatic pressure models are developed based on the incompressible Navier-Stokes equati...In order to accurately simulate strong three-dimensional （3-D） free surface flows and sediment transport, the fully 3- D non-hydrostatic pressure models are developed based on the incompressible Navier-Stokes equations and convection-diffusion equation of sediment concentration with the mixing triangle and quadrilateral grids. The governing equations are discretized with the unstructured finite volume method in order to provide conservation properties of mass and momentum, and flexibility with practical application. It is shown that it is first-order accurate on nonuniform plane two-dimensional （2-D） grids and second-order accurate on uniform plane grids. A third-order approximation of the vertical velocity at the top-layer is applied. In such a way, free surface zero stress boundary condition is satisfied maturely, and very few vertical layers are needed to give an accurate solution even for complex discontinuous flow and short wave simulation. The model is applied to four examples to simulate strong 3-D free surface flows and sediment transport where non-hydrostatic pressures have a considerable effect on the velocity field. The newly developed model is verified against analytical solutions with an excellent agreement.展开更多
How to properly consider the impacts of non-hydrostatic perturbations is one of the challenging issues in developing non-hydrostatic dynamics solvers（NHDSs） for high-resolution atmospheric models. To overcome the dr...How to properly consider the impacts of non-hydrostatic perturbations is one of the challenging issues in developing non-hydrostatic dynamics solvers（NHDSs） for high-resolution atmospheric models. To overcome the drawbacks of current approaches to tackling this issue, this study analyzed the differences between hydrostatic dynamics solvers（HDSs） and their non-hydrostatic counterparts.The analysis then motivated a flexible approach to adjusting existing hydrostatic atmospheric models,especially those adopted in climate simulations for the impacts of non-hydrostatic perturbations.In this approach, the impacts of non-hydrostatic perturbations, reflecting the differences between HDSs and NHDSs, were encapsulated into a single term in the vertical momentum equation for the atmosphere. At each time step, this term was estimated by a separate sub-model, and then it was used to adjust the dynamics of the atmosphere. The adjustment was optional, and could be turned on and off flexibly by utilizing different initial conditions. The approach was illustrated using the Weather Research and Forecasting（WRF） model as an example, and was preliminarily validated by running the 3D baroclinic-wave test case in the model. Results showed that the modified dynamics solver produced simulation results that were very close to those given by the standard NHDS in the WRF model, implying that the approach was basically effective in capturing the non-hydrostatic features of the atmosphere.展开更多
When pycnocline thickness of ocean density is relatively small, density stratification can be well represented as a two-layer system. In this article, a depth integrated model of the two-layer fluid with constant dens...When pycnocline thickness of ocean density is relatively small, density stratification can be well represented as a two-layer system. In this article, a depth integrated model of the two-layer fluid with constant density is considered,and a variant of the edge-based non-hydrostatic numerical scheme is formulated. The resulting scheme is very efficient since it resolves the vertical fluid depth only in two layers. Despite using just two layers, the numerical dispersion is shown to agree with the analytical dispersion curves over a wide range of kd, where k is the wave number and d the water depth. The scheme was tested by simulating an interfacial solitary wave propagating over a flat bottom, as well as over a bottom step. On a laboratory scale, the formation of an interfacial wave is simulated,which also shows the interaction of wave with a triangular bathymetry. Then, a case study using the Lombok Strait topography is discussed, and the results show the development of an interfacial wave due to a strong current passing through a sill.展开更多
An investigation of the effects of a uniform current strength direction(following or opposing wave propagation) on the nonlinear transformation of irregular waves over a submerged trapezoidal sill is carried out using...An investigation of the effects of a uniform current strength direction(following or opposing wave propagation) on the nonlinear transformation of irregular waves over a submerged trapezoidal sill is carried out using SWASH,a non-hydrostatic numerical wave model.The nonlinear parameters(i.e.,asymmetry,skewness,and kurtosis) are calculated,and the empirical formulas for these parameters are presented as a function of the local Ursell number based on the present numerical data measured.In the shoaling area of the submerged sill,the nonlinear characteristics of waves are more obvious when waves propagate in the same direction as the currents than when waves propagate in the opposite direction.Whereas nonlinear parameters grow with the strengthening of the following currents over the crest,they tend to decrease as the adverse current velocity increases over the crest area of the submerged sill.展开更多
The vertical two-dimensional non-hydrostatic pressure models with multiple layers can make prediction more accurate than those obtained by the hydrostatic pres- sure assumption. However, they are time-consuming and un...The vertical two-dimensional non-hydrostatic pressure models with multiple layers can make prediction more accurate than those obtained by the hydrostatic pres- sure assumption. However, they are time-consuming and unstable, which makes them unsuitable for wider application. In this study, an efficient model with a single layer is developed. Decomposing the pressure into the hydrostatic and dynamic components and integrating the x-momentum equation from the bottom to the free surface can yield a horizontal momentum equation, in which the terms relevant to the dynamic pressure are discretized semi-implicitly. The convective terms in the vertical momentum equation are ignored, and the rest of the equation is approximated with the Keller-box scheme. The velocities expressed as the unknown dynamic pressure are substituted into the continuity equation, resulting in a tri-diagonal linear system solved by the Thomas algorithm. The validation of solitary and sinusoidal waves indicates that the present model can provide comparable results to the models with multiple layers but at much lower computation cost.展开更多
The symmetries and the exact solutions of the （3＋l）-dimensional nonlinear incompressible non-hydrostatic Boussi- nesq （INHB） equations, which describe atmospheric gravity waves, are studied in this paper. The cal...The symmetries and the exact solutions of the （3＋l）-dimensional nonlinear incompressible non-hydrostatic Boussi- nesq （INHB） equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the （3＋ 1）-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the （3＋1）-dimensional INHB system.展开更多
Exact solutions of the atmospheric(2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq(INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, severa...Exact solutions of the atmospheric(2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq(INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space.展开更多
A numerical study of linear wave scattering over a floating platform has been simulated by an efficient numericalmodel in this letter.The non-hydrostatic model is used to simulate the free surface and the uneven botto...A numerical study of linear wave scattering over a floating platform has been simulated by an efficient numericalmodel in this letter.The non-hydrostatic model is used to simulate the free surface and the uneven bottom.For thesolid body modelling,the immersed boundary method(IBM)is implemented by introducing a virtual boundaryforce into the momentum equations to emulate the boundary conditions.This implementation enhances theability of the model to simulate interactions between waves and floating structures.A numerical case involvingwave interactions with a floating platform is studied to validate the numerical model.By simulating the wavepropagation,the numerical model captures the variation of the wave scattering very well,which verifies theperformance of the numerical model and the robust strategy of the IBM.展开更多
Shallow moment models are extensions of the hyperbolic shallow water equations.They admit variations in the vertical profile of the horizontal velocity.This paper introduces a non-hydrostatic pressure to this framewor...Shallow moment models are extensions of the hyperbolic shallow water equations.They admit variations in the vertical profile of the horizontal velocity.This paper introduces a non-hydrostatic pressure to this framework and shows the systematic derivation of dimensionally reduced dispersive equation systems which still hold information on the vertical profiles of the flow variables.The derivation from a set of balance laws is based on a splitting of the pressure followed by a same-degree polynomial expansion of the velocity and pressure fields in a vertical direction.Dimensional reduction is done via Galerkin projections with weak enforcement of the boundary conditions at the bottom and at the free surface.The resulting equation systems of order zero and one are presented in linear and nonlinear forms for Legendre basis functions and an analysis of dispersive properties is given.A numerical experiment shows convergence towards the resolved reference model in the linear stationary case and demonstrates the reconstruction of vertical profiles.展开更多
This paper presents a mass and momentum conservative semi-implicit finite volume(FV)scheme for complex non-hydrostatic free surface flows,interacting with moving solid obstacles.A simplified incompressible Baer-Nunzia...This paper presents a mass and momentum conservative semi-implicit finite volume(FV)scheme for complex non-hydrostatic free surface flows,interacting with moving solid obstacles.A simplified incompressible Baer-Nunziato type model is considered for two-phase flows containing a liquid phase,a solid phase,and the surrounding void.According to the so-called diffuse interface approach,the different phases and consequently the void are described by means of a scalar volume fraction function for each phase.In our numerical scheme,the dynamics of the liquid phase and the motion of the solid are decoupled.The solid is assumed to be a moving rigid body,whose motion is prescribed.Only after the advection of the solid volume fraction,the dynamics of the liquid phase is considered.As usual in semi-implicit schemes,we employ staggered Cartesian control volumes and treat the nonlinear convective terms explicitly,while the pressure terms are treated implicitly.The non-conservative products arising in the transport equation for the solid volume fraction are treated by a path-conservative approach.The resulting semi-implicit FV discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure which can be efficiently solved with a nested Newton-type technique.The time step size is only limited by the velocities of the two phases contained in the domain,and not by the gravity wave speed nor by the stiff algebraic relaxation source term,which requires an implicit discretization.The resulting semi-implicit algorithm is first validated on a set of classical incompressible Navier-Stokes test problems and later also adds a fixed and moving solid phase.展开更多
A river plume dynamics analysis was made in Namtso Lake by using a sigma coordinate non-hydrostatic numerical ocean model, the Bergen Ocean Model. Simulations were carried out by hydrostatic and non-hydrostatic models...A river plume dynamics analysis was made in Namtso Lake by using a sigma coordinate non-hydrostatic numerical ocean model, the Bergen Ocean Model. Simulations were carried out by hydrostatic and non-hydrostatic models with horizontal resolution of 5.00 m, 2.50 m and 1, 25 m, respectively. The simulation results for the homogeneous lake are robust to the grid size, and the non-hydrostatic pressure effect is not important in this ease. For the stratified case, the results are sensitive to both the grid size and non-hydrostatic pressure corrections.展开更多
Using a double-parameter non-hydrostatic elastic three-dimensional model with detailed microphysical processes, the authors simulate the heavy rainfall event in South China which occurred on 9 June 1998 and lasted Tor...Using a double-parameter non-hydrostatic elastic three-dimensional model with detailed microphysical processes, the authors simulate the heavy rainfall event in South China which occurred on 9 June 1998 and lasted Tor more than 3 hours. This case is a supercell, and the upward and downward drafts interact with each other, which transfers rich water vapor at the converging position to upper levels, and the two drafts together maintain the convective course. The vertical heating profiles and contributions to water matter of five kinds of micro-phase processes are revealed quantitatively in the results. Condensation releases the most heat, which is more than that of the absorption by evaporation and melting. The rain particles first come from the autoconversion of cloud particles, the warm-rain process; later from the cold-rain process, the melting of grauple particles. The precipitation intensity reaches 75 mm h?1 while its efficiency remains high. The total amount of rain is 32 mm, a value close to the observations of nearby stations.展开更多
基金Project(52178402)supported by the National Natural Science Foundation of ChinaProject(2021-Key-09)supported by the Science and Technology Research and Development Program Project of China Railway Group LimitedProject(2021zzts0216)supported by the Innovation-Driven Project of Central South University,China。
文摘Due to the long-term plate tectonic movements in southwestern China,the in-situ stress field in deep formations is complex.When passing through deep soft-rock mass under non-hydrostatic high in-situ stress field,tunnels will suffer serious asymmetric deformation.There is no available support design method for tunnels under such a situation in existing studies to clarify the support time and support stiffness.This study first analyzed the mechanical behavior of tunnels in non-hydrostatic in-situ stress field and derived the theoretical equations of the ground squeezing curve(GSC)and ground loosening curve(GLC).Then,based on the convergence confinement theory,the support design method of deep soft-rock tunnels under non-hydrostatic high in-situ stress field was established considering both squeezing and loosening pressures.In addition,this method can provide the clear support time and support stiffness of the second layer of initial support.The proposed design method was applied to the Wanhe tunnel of the China-Laos railway in China.Monitoring data indicated that the optimal support scheme had a good effect on controlling the tunnel deformation in non-hydrostatic high in-situ stress field.Field applications showed that the secondary lining could be constructed properly.
基金supported by the National Natural Science Foundation of China(Grant Nos.42375153,42075151).
文摘In relatively coarse-resolution atmospheric models,cumulus parameterization helps account for the effect of subgridscale convection,which produces supplemental rainfall to the grid-scale precipitation and impacts the diurnal cycle of precipitation.In this study,the diurnal cycle of precipitation was studied using the new simplified Arakawa-Schubert scheme in a global non-hydrostatic atmospheric model,i.e.,the Yin-Yang-grid Unified Model for the Atmosphere.Two new diagnostic closures and a convective trigger function were suggested to emphasize the job of the cloud work function corresponding to the free tropospheric large-scale forcing.Numerical results of the 0.25-degree model in 3-month batched real-case simulations revealed an improvement in the diurnal precipitation variation by using a revised trigger function with an enhanced dynamical constraint on the convective initiation and a suitable threshold of the trigger.By reducing the occurrence of convection during peak solar radiation hours,the revised scheme was shown to be effective in delaying the appearance of early-afternoon rainfall peaks over most land areas and accentuating the nocturnal peaks that were wrongly concealed by the more substantial afternoon peak.In addition,the revised scheme enhanced the simulation capability of the precipitation probability density function,such as increasing the extremely low-and high-intensity precipitation events and decreasing small and moderate rainfall events,which contributed to the reduction of precipitation bias over mid-latitude and tropical land areas.
文摘A numerical investigation on the effectiveness of the actuator disc method in producing the interactions of multiple tidal stream devices via the 3D-RANS finite element model Telemac3D is explored. The methodology for the implementation of the source term to represent an array of 20 m rotor diameter turbines deployed in an idealized channel is reviewed and discussed in detail. Flow interactions between multiple turbines are investigated for a single row arrangement with only two turbines and a two row arrangement containing three turbines. The results demonstrate that the non-hydrostatic solver shows better agreement when validated against published experimental data. Notably,the mesh density at the device location can strongly influence the simulated thrust from the disc. Although the actuator disc model can generally replicate the wake interactions well, the results indicate that it cannot accurately characterize the flow for regions with high turbulences. While a model setup with the largest lateral spacing(1.5D) demonstrates excellent agreement with the experimental data, the 0.5D model(smallest gap) deviates by up to 25%. These findings demonstrate the effectiveness of the applied source term in reproducing the wake profile, which is comparable with the published data, and highlight the inherent nature of the RANS and actuator disc models.
基金National Natural Science Funds of China (Grant Nos. 41130104, and 41475031)Open Research Program of Key Laboratory for Aerosol-Cloud-Precipitation of China Meteorological Administration from Nanjing University of Information Science and Technology (Grant No. KDW1302)+4 种基金the Public Meteorology Special Foundation of MOST (Grant No. GYHY201406023)the National Key Basic Research and Development Program (973 Program, 2011CB403401)Teruyuki NAKAJIMA is supported by projects from JAXA/EarthC ARE, MEXT/VL for Climate System Diagnosticsthe MOE/Global Environment Research Fund A-1101, NIES/GOSAT, NIES/CGER, MEXT/RECCA/SALSAthe S-12 of the MOE
文摘Aerosol optical properties are simulated using the Spectral Radiation Transport Model I~）r Aerosol Species （SPRINTARS） coupled with the Non-hydrostatic ICosahedral Atmospheric Model （NICAM）. The 3-year global mean all-sky aerosol optical thickness （AOT） at 550 nm, theAngstr/Sm Exponent （AE） based on AOTs at 440 and 870 nm, and the single scattering albedo （SSA） at 550 nm are estimated at 0.123, 0.657 and 0.944, respectively. For each aerosol species, the mean AOT is within the range of the AeroCom models. Both the modeled all-sky and clear-sky results are compared with observations from the Moderate Resolution Imaging Spectroradiometer （MODIS） and the Aerosol Robotic Network （AERONET）. The simulated spatiotemporal distributions of all-sky AOTs can generally reproduce the MODIS retrievals, and the correlation and model skill can be slightly improved using the clear-sky results over most land regions. The differences between clear-sky and all-sky AOTs are larger over polluted regions. Compared with observations from AERONET, the modeled and observed all-sky AOTs and AEs are generally in reasonable agreement, whereas the SSA variation is not well captured. Although the spatiotemporal distributions of all-sky and clear-sky results are similar, the clear-sky results are generally better correlated with the observations. The clear-sky AOT and SSA are generally lower than the all-sky results, especially in those regions where the aerosol chemical composition is contributed to mostly by sulfate aerosol. The modeled clear-sky AE is larger than the all-sky AE over those regions dominated by hydrophilic aerosol, while the＇opposite is found over regions dominated by hydrophobic aerosol.
基金Supported by the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institute under Grant No. 408YKQ09the National Natural Science Foundation of China under Grant No. 10735030
文摘The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. Calculation shows the INHB equations are invariant under some Galilean transformations, scaling transformations, and space-time translations. The symmetry reduction equations and similar solutions of the INHB equations are proposed.
文摘This paper discusses the calculation of plastic zone properties around circular tunnels to rock-masses that satisfy the Hoek–Brown failure criterion in non-hydrostatic condition,and reviews the calculation of plastic zone and displacement,and the basis of the convergence–confinement method in hydrostatic condition.A two-dimensional numerical simulation model was developed to gain understanding of the plastic zone shape.Plastic zone radius in any angles around the tunnel is analyzed and measured,using different values of overburden(four states)and stress ratio(nine states).Plastic zone radius equations were obtained from fitting curve to data which are dependent on the values of stress ratio,angle and plastic zone radius in hydrostatic condition.Finally validation of this equation indicate that results predict the real plastic zone radius appropriately.
基金supported by the State Ocean Administration People’s Republic of China(Grant No.201405025)the Key Laboratory for Sea Area Management Technology(SOA)(Grant No.201603)
文摘A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.
基金The Key Project of NSFC-Shangdong Joint Research Funding under contract No.U1906230the Fundamental Research Funds for the Central Universities under contract No.B200202064+1 种基金the National Natural Science Foundation of China under contract Nos 41930538 and 51879096Marine Science and Technology Innovation Project of Jiangsu Province under contract No.HY2018-15。
文摘The wave-induced setup and circulation in a two dimensional horizontal(2DH)reef-lagoon-channel system is investigated by a non-hydrostatic model.The simulated results agree well with observations from the laboratory experiments,revealing that the model is valid in simulating wave transformation and currents over reefs.The effects of incident wave height,period,and reef flat water depth on the mean sea level and wave-driven currents are examined.Results show that the distributions of mean sea level and current velocities on the reef flat adjacent to the channel vary significantly from those in the area close to the side walls.From the wave averaged current field,an obvious alongshore flux flowing from the reef flat to the channel is captured.The flux from the reef flat composes the second source of the offshore rip current,while the first source is from the lagoon.A detailed momentum balance analysis shows that the alongshore current is mainly induced by the pressure gradient between the reef flat and the channel.In the lagoon,the momentum balances are between the pressure and radiation stress gradient,which drives flow towards the channel.Along the channel,the offshore current is mainly driven by the pressure gradient.
基金financially supported by the Science and Technology Project of the Ministry of Transport(Grant No.2013328352570)
文摘In order to accurately simulate strong three-dimensional （3-D） free surface flows and sediment transport, the fully 3- D non-hydrostatic pressure models are developed based on the incompressible Navier-Stokes equations and convection-diffusion equation of sediment concentration with the mixing triangle and quadrilateral grids. The governing equations are discretized with the unstructured finite volume method in order to provide conservation properties of mass and momentum, and flexibility with practical application. It is shown that it is first-order accurate on nonuniform plane two-dimensional （2-D） grids and second-order accurate on uniform plane grids. A third-order approximation of the vertical velocity at the top-layer is applied. In such a way, free surface zero stress boundary condition is satisfied maturely, and very few vertical layers are needed to give an accurate solution even for complex discontinuous flow and short wave simulation. The model is applied to four examples to simulate strong 3-D free surface flows and sediment transport where non-hydrostatic pressures have a considerable effect on the velocity field. The newly developed model is verified against analytical solutions with an excellent agreement.
基金supported by the National Key Research and Development Program[grant number 2016YFB0200805]the National Natural Science Foundation of China[grant number 41622503]
文摘How to properly consider the impacts of non-hydrostatic perturbations is one of the challenging issues in developing non-hydrostatic dynamics solvers（NHDSs） for high-resolution atmospheric models. To overcome the drawbacks of current approaches to tackling this issue, this study analyzed the differences between hydrostatic dynamics solvers（HDSs） and their non-hydrostatic counterparts.The analysis then motivated a flexible approach to adjusting existing hydrostatic atmospheric models,especially those adopted in climate simulations for the impacts of non-hydrostatic perturbations.In this approach, the impacts of non-hydrostatic perturbations, reflecting the differences between HDSs and NHDSs, were encapsulated into a single term in the vertical momentum equation for the atmosphere. At each time step, this term was estimated by a separate sub-model, and then it was used to adjust the dynamics of the atmosphere. The adjustment was optional, and could be turned on and off flexibly by utilizing different initial conditions. The approach was illustrated using the Weather Research and Forecasting（WRF） model as an example, and was preliminarily validated by running the 3D baroclinic-wave test case in the model. Results showed that the modified dynamics solver produced simulation results that were very close to those given by the standard NHDS in the WRF model, implying that the approach was basically effective in capturing the non-hydrostatic features of the atmosphere.
基金financially supported by the Institut Teknologi Bandung Research(Grant No.107a/I1.C01/PL/2017)
文摘When pycnocline thickness of ocean density is relatively small, density stratification can be well represented as a two-layer system. In this article, a depth integrated model of the two-layer fluid with constant density is considered,and a variant of the edge-based non-hydrostatic numerical scheme is formulated. The resulting scheme is very efficient since it resolves the vertical fluid depth only in two layers. Despite using just two layers, the numerical dispersion is shown to agree with the analytical dispersion curves over a wide range of kd, where k is the wave number and d the water depth. The scheme was tested by simulating an interfacial solitary wave propagating over a flat bottom, as well as over a bottom step. On a laboratory scale, the formation of an interfacial wave is simulated,which also shows the interaction of wave with a triangular bathymetry. Then, a case study using the Lombok Strait topography is discussed, and the results show the development of an interfacial wave due to a strong current passing through a sill.
基金supported financially by the National Nature Science Foundation(Nos.51422901,51679031)a Foundation for the Author of National Excellent Doctoral Dissertation of P.R.China(No.201347)+3 种基金National Key Research and Development Program(No.2017YFC 1404205)High-Tech Ship Research Projects Sponsored by the Ministry of Industry and Information Technology(MIIT) of Chinathe Fundamental Research Funds for the Central Universities(No.DUT16TD08)State Key Laboratory of Hydraulic Engineering Simulation and Safety,Tianjin University(HESS-1610)
文摘An investigation of the effects of a uniform current strength direction(following or opposing wave propagation) on the nonlinear transformation of irregular waves over a submerged trapezoidal sill is carried out using SWASH,a non-hydrostatic numerical wave model.The nonlinear parameters(i.e.,asymmetry,skewness,and kurtosis) are calculated,and the empirical formulas for these parameters are presented as a function of the local Ursell number based on the present numerical data measured.In the shoaling area of the submerged sill,the nonlinear characteristics of waves are more obvious when waves propagate in the same direction as the currents than when waves propagate in the opposite direction.Whereas nonlinear parameters grow with the strengthening of the following currents over the crest,they tend to decrease as the adverse current velocity increases over the crest area of the submerged sill.
基金Project supported by the Specialized Research Fund for the Doctoral Program of Higher Education(No. 20110142110064)the Ministry of Water Resources’ Science and Technology Promotion Plan Program (No. TG1316)
文摘The vertical two-dimensional non-hydrostatic pressure models with multiple layers can make prediction more accurate than those obtained by the hydrostatic pres- sure assumption. However, they are time-consuming and unstable, which makes them unsuitable for wider application. In this study, an efficient model with a single layer is developed. Decomposing the pressure into the hydrostatic and dynamic components and integrating the x-momentum equation from the bottom to the free surface can yield a horizontal momentum equation, in which the terms relevant to the dynamic pressure are discretized semi-implicitly. The convective terms in the vertical momentum equation are ignored, and the rest of the equation is approximated with the Keller-box scheme. The velocities expressed as the unknown dynamic pressure are substituted into the continuity equation, resulting in a tri-diagonal linear system solved by the Thomas algorithm. The validation of solitary and sinusoidal waves indicates that the present model can provide comparable results to the models with multiple layers but at much lower computation cost.
基金Project supported by the Natural Science Foundation of Guangdong Province, China (Grant Nos. 10452840301004616 and S2011040000403)the National Natural Science Foundation of China (Grant No. 41176005)the Science and Technology Project Foundation of Zhongshan, China (Grnat No. 20123A326)
文摘The symmetries and the exact solutions of the （3＋l）-dimensional nonlinear incompressible non-hydrostatic Boussi- nesq （INHB） equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the （3＋ 1）-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the （3＋1）-dimensional INHB system.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11305031 and 11305106Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No.Yq2013205
文摘Exact solutions of the atmospheric(2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq(INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space.
基金supported by Shanghai 2021“Science and Technology Innovation Action Plan”:Scientific and Technological Projects for Social Development(Grant No.21DZ1202701).
文摘A numerical study of linear wave scattering over a floating platform has been simulated by an efficient numericalmodel in this letter.The non-hydrostatic model is used to simulate the free surface and the uneven bottom.For thesolid body modelling,the immersed boundary method(IBM)is implemented by introducing a virtual boundaryforce into the momentum equations to emulate the boundary conditions.This implementation enhances theability of the model to simulate interactions between waves and floating structures.A numerical case involvingwave interactions with a floating platform is studied to validate the numerical model.By simulating the wavepropagation,the numerical model captures the variation of the wave scattering very well,which verifies theperformance of the numerical model and the robust strategy of the IBM.
基金supported by the Research Training Group Energy,Entropy,and Dissipative Dynamics(EDDy),Project No.320021702/RTG2326,of the German Research Foundation(DFG).
文摘Shallow moment models are extensions of the hyperbolic shallow water equations.They admit variations in the vertical profile of the horizontal velocity.This paper introduces a non-hydrostatic pressure to this framework and shows the systematic derivation of dimensionally reduced dispersive equation systems which still hold information on the vertical profiles of the flow variables.The derivation from a set of balance laws is based on a splitting of the pressure followed by a same-degree polynomial expansion of the velocity and pressure fields in a vertical direction.Dimensional reduction is done via Galerkin projections with weak enforcement of the boundary conditions at the bottom and at the free surface.The resulting equation systems of order zero and one are presented in linear and nonlinear forms for Legendre basis functions and an analysis of dispersive properties is given.A numerical experiment shows convergence towards the resolved reference model in the linear stationary case and demonstrates the reconstruction of vertical profiles.
基金funded by the Italian Ministry of Education,University and Research(MIUR)in the frame of the Departments of Excellence Initiative 2018-2027 attributed to DICAM of the University of Trento(grant L.232/2016)in the frame of the PRIN 2017 project Innovative numerical methods for evolutionary partial differential equations and applications,the PRIN 2022 project High order structure-preserving semi-implicit schemes for hyperbolic equations.D.is member of INdAM GNCS and was also co-funded by the European Union NextGenerationEU(PNRR,Spoke 7 CN HPC).Views and opinions expressed are however those of the author(s)only and do not necessarily reflect those of the European Union or the European Research Council.Neither the European Union nor the granting authority can be held responsible for them.
文摘This paper presents a mass and momentum conservative semi-implicit finite volume(FV)scheme for complex non-hydrostatic free surface flows,interacting with moving solid obstacles.A simplified incompressible Baer-Nunziato type model is considered for two-phase flows containing a liquid phase,a solid phase,and the surrounding void.According to the so-called diffuse interface approach,the different phases and consequently the void are described by means of a scalar volume fraction function for each phase.In our numerical scheme,the dynamics of the liquid phase and the motion of the solid are decoupled.The solid is assumed to be a moving rigid body,whose motion is prescribed.Only after the advection of the solid volume fraction,the dynamics of the liquid phase is considered.As usual in semi-implicit schemes,we employ staggered Cartesian control volumes and treat the nonlinear convective terms explicitly,while the pressure terms are treated implicitly.The non-conservative products arising in the transport equation for the solid volume fraction are treated by a path-conservative approach.The resulting semi-implicit FV discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure which can be efficiently solved with a nested Newton-type technique.The time step size is only limited by the velocities of the two phases contained in the domain,and not by the gravity wave speed nor by the stiff algebraic relaxation source term,which requires an implicit discretization.The resulting semi-implicit algorithm is first validated on a set of classical incompressible Navier-Stokes test problems and later also adds a fixed and moving solid phase.
文摘A river plume dynamics analysis was made in Namtso Lake by using a sigma coordinate non-hydrostatic numerical ocean model, the Bergen Ocean Model. Simulations were carried out by hydrostatic and non-hydrostatic models with horizontal resolution of 5.00 m, 2.50 m and 1, 25 m, respectively. The simulation results for the homogeneous lake are robust to the grid size, and the non-hydrostatic pressure effect is not important in this ease. For the stratified case, the results are sensitive to both the grid size and non-hydrostatic pressure corrections.
基金This work was supported jointly by National Key Basic Research Project G1998040912,95 Special Topic of Key National Project:"Torrential Rainfall Experiment over the Both Side of the Taiwan Strait and Adjacent Area"(95-special-03) and the National
文摘Using a double-parameter non-hydrostatic elastic three-dimensional model with detailed microphysical processes, the authors simulate the heavy rainfall event in South China which occurred on 9 June 1998 and lasted Tor more than 3 hours. This case is a supercell, and the upward and downward drafts interact with each other, which transfers rich water vapor at the converging position to upper levels, and the two drafts together maintain the convective course. The vertical heating profiles and contributions to water matter of five kinds of micro-phase processes are revealed quantitatively in the results. Condensation releases the most heat, which is more than that of the absorption by evaporation and melting. The rain particles first come from the autoconversion of cloud particles, the warm-rain process; later from the cold-rain process, the melting of grauple particles. The precipitation intensity reaches 75 mm h?1 while its efficiency remains high. The total amount of rain is 32 mm, a value close to the observations of nearby stations.
