Advection Parameter Research Articles

Exploring Long-Term Persistence in Sea Surface Temperature and Ocean Parameters via Detrended Cross-Correlation Approach

Long-term cross-correlational structures are examined for pairs of sea surface temperature anomalies (SSTAs) and advective forcing parameters and sea surface height anomalies (SSHAs) and current velocity anomalies (CVAs) in the East/Japan Sea (EJS); all these satellite datasets were collected between 1993 and 2023. By utilizing newly modified detrended cross-correlation analysis algorithms, incorporating local linear trend and local fluctuation level of an SSTA, the analyses were performed on timescales of 400–3000 days. Long-term cross-correlations between SSTAs and SSHAs are strongly persistent over nearly the entire EJS; the strength of persistence is stronger during rising trends and low fluctuations of SSTAs, while anti-persistent behavior appears during high fluctuations of SSTAs. SSTA-CVA pairs show high long-term persistence only along main current pathways: the zonal currents for the Subpolar Front and the meridional currents for the east coast of Korea. SSTA-CVA pairs also show negative long-term persistent behaviors in some spots located near the coasts of Korea and Japan: the zonal currents for the eastern coast of Korea and the meridional currents for the western coast of Japan; these behaviors seem to be related to the coastal upwelling phenomena. Further, these persistent characteristics are more conspicuous in the recent decades (2008~2023) rather than in the past (1993~2008).

Global existence and singularity formation for the generalized Constantin–Lax–Majda equation with dissipation: the real line vs. periodic domains

The question of global existence versus finite-time singularity formation is considered for the generalized Constantin–Lax–Majda equation with dissipation , where , both for the problem on the circle and the real line. In the periodic geometry, two complementary approaches are used to prove global-in-time existence of solutions for and all real values of an advection parameter a when the data is small. We also derive new analytical solutions in both geometries when a = 0, and on the real line when , for various values of σ. These solutions exhibit self-similar finite-time singularity formation, and the similarity exponents and conditions for singularity formation are fully characterized. We revisit an analytical solution on the real line due to Schochet for a = 0 and σ = 2, and reinterpret it terms of self-similar finite-time collapse. The analytical solutions on the real line allow finite-time singularity formation for arbitrarily small data, even for values of σ that are greater than or equal to one, thereby illustrating a critical difference between the problems on the real line and the circle. The analysis is complemented by accurate numerical simulations, which are able to track the formation and motion of singularities in the complex plane. The computations validate and build upon the analytical theory.

Inclusion of hydrodynamic properties of bathing waters is critical in selecting faecal indicators to assess public health impacts of faecal contamination

The EU Bathing Water Directive (BWD) requires member states to assess bathing water quality according to the levels of faecal indicator bacteria (FIB) in designated bathing areas. However, this criterion has two significant limitations given that the BWD does not; (i) account for differences in hydrodynamic properties of bathing waters and, (ii) assumes that all faecal pathogens decay equally in aquatic environments. This study simulated sewage discharge events in three hypothetical aquatic environments characterised by different advection and dispersion parameters in the solute transport equation. Temporal changes in the downstream concentration of six faecal indicators were determined in simulations that utilised measured decay rates of each faecal indicator from a programme of controlled microcosm experiments in fresh and seawater environments. The results showed that the decay rates of faecal indicators are not a critical parameter in advection dominant water bodies, such as in fast-flowing rivers. Therefore, faecal indicator selection is less important in such systems and for these, FIB remains the most cost-effective faecal indicator to monitor the public health impacts of faecal contamination. In contrast, consideration of faecal indicator decay is important when assessing dispersion and advection/dispersion dominant systems, which would pertain to transitional (estuarine) and coastal waterbodies. Results suggest that the inclusion of viral indicators, such as crAssphage and PMMoV, could improve the reliability of water quality modelling and minimise the risk of waterborne illnesses from faecal contamination.

Regularity, Asymptotic Solutions and Travelling Waves Analysis in a Porous Medium System to Model the Interaction between Invasive and Invaded Species

This work provides an analytical approach to characterize and determine solutions to a porous medium system of equations with views in applications to invasive-invaded biological dynamics. Firstly, the existence and uniqueness of solutions are proved. Afterwards, profiles of solutions are obtained making use of the self-similar structure that permits showing the existence of a diffusive front. The solutions are then studied within the Travelling Waves (TW) domain showing the existence of potential and exponential profiles in the stable connection that converges to the stationary solutions in which the invasive species predominates. The TW profiles are shown to exist based on the geometry perturbation theory together with an analytical-topological argument in the phase plane. The finding of an exponential decaying rate (related with the advection and diffusion parameters) in the invaded species TW is not trivial in the nonlinear diffusion case and reflects the existence of a TW trajectory governed by the invaded species runaway (in the direction of the advection) and the diffusion (acting in a finite speed front or support).

An Eulerian Model for the Transport and Diffusion of Floating Particles Within Regions of Emergent Vegetation

AbstractEmergent vegetation has a significant impact on floating particle transport and diffusion in open channel flow. The random walk model of a Lagrangian approach has proven more than suitable to describe the rather unpredictable moving trajectory of particles within emergent vegetation. However, compared to the large computational costs of the Lagrangian model, which also requires more input data, a simplified model based on the Eulerian approach can be by far preferable and cost‐effective for rapid first‐order prediction of particle transport and diffusion within vegetated areas. In this study, we developed a one‐dimensional advection‐diffusion model to simulate particle transport processes within vegetated areas, and to explore the impacts of vegetation on particles transport, diffusion and removal. The model parameters, including the probability of a particle colliding with a stem, and the probability of it being temporarily trapped or permanently captured by a stem, as well as the mean retention time that govern the random walk model, are introduced to estimate the mean velocity, diffusion coefficient, removal rate of particles of Eulerian model, distinguishing from the standard advection and diffusion parameters. The validity of the parameters is verified through the stochastic model with a large number of realizations. The comparison between the dispersal kernel as well as the spatio‐temporal distribution of floating particles predicted by Eulerian model and stochastic model is quite satisfactory and suggests that the Eulerian model we proposed is properly described.

Geocomputação aplicada no problema de transporte acoplado ao fluxo subterrâneo em aquífero livre

A geocomputação, sendo a aplicação de métodos e técnicas computacionais para apoiar a resolução de problemas georreferenciados, auxilia a compreensão de fenômenos naturais relacionados aos recursos hídricos. Algumas ferramentas de geoprocessamento proporcionam mapas digitais que delimitam a bacia hidrográfica em estudo e ainda, a distribuição potenciométrica em conhecidas coordenadas no domínio computacional podem ser usadas na condição inicial e de fronteira do modelo hidrogeológico. Neste sentido, o artigo visa a implementação de técnicas da geocomputação na solução do problema do transporte de contaminante em aquífero livre. A metodologia proposta inicia na geração de uma malha não estruturada; gera a função para a condição de fronteira; aplica um método de iterações de Picard com estimativa inicial calculada numericamente; simula o campo de velocidades de águas subterrâneas em situações de poços de bombeamento e áreas de recarga e, finalmente, acopla a solução estacionária e não-linear do fluxo livre, obtida pelo método de elementos finitos, nos parâmetros advectivo e dispersivo da equação transiente do transporte de contaminantes. Resultados gráficos ilustram a simulação do comportamento hidráulico e as isolinhas de concentração em subsuperfície georreferenciada da bacia hidrográfica do Reservatório do Lobo no município de Itirapina-SP.

Parameters of magma chambers

The Earth’s early (“pregeological”) thermal history has been reviewed, and primordial conditions of the tectonosphere’s thermal evolution during the subsequent period (4.2 to 0.0 billion years ago) have been formulated. It is shown that periodic displacement of the material in volumes measuring about 120±60 thousand km3 or in n-fold amounts are inevitable. The mantle advection parameters make it possible to forecast depths of magma chambers and temperatures within them, something that can be corroborated by experimental data

On FTCS Approach for Box Model of Three-Dimension Advection-Diffusion Equation

This paper describes a numerical solution for mathematical model of the transport equation in a simple rectangular box domain. The model of street tunnel pollution distribution using two-dimension advection and three-dimension diffusion is solved numerically. Because of the nature of the problem, the model is extended to become three-dimension advection and three-dimension diffusion to study the sea-sand mining pollution distribution. This model with various advection and diffusion parameters and the boundaries conditions is also solved numerically using a finite difference (FTCS) method.

RETRACTED: On the estimation of moisture permeability and advection coefficients of a wood fibre material using the optimal experiment design approach

This paper presents a practical application of the concept of Optimal Experiment Design (OED) for the determination of properties of porous materials with in-situ measurements and an identification method. First, an experimental set-up was presented and used for the measurement of relative humidity within a wood fibre material submitted to single and multiple steps of relative humidity variation. Then, the application of OED enabled to plan the experimental conditions in terms of sensor positioning and boundary conditions out of 20 possible designs. The OED search was performed using the Fisher information matrix and a priori knowledge of the parameters. It ensures to provide the best accuracy of the identification method and thus the estimated parameter. Optimal design results have been found for single steps from the relative humidity phi = 10 to 75%, with one sensor located at the position X between 4 and 6 cm, for the estimation of moisture permeability coefficients, while from phi = 75% to phi = 33%, with one sensor located at X{\deg} = 3 cm, for the estimation of the advection coefficient. The OED has also been applied for the identification of couples of parameters. A sample submitted to multiple relative humidity steps (phi = 10-75-33-75%) with a sensor placed at X{\deg} = 5 cm was found as the best option for determining both properties with the same experiment. These OED parameters have then been used for the determination of moisture permeability and advection coefficients. The estimated moisture permeability coefficients are twice higher than the a priori values obtained using standard methods. The advection parameter corresponds to the mass average velocity of the order of v = 0.01 mm/s within the material and may play an important role on the simulation of moisture front.

Stochastic variational multiscale analysis of the advection–diffusion equation: Advective–diffusive regime and multi-dimensional problems

We present the variational multiscale (VMS) formulation for the stochastic advection–diffusion equation in which the source of uncertainty may arise from random advective and diffusive fields (or material parameters), a random source term, or a combination among them. In this formulation, a stabilization parameter arises that, for the advection–diffusion equation, is a complicated function of the uncertain advection and diffusion parameters. To efficiently incorporate the stochastic stabilization parameter in the numerical method, we develop a projection-based approach to obtain an approximation of the stabilization parameter in the form of a generalized polynomial chaos (gPC) expansion. We demonstrate the current approach for problems which span the advective and diffusive regimes in the stochastic domain. Specifically, four cases are considered with multi-dimensional physical and stochastic domains. These cases include an advection-dominated case with an uncertain advection parameter, a case spanning both the advective and diffusive regimes with uncertain advection and diffusion parameters, a case with an uncertain source term, and a case with scalar transport under an uncertain advection field in a channel with multiple branches. For the latter case uniform and non-uniform meshes are employed. The expectation and variance from the stochastic Galerkin and VMS formulations are compared against their counterparts from analytical or Monte Carlo sampling methods where appropriate. In summary, an accurate and stable numerical solution is obtained using the VMS formulation with projection-based approximation of the stochastic stabilization parameter for multi-dimensional problems including non-trivial physical discretization.

The influence of large-scale magnetic field in the structure of supercritical accretion flow with outflow

We present the effects of ordered large-scale magnetic field on the structure of supercritical accretion flow in the presence of an outflow. In the cylindrical coordinates (r, φ, z), we write the 1.5-dimensional, steady-state (⁠|$\frac{\partial }{\partial t}= 0$|⁠) and axisymmetric (⁠|$\frac{\partial }{\partial \varphi }= 0$|⁠) inflow–outflow equations by using self-similar solutions. Also, a model for radiation pressure supported accretion flow threaded by both toroidal and vertical components of magnetic field has been formulated. For studying the outflows, we adopt a radius-dependent mass accretion rate as |$\dot{M}=\dot{M}_{{\rm out}}{(\frac{r}{r_{{\rm out}}})^{s+\frac{1}{2}}}$| with |$s = \frac{1}{2}$|⁠. Also, by following the previous works, we have considered the interchange of mass, radial and angular momentum and the energy between inflow and outflow. We have found numerically that two components of magnetic field have the opposite effects on the thickness of the disc and similar effects on the radial and angular velocities of the flow. We have found that the existence of the toroidal component of magnetic field will lead to an increase in the radial and azimuthal velocities as well as the relative thickness of the disc. Moreover, in a magnetized flow, the thickness of the disc decreases with increase in the vertical component of magnetic field. The solutions indicated that the mass inflow rate and the specific energy of outflow strongly affect the advection parameter. We have shown that by increasing the two components of magnetic field, the temperature of the accretion flow decreases significantly. On the other hand, we have shown that the bolometric luminosity of the slim discs for high values of |$\dot{m} (\dot{m}>>1)$||$\dot{m}\,(\dot{m}\gg 1)$| is not sensitive to mass accretion rate and is kept constant (L ≈ 10LE).

ROSSBY WAVE INSTABILITY IN THE ACCRETION FLOWS AROUND BLACK HOLES

ABSTRACT The roles of the Rossby wave instability (RWI) have been significantly developed in some important processes, such as planet formation and angular momentum transport through thin accretion disks. However, their development on accretion flows with advection is insignificant. In this paper, we investigate the effect of advection in the occurrence of RWI through accretion flows around black holes (BHs). In the absence of advection, the occurrence of RWI is extremely low because of high viscosity in the accretion flows around BHs. The results of this paper show that there is a significant chance for the occurrence of RWI in some wavelengths if we consider advection even in low amounts. Therefore, the RWI can be a suitable candidate for angular momentum transport in the accretion flows around BHs. Also, the results show that the advection parameter and the ratio of heat capacity, which are special characters of advection flows, play important roles in the occurrence of RWI.

The verification of the estimation of transport and sorption parameters in the MATLAB environment. Column test

Mathematical modelling of the migration of pollutants in the groundwater environment requires knowledge of the values of transport and sorption parameters. The aim of this study was 1) to determine the values of advection, dispersion and sorption parameters of selected tracers that are transported through a porous medium, and 2) to verify the applied parameters estimation procedure. The authors examined the migration of a solution containing conservative and reactive tracers (chloride, nitrate, lithium and ammonium ions) through a sample of medium sand. The soil sample for the column test was taken from an aquifer near the Tursko groundwater intake (Wielkopolska province, Poland). The parameter estimation procedure, conducted in the MATLAB environment, included the numerical solution of the differential equations of transport and sorption, and the application of the numerical optimization method. During the identification, the authors tested twelve mathematical models including the advection-dispersion model, as well as single and hybrid (i.e. two-site) sorption models. The authors made a comparison of parameter values obtained by means of the global and local optimization method. The fitting quality was assessed by calculating the root mean square error RMSE and correlation coefficient r. As a result of the research, the authors determined the values of the advection-dispersion parameters: hydraulic conductivity k, effective porosity ne, and longitudinal dispersivity α. The authors found out that the nature of lithium ions migration is best captured by the single sorption model (equilibrium sorption), whereas the nature of ammonium ions migration is by the hybrid model with irreversible sorption. Lithium ions on the tested soil revealed low sorption intensity, ammonium ions showed medium intensity, while nitrate ions were transported at the same rate as chloride ions, exhibiting no retardation. The verification of parameter estimation in the MATLAB environment was carried out by comparing it against the alternative, well-known and often tested method, based on analytical solutions of the transport and sorption equation, combined with optimization within the FIELD and KLUTE-STEP programmes.

THE INFLUENCE OF OUTFLOW IN SUPERCRITICAL ACCRETION FLOWS

ABSTRACT We solve the radiation-hydrodynamic equations of supercritical accretion flows in the presence of radiation force and outflow by using self-similar solutions. Similar to the pioneering works, in this paper we consider a power-law function for mass inflow rate as . We found that s = 1 when the radiative cooling term is included in the energy equation. Correspondingly, the effective temperature profile with respect to the radius was obtained as . In addition, we investigated the influence of the outflow on the dynamics of the accretion flow. We also calculated the continuum spectrum emitted from the disk surface as well as the bolometric luminosity of the accretion flow. Furthermore, our results show that the advection parameter, f, depends strongly on mass inflow rate.

VERTICAL STRUCTURE OF ADVECTION-DOMINATED ACCRETION FLOWS

We solve the set of hydrodynamic (HD) equations for optically thin Advection Dominated Accretion Flows (ADAFs) by assuming radially self-similar in spherical coordinate system $ (r, \theta, \phi) $. The disk is considered to be steady state and axi-symmetric. We define the boundary conditions at the pole and the equator of the disk and to avoid singularity at the rotation axis, the disk is taken to be symmetric with respect to this axis. Moreover, only the $ \tau_{r \phi} $ component of viscous stress tensor is assumed and we have set $ v_{\theta} = 0 $. The main purpose of this study is to investigate the variation of dynamical quantities of the flow in the vertical direction by finding an analytical solution. As a consequence, we found that the advection parameter, $ f^{adv} $, varies along the $ \theta $ direction and reaches to its maximum near the rotation axis. Our results also show that, in terms of no-outflow solution, thermal equilibrium still exists and consequently advection cooling can balance viscous heating.

An optimal time-stepping algorithm for unsteady advection–diffusion problems

We consider the numerical solution of a linear time dependent advection–diffusion problem by an implicit two-weight, three-point finite difference scheme. We extend the scheme proposed by Chadha and Madden (2011), to incorporate an optimal time step selection algorithm for the method. The optimal values of the weights involved in the scheme have been obtained by using the notion of an equivalent differential equation (Warming and Hyett, 1974), and, by enforcing certain constraints due to von Neumann stability and a discrete maximum principle, we obtain sharp bounds for optimal time-stepping in terms of mesh width and problem data. Furthermore, we formulate the time step selection as a root-finding problem, and use this to show the optimal time step exists and is unique. The resulting method, based on optimal values of weights and optimal time-stepping, is of fifth-order in space, and third-order in time. The results of extensive numerical experiments are presented for several classic test problems for various values of the advection and diffusion parameters. These show that our proposed method is superior (quantitatively and qualitatively) to other schemes that can be represented within the framework of two-weighted schemes. We also present comparisons with other high-order methods, and an application of the method to a problem with non-smooth data.

Pollutant’s Horizontal Dispersion Along and Against Sinusoidally Varying Velocity from a Pulse Type Point Source

An analytical solution of a two-dimensional advection diffusion equation with time dependent coefficients is obtained by using Laplace Integral Transformation Technique. The horizontal medium of solute transport is considered of semi-infinite extent along both the longitudinal and lateral directions. The input concentration is assumed at an intermediate position of the domain. It helps to evaluate concentration level along the flow as well as against the flow through one model only. The source of the input concentration is considered to be of pulse type. In the presence of the source, it is assumed to be decreasing very slowly with time, and just after the elimination of the source it is assumed to be zero. The dispersion coefficient and the advection parameter are considered directly proportional to each other. The analytical solution may be used to predict the solute concentration level with position and time in an open medium as well as in a porous medium. The effect of heterogeneity on the solute transport may also be predicted.

Interpreting layer thickness advection in terms of eddy–topography interaction

A parameterization for the spatial pattern of the eddy induced thickness advection parameter estimated from a dynamically consistent data assimilation procedure is presented. Values of the thickness advection parameter are predominantly negative (positive) over seamounts, and positive (negative) over the deep ocean in the southern (northern) hemisphere along strong currents; its magnitude is large at high latitudes but low in the tropical regions. Those characteristics motivate a parameterization based on the Coriolis parameter, the bottom depth and an eddy length scale. As a parameterization for an eddy streamfunction, the associated bolus velocities advect density anti-cyclonically (cyclonically) around seamounts (troughs). Although the parameterization has the same form as Holloway’s streamfunction for the Neptune effect, and is also related to eddy–topography interactions, Holloway’s streamfunction is in contrast applied to the momentum equation. The parameterization is independently confirmed by the flux-mean gradient relation from the output of a high resolution model. The effect of the proposed scheme is investigated using a channel model with idealized bottom topographies and a global ocean circulation model with realistic bottom topography. In agreement with the high resolution model, our scheme generates cold (warm) domes and cyclonic circulations over seamounts (troughs), which is consistent with the eddy movement in presence of the topographic β effect. This provides a different mechanism for eddy–topography interaction than the Neptune effect, which generates circulations of opposing sign.

Development of a methodology for the application of synthetic DNA in stream tracer injection experiments

[1] Stream tracer injection experiments are useful for characterizing hydrological and biogeochemical processes in streams. We used nonconservative synthetic DNA and conservative NaCl in six instantaneous tracer injection experiments in streams in the Benelux. The main aim was to compare the performance of injected synthetic DNA tracer “T23” with NaCl. In all experiments, the shapes of the T23 and NaCl breakthrough curves (BTCs) were similar. Recovered T23 mass ranged from 2.9 to 52.6%, while recovered NaCl tracer mass ranged from 66.7% to complete mass recovery. In batch experiments, T23 decay was not detected. However, in those batches, we observed an unexplained initial T23 mass loss of 40–97%. In batches with sediment, T23 attachment rate coefficients ranged from close to zero to 0.2 hr−1. Advective and dispersive transport parameters of both NaCl and T23 fitted with STAMMT-L were similar. However, compared to T23, fitted storage zone areas of NaCl were 2–5 times larger, while storage zone exchange coefficients were two times larger. Fitted mass dilution factors of T23 ranged from 1.6 to 34.8. Together, these results pointed toward the disappearance of a part of the T23 mass due to both initial losses and attachment or sorption of T23 mass in those storage zone(s), while decay was not important. Our research demonstrated that artificial DNA can be a valuable tool to determine advective and dispersive transport in brooks, but not to assess solute mass exchange processes related to surface transient storage or hyporheic exchange.

Radiation spectrum of a magnetized supercritical accretion disc with thermal conduction

We examine the effect of thermal conduction on the observational properties of a super critical hot magnetized flow. We obtained self-similar solution of a magnetized disc when the thermal conduction plays an important role. Follow of our first paper (Ghasemnezhad et al. 2012 (hereafter GKA12)) we have extended our solution on the observational appearance of the disc to show how physical condition such as thermal conduction, viscosity, and advection will change the observed luminosity of the disc, Continuous spectra and surface temperature of such discs was plotted. We apply the present model to black-hole X-ray binary LMC X-3 and narrow-line seyfert 1 galaxies, which are supposed to be under critical accretion rate. Our results show clearly that the surface temperature is strongly depends on the thermal conduction, the magnetic field and advection parameter. However we see that thermal conduction acts to oppose the temperature gradient as we expect and observed luminosity of the disc will reduce when thermal conduction is high. We have shown that in this model the spectra of critical accretion flows strongly depends on the inclination angle.