Advection Terms Research Articles

Prospective Evolution of Meteorological Drought in the Haihe River Basin and Its Connection With Large‐Scale Atmospheric Circulations Using CMIP6 Multimodel Ensemble

AbstractClimate change modifies monsoon rainfall patterns, leading to significant impacts on future meteorological droughts. This study investigated the spatiotemporal pattern of future precipitation, drought features, and the dynamic mechanisms governing their evolution induced by teleconnected atmospheric circulation in the Haihe River Basin, situated in the north China monsoon region. The investigation was conducted under SSP1‐2.6, SSP2‐4.5, and SSP5‐8.5 scenarios of CMIP6, utilizing the Standardized Precipitation Index and an improved run theory at seasonal and annual scales. The findings revealed that high‐emission scenarios cause a wetter climate trend, particularly in autumn and winter, related to the attenuation of the East Asian Trough from climate warming. The uneven intra‐annual precipitation patterns within the basin, induced by the Asian monsoon climate, are expected to improve in the far future, particularly under the SSP2‐4.5 scenarios. The drought frequency, intensity, and duration of future meteorological drought are expected to improve compared to historical conditions under all three scenarios. SSP2‐4.5 shows the shortest duration and lightest intensity of annual droughts. Extreme droughts are primarily driven by strong subsidence with low‐level moisture divergence. However, in the far future, the eastward shift of the western Pacific subtropical high results in reducing moisture transport from the western Pacific, leading to increasing contribution of advection term to atmospheric drying, particularly under the SSP1‐2.6. In winter, the increase in radiative forcing leads to enhanced evapotranspiration from the Eurasian continent, providing additional moisture and alleviating drought, especially in the far future under the SSP1‐2.6 and SSP2‐4.5 scenarios.

Dynamics of the Agulhas Current Influenced by the North–South Shift of Subtropical Front

Abstract The influence of meridional shift of the oceanic subtropical front (STF) on the Agulhas Current (AC) regime shifts is studied using satellite altimeter data and a 1.5-layer ocean model. The satellite observations suggest the northward shift of the STF leads to the AC leaping across the gap with little Agulhas leakage, and the southward shift of the STF mainly results in the AC intruding into the Atlantic Ocean in the forms of a loop current and an eddy-shedding path, while there are three flow patterns of AC for moderate latitude of the STF. The ocean model results suggest no hysteresis (associated with multiple equilibrium states) exists in the AC system. The model reproduces similar AC regimes depending on different gap widths as in the observations, and model results can be used to explain the observed Agulhas leakage well. We also present the parameter space of the critical AC strength that results in different AC flow patterns as a function of the gap width. The vorticity dynamics of the AC regime shift suggests that the β term is mainly balanced by the viscosity term for the AC in the leaping and loop current paths, while the β and instantaneous vorticity terms are mainly balanced by the advection and viscosity terms for the AC in the eddy-shedding path. These findings help explain the dynamics of the AC flowing across the gateway beyond the tip of Africa affected by the north–south shift of the STF in the leaping regime or penetrating regime.

Different Propagation Mechanisms of Deep and Shallow Wintertime Extratropical Cyclones over the North Pacific

Abstract Extratropical cyclones (ETCs) are three-dimensional synoptic systems in the middle and high latitudes. Previous studies on ETC propagation have typically focused on cyclones identified at a single level. However, more recent studies have found that ETCs have diverse vertical structures and cyclones with different vertical extents always exhibit distinct characteristics and surface impacts. In this work, we study the movement of wintertime (December–February) extratropical cyclones by classifying North Pacific ETCs into deep cyclones, shallow low-level cyclones, and shallow upper-level cyclones, based on reanalysis data from 1979 to 2019. Applying a Lagrangian perspective, we track the cyclones at different vertical levels to investigate the different characteristics and mechanisms for the propagation of deep and shallow ETCs. A potential vorticity (PV) tendency analysis of cyclone-tracking composites reveals that, for deep cyclones, the diabatic heating at 850 hPa and the horizontal advection by the stationary flow at 500 hPa are the main contributors to the poleward movement. For shallow cyclones, the nonlinear advection terms play a dominant role in their meridional motion, advecting shallow low-level cyclones poleward but shallow upper-level cyclones equatorward. A piecewise PV inversion analysis suggests that the nonlinear advection by winds induced from upper-level PV anomalies is responsible for the different performance of nonlinear advection terms for shallow low-level and upper-level cyclones. These findings further our understanding of the mechanisms and variations of cyclone propagation. Significance Statement Extratropical cyclones (ETCs) can be identified at different levels in the troposphere. These mobile low pressure cyclonic storms are the main sources of synoptic variability in the extratropics and often bring severe or even disastrous weather. Previous studies on ETC movement have typically been restricted to cyclones identified at a single level. Our study, by identifying ETCs at multiple levels, classifies cyclones into deep, shallow low-level, and shallow upper-level cyclones. For deep cyclones, their poleward movement is found to be a result of diabatic heating at lower levels and dominated by the stationary circulation at upper levels. For shallow cyclones, nonlinear advection determines whether they propagate poleward or equatorward. These findings further our understanding of the mechanisms of cyclone propagation and imply that the movement of deep and shallow cyclones may undergo different changes with different weather and climate impacts in the future, given the enhanced diabatic heating under global warming, which deserves further investigation.

Near-infrared imaging-based diffusion coefficient mapping for acid–base reactions

This study describes a method based on near-infrared concentration imaging and advection–diffusion–reaction modeling for the simultaneous determination of the diffusion coefficient distributions of acids, bases, and salts during the neutralization reaction. The reactions between parallel streams of aqueous solutions of H2SO4 and NaOH, and HCl and KOH through a microfluidic channel are investigated. The measured concentration profiles were approximated by a Gaussian or error function, to calculate the advection, diffusion, and reaction terms analytically and robustly. The diffusion coefficients differ significantly within the channel; those at the reaction interface are the largest than the literature values measured under non-reactive conditions, indicating temperature and concentration dependence, and anomalous features. The proposed method facilitates the in-situ visual and quantitative analysis of diffusion reactions.

A flexible z-layers approach for the accurate representation of free surface flows in a coastal ocean model (SHYFEM v. 7_5_71)

Abstract. We propose a discrete multilayer shallow water model based on z-layers, which, thanks to the insertion and removal of surface layers, can deal with an arbitrarily large tidal oscillation independently of the vertical resolution. The algorithm is based on a classical two-step procedure used in numerical simulations with moving boundaries (grid movement followed by a grid topology change, that is, the insertion/removal of surface layers), which avoids the appearance of surface layers with very small or negative thickness. With ad hoc treatment of advection terms at nonconformal edges that may appear owing to insertion/removal operations, mass conservation and the compatibility of the tracer equation with the continuity equation are preserved at a discrete level. This algorithm called z-surface-adaptive, can be reduced, as a particular case when all layers are moving, to the z-star coordinate. With idealized and realistic numerical experiments, we compare the z-surface-adaptive against z-star and we show that it can be used to simulate coastal flows effectively.

Concentration phenomenon of single phytoplankton species with changing-sign advection term

In this paper, a nonlocal reaction-diffusion equation modeling the growth of phytoplankton species with changing-sign advection in a vertical water column is investigated, where the species depends solely on light for its metabolism. We mainly study the concentration phenomenon of the phytoplankton with large advection amplitude and small diffusion rate. Firstly, we study the threshold-type dynamics of the population by critical death rate d⁎. Secondly, we examine the concentration phenomenon with large advection amplitude and small diffusion in two cases: (i) the advection function h(x) changes sign only once from positive to negative in water column [0,1]. We find that the phytoplankton will concentrate at certain critical point with large advection amplitude and small diffusion; (ii) the advection function h(x)<0 in [0,κ) with ∫0xh(s)a(s)ds<0 for all x∈(0,1], the phytoplankton will concentrate at the surface of water column with large advection amplitude and small diffusion. We also investigate the limiting distribution of phytoplankton as diffusion rate D→+∞: the phytoplankton tends to even distribution in water column.

Fine scale simulation of sea salt aerosol under strong wind: WRF sensitivity test on PBL schemes and LES under Typhoon Hagibis

Identifying which factors among the planetary boundary layer (PBL) scheme, grid resolution, and source or sink terms dominantly influence the sea salt aerosol (SSA) spatial distribution is necessary. The dependence of SSA transport on PBL processes was investigated using a numerical weather prediction (NWP) model with a grid scale of ∼143 m. Size-segregated SSA transport during Typhoon Hagibis, which made landfall in Japan in 2019, was simulated using the Weather Research and Forecasting (WRF) model. The PBL schemes of Yonsei University (YSU), scale-aware YSU (Shin and Hong, 2015's scheme, SH) and Mellor-Yamada Nakanishi-Niino (MYNN), and large-eddy simulation (LES) subjected to turbulence transition enhancement via a cell perturbation method were tested to evaluate the reproducibility of observed values of wind speed, surface pressure, relative humidity, and temperature at meteorology masts. The results showed that wind speed was most influenced by the selection of the PBL scheme and LES. The distance from the coastline, as determined by the wind direction during the most intense typhoon stage, was correlated with a decrease in the time averaged SSA concentration when the storm moved inland. Despite the simulated SSA emission scheme's high sensitivity to wind speed (nearly 3rd power), the near-surface average concentration was less sensitive to the PBL schemes and LES selection than wind speed. However, the maximum arrival of the SSA differed by ∼20 % during the most vigorous stage of the typhoon. Budget analysis of the SSA transport equation highlighted that the advection term and gravity settling were most dependent on the PBL schemes and LES. The impacts of both factors on SSA transport were not limited to near-surface tendencies but were in a broader range over the atmosphere, up to 1–2 km. These results indicated that the vertical structure of the SSA field over the boundary layer depended on the PBL schemes and LES, thereby modulating the inland arrival of the SSA.

High order conservative Lagrangian scheme for three-temperature radiation hydrodynamics

The three-temperature (3-T) radiation hydrodynamics (RH) equations are widely used in modeling various optically thick high-energy-density-physics environments, such as those in astrophysics and inertial confinement fusion (ICF). In this paper, we will discuss the methodology to construct a high order conservative Lagrangian scheme solving 3-T RH equations. Specifically, the three new energy variables are defined first, in the form of which the three energy equations of the 3-T RH equations are rewritten. The main advantage of this formulation is that it facilitates the design of a scheme with both conservative property and arbitrary high order accuracy. Starting from one dimension and based on the multi-resolution WENO reconstruction and the strong stability preserving (SSP) high order time discretizations, taken as an example, we design a third order conservative Lagrangian scheme both in space and time. To determine the numerical flux for the conservative advection terms in the 3-T RH equations, we propose a HLLC numerical flux which is derived from the divergence theorem rigorously and is suitable for multi-material problems with the ideal-gas equations of state. After that, we discuss how to design a class of high order positivity-preserving explicit Lagrangian schemes to solve the 3-T RH equations which only contain the conservative advection terms in space. Preliminary extension to the two dimensional case is also considered. Finally, various numerical tests are given to verify the desired properties of the high order Lagrangian schemes such as high order accuracy, non-oscillation, conservation and adaptation to multi-material problems.

Solver algorithm for stabilized space-time formulation of advection-dominated diffusion problem

This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution using higher-order continuous B-spline basis functions in both spatial and temporal dimensions. This problem is very difficult to solve numerically using the standard Galerkin finite element method due to artificial oscillations present when the advection term dominates the diffusion term. However, a first-order constraint least-square formulation allows us to obtain numerical solutions avoiding oscillations. The advantages of space-time formulations are the use of high-order methods and the feasibility of developing space-time mesh adaptive techniques on well-defined discrete problems. We develop a solver for a least-square formulation to obtain a stabilized and symmetric problem on finite element meshes. The computational cost of our solver is bounded by the cost of the inversion of the space-time mass and stiffness (with one value fixed at a point) matrices and the cost of the GMRES solver applied for the symmetric and positive definite problem. We illustrate our findings on an advection-dominated diffusion space-time model problem and present two numerical examples: one with isogeometric analysis discretizations and the second one with an adaptive space-time finite element method.

On the theory of fast projection methods for high-order Navier-Stokes solvers

We propose a new framework for the design of fast-projection solvers for the Navier-Stokes equations using Runge-Kutta integrators. The framework uses the full nonlinear equations along with rooted trees and exposes the need to track non-linear advection terms for fourth-order and higher integrators as those introduce irreducible elementary derivatives in the truncation error. The framework is then used to derive approximations to the pressure projection by replacing those with suitable approximations that do not affect formal order of accuracy. The proposed pseudo-pressure approximations are easy-to-implement with some of the variants including parametric coefficients that can be exploited to optimize fast-projection solvers for stability or other desirable properties. In addition, we report approximations for adaptive timestepping. Both the parametric and adaptive timestepping results are being reported for the first time in the literature. The proposed approximations are verified with computations of the full Navier-Stokes equations on two benchmark problems with steady and unsteady boundary conditions and fixed and adaptive timestepping. All calculations agree with the theoretical results and produce the correct formal order of accuracy. The proposed framework lays the foundation for future work on fast-projection methods and can be used to reproduce existing results in the literature.

A monotone finite volume scheme for single phase flow with reactive transport in anisotropic porous media

This paper deals with development and analysis of a finite volume scheme for a nonlinear parabolic equation modeling a single phase flow with reactive solute transport, including equilibrium sorption, in heterogeneous porous media. We present a second-order, finite volume scheme by combining a nonlinear two point flux approximation for the diffusion term, and an upwind method for the advective term on unstructured meshes. It is shown that, under a CFL condition, this scheme ensures the non-negativity of the discrete solution, taking into account the anisotropy and heterogeneity of the domain. The existence of a solution for the discrete nonlinear system is studied, and the convergence of a fixed point method is proved. Our theoretical results are illustrated by numerical simulations in a bidimensional domain, in particular we show the second-order convergence rate for the numerical solution and confirm the monotonicity of the scheme.

Comparison of Hydrodynamic Processes Modelling Results in Shallow Water Bodies Based on 3D Model and 2D Model Averaged by Depth

Introduction. Two-dimensional hydrodynamic models have proven their ability to adequately describe the processes of runoff and transportation in rivers, lakes, estuaries, deltas and seas. Practice shows that even where significant three-dimensional effects are expected, for example, with wind flows, a two-dimensional approach can work effectively. However, in some cases, the two-dimensional model does not accurately reflect the actual flow structures. For example, in shallow waters with complex bathymetry, heterogeneous terrain and dynamics can lead to a non-uniform velocity profile. The aim of the study is to develop a basis for determining in which cases a two-dimensional model averaged in depth is sufficient for modelling hydrodynamic processes in shallow waters like the Azov Sea, and in which cases it is advisable to use a three-dimensional model to obtain accurate results.Materials and Methods. Local analytical solutions have been obtained for the propagation of the predominant singular progressive wave in a shallow, well-mixed reservoir. Advective terms and Coriolis terms are neglected, the vortex viscosity is assumed to be constant, and the lower friction term is linearized. Special attention is paid to the latter, since the characteristics of the models significantly depend on the method of determining the coefficients of lower friction. The analytical method developed in the study shows that certain combinations of higher flow velocities (u ≈˃ 1 m/s) and water depths (d ˃ 50 m) can cause significant differences between the results of the depth-averaged model and the model containing vertical information.Results. The results obtained are verified by numerical simulation of stationary and non-stationary periodic flows in a schematized rectangular basin. The results obtained as a result of three-dimensional modelling are compared with the results of two-dimensional modelling averaged in depth. Both simulations show good compliance with analytical solutions.Discussion and Conclusions. Analytical solutions were found by linearization of the equations, which obviously has its limitations. A distinction is made between two types of nonlinear effects — nonlinearities caused by higher-order terms in the equations of motion, i.e. terms of advective acceleration and friction, and nonlinear effects caused by geometric nonlinearities, this is due, for example, to different water depths and reservoir widths, which will be important when modelling a real sea.

Dewatering and consolidation of clay slurries

Dewatering, which is the process of separating (colloidal) suspended particles from a solvent (usually water), is used in many engineering applications (sanitary engineering, dredging engineering…). Key questions associated with dewatering in the context of the reuse of dredged sediment are (1) what is the process kinetics, (2) how can these processes be optimized and (3) can the dewatered sludge be reused and for which application? Dewatering and consolidation are functions of the suspended particles’ size and type, and their solvent-mediated interaction. In this presentation, some examples will be given about the dewatering of suspensions and slurries as found in engineering applications [1]. The presentation will focus on the behaviour of mineral clay suspensions (kaolinite, montmorillonite, illite…) composed of particles of different particle sizes [2-5]. We will show that, depending on the particle size distribution and solvent properties, the system is either undergoing a slow sedimentation dominated by thermodynamic forces or a rapid sedimentation dominated by gravity. The sedimentation is followed in time using NMR and inferential image analysis, and the particles are characterized by size, density and electrokinetic charge. We show that the time evolution of the sedimentation behaviour can be modelled using an advection-diffusion equation. The advective term is a function of gravity, whereas the diffusion term represents either a hard-sphere repulsion or an effective stress, depending on whether thermodynamic forces dominate the system [6-8]. We show that after solving this advection-diffusion equation numerically, the results based on the theory of Gibson does match the experimental data collected from NMR in the phase of slow kinetics. For the early stages of settling and consolidation, where the system kinetics are fast, we show that the data are contaminated by artifacts due to the limited time of signal acquisition imposed by the NMR method. We show that is possible to overcome those limitations by either sacrificing some information related to particle’s sizes using the NMR or by combining the NMR method with excess pore pressure measurements along the height of the settling columns.

Simulation of Fixed-Bed Chromatographic Processes Considering the Nonlinear Adsorption Isotherms.

This paper presents the numerical approximation of a nonlinear equilibrium-dispersive (ED) model of multicomponent mixtures for simulating single-column chromatographic processes. Using Danckwerts boundary conditions (DBCs), the ED is studied for both generalized and standard bi-Langmuir adsorption isotherms. Advection-diffusion partial differential equations are used to represent fixed-bed chromatographic processes. As the diffusion term is significantly weaker than the advection term, sophisticated numerical techniques must be applied for solving such model equations. In this study, the model equations are numerically solved by using the Runge-Kutta discontinuous Galerkin (RKDG) finite element method. The technique is designed to handle sudden changes (sharp discontinuities) in solutions and to produce highly accurate results. The method is tested with several case studies considering different parameters, and its results are compared with the high-resolution finite volume scheme. One-, two-, and three-component liquid chromatography elutions on fixed beds are among the case studies being considered. The dynamic model and its accompanying numerical case studies provide the initial step toward continuous monitoring, troubleshooting, and effectively controlling the chromatographic processes.

Real-time tsunami forecasting system with nonlinear effects using Green’s functions: application to near-shore tsunami behavior in complex bay topography

ABSTRACT In this study, a real-time tsunami estimation method was developed using the linear superposition of Green’s functions, which account for nonlinear tsunami effects around coastal areas. To this end, first, the nonlinear effects associated with the inundation and bottom friction and advection terms in a nonlinear long-wave model were investigated, focusing on large tsunamis around Urado Bay in Kochi Prefecture, Japan, which is at risk of future damage from tsunamis produced by the Nankai Trough earthquake. The results indicate that the effects of advection play a more significant role than those of the inundation and bottom friction in terms of accurately estimating near-shore tsunami propagation. Then, based on these results, Green’s functions were modified to account for the linearly approximated effects of the advection terms. By applying the developed method to tsunamis around Urado Bay, it was demonstrated that accurate estimations of the water surface level and flow velocity changes could be quickly obtained at any location around the bay. The developed method can be applied to real-time tsunami inundation forecasting and off-shore evacuation simulations of vessels to support optimal evacuation decisions.

Seasonal and Geographical Variations in Fundamental Weather Patterns during Extreme Precipitation as Identified from Omega Equation Forcing

Abstract We investigate the large-scale weather patterns during extreme precipitation (PEx) events over the conterminous United States (CONUS) by applying a version of the quasigeostrophic (QG) omega equation. This work aims to develop a climatology of the weather patterns most related to PEx events during current climate. Extreme events are examined for each of seven regions defined by consistent annual cycles of precipitation and spanning the CONUS. For the CONUS we train several self-organizing maps (SOM) on a pressure–time series of vertical velocity from each of the advective forcing terms in the QG omega equation for each extreme event. The unsupervised learning of the SOM allows us to identify the most descriptive set of nine patterns in vertical velocity associated with precipitation extremes. This method finds multiple frontal- and cyclone-driven patterns while grouping primarily convective events into one pattern. Frontal events include a synoptic pattern consistent with West Coast atmospheric river events as well as pattern groups linked to developing and to mature (“occluded”) frontal cyclones. The primary patterns found during PEx events vary seasonally and geographically. Frontal cyclone patterns are most common during PEx events during summer in the part of the Great Plains and during winter for the Northeast, Southeast, Pacific Northwest, and Southwest. Convection is the most common pattern during summer in all regions. Except in the Southeast, the annual cycles of monthly number of PEx events and average precipitation match well, partially validating our choice of regions to aggregate PEx events.

Wake interaction of aligned wind turbines over two-dimensional hills

An experimental investigation was carried out to explore the interaction and wake statistics of model wind turbines operating individually and in pairs over two-dimensional hills with varying heights. The hills shared a sinusoidal shape and extended L/D=20 in the streamwise direction, where D represents the diameter of the turbine rotor. The peak heights of the hills were H/D=0, 0.5, 1, and 1.5. The first turbine was located at the beginning of the hill development, and the second turbine was positioned halfway between the first and the hill's peak, downwind. The flow in the intermediate wake regions was characterized using particle image velocimetry, focusing on the recovery mechanisms of streamwise momentum on the windward side of the hills, ranging from gentle to steep-up slopes. The results indicate that the advection terms play a more significant role than turbulence in the wake recovery mechanism with steeper hill slopes. Associated reduced turbulence levels are attributed to flow acceleration, which led to a higher power availability at the top of the hills.

The Impact of Coastline and Bathymetry Changes on the Storm Tides in Zhejiang Coasts

Coastal evolutions are expected to have a significant impact on storm tides, disproportionately aggravating coastal flooding. In this study, we utilize a nested storm tide model to provide an integrated investigation of storm tide responses to changes in coastline and bathymetry along the Zhejiang coasts. We selected coastline and bathymetry data from 1980 and 2016, as well as data from three typical typhoon events (i.e., Winnie, Haikui, and Chan-hom) for simulating the storm surge processes. The results indicate that changes in the coastline and bathymetry from 1980 to 2016 have resulted in an increase in storm tides in the northern part and a decrease in the central part of Zhejiang. Specifically, storm tides in Hangzhou Bay have increased significantly, with an average increase of about 0.3 m in the maximum storm tides primarily attributed to coastline changes. On the contrary, in smaller basins like Sanmen Bay, while reclamation itself has reduced peak storm surges, rapid siltation has consequently exacerbated the storm surge. By decomposing storm tides into astronomical tides and storm surges, we discovered that the change in tidal levels was twice as significant as the surge change. Moreover, the nonlinear tide–surge interaction was nearly four times that of the pure surge, significantly contributing to storm surge variation. Alterations in the momentum balance reveal that the water depth-induced bottom friction and wind stress increase contributes to the local enlargement of storm tides at the bay head, while the coastline changes exaggerate nearshore storm tides through an increase in the advection term.

The logistic problem with nonlinear directed advection

We are concerned with the study of positive solutions to the logistic model −Δu+a(x)⋅∇up=λu−b(x)f(u)in Ω,u=0on ∂Ω, where Ω is a smooth and bounded domain of the Euclidean space RN (N≥2), 0<p<1, a∈C(Ω¯)N, b∈C(Ω¯), b≥0. It is assumed that λ>0 is a real parameter and f∈C1[0,∞) is nonnegative and satisfies some growth conditions at 0 and ∞. The two main difficulties in the study of the above problem are the indefinite sign of the advection term a(x)⋅∇up and the fact that ∇up=pup−1∇u may be singular around the boundary of Ω. We discuss the existence of a positive solution as well as its C1-regularity at ∂Ω. Our results extend those recently obtained in Cintra et al. (2022) for the case p>1.

Bifurcation analysis of a delayed reaction–diffusion–advection Nicholson’s blowflies equation

In this paper, we investigate the dynamics of a reaction-diffusion Nicholson’s blowflies equation with advection. The stability of positive steady state and existence of Hopf bifurcation are obtained by analyzing the distribution of the eigenvalues. Moreover, by using the center manifold theory and normal form method, an explicit algorithm for determining the direction and stability of the Hopf bifurcation is derived. Meanwhile, we find out that the bifurcation value is increasing with respect to the advection rate. Finally, numerical results demonstrate that the advection term causes the population to move from upstream to downstream, which also indicates that advection term plays a key role in the description and interpretation of some common natural phenomena.