Dominant Advection Research Articles

Singularly perturbative behaviour of nonlinear advection–diffusion-reaction processes

The purpose of this paper is to use a wavelet technique to generate accurate responses for models characterized by the singularly perturbed generalized Burgers-Huxley equation (SPGBHE) while taking multi-resolution features into account. The SPGBHE’s behaviours have been captured correctly depending on the dominance of advection and diffusion processes. It should be noted that the required response was attained through integration and by marching on time. The wavelet method is seen to be very capable of solving a singularly perturbed nonlinear process without linearization by utilizing multi-resolution features. Haar wavelet method results are compared with corresponding results in the literature and are found in agreement in determining the numerical behaviour of singularly perturbed advection–diffusion processes. The most outstanding aspects of this research are to utilize the multi-resolution properties of wavelets by applying them to a singularly perturbed nonlinear partial differential equation and that no linearization is needed for this purpose.

Swirl driven solute mixing in narrow cylindrical channel

We investigate the mixing of constituent components transported through a narrow fluidic cylindrical channel in a swirling flow environment. We solve for the flow field analytically using the separation of variables method under the framework of fully developed axial velocity and no-slip condition at fluid–solid interface and validate the same with numerical solution. The swirl velocity profile, which is a function of Reynolds number (Re), exhibits exponential decay along the length of the fluidic channel. We numerically solve the species transport equation for the Peclet number in the range of 102 to 104 coupled with the swirl velocity obtained for 0.1≤Re≤100, by using our in-house developed code essentially for the concentration distribution in the field. As seen, an increase in the Reynolds number results in complete rotation of fluids in the pathway, which, in turn, forms an engulfment flow (onset of chaotic convection) and enhances the underlying mixing efficiency substantially. The results show that inlet swirl promotes advection dominated mixing, while the dominance of advection increases substantially for the higher Reynolds number. We show that adding a small magnitude of swirl velocity at the inlet significantly reduces the channel length required for complete mixing even after the swirl velocity has decayed completely.

Drop impact on superheated surfaces: from capillary dominance to nonlinear advection dominance

Ambient air cushions the impact of drops on solid substrates, an effect usually revealed by the entrainment of a bubble, trapped as the air squeezed under the drop drains and liquid–solid contact occurs. The presence of air becomes evident for impacts on very smooth surfaces, where the gas film can be sustained, allowing drops to bounce without wetting the substrate. In such a non-wetting situation, Mandre & Brenner (J. Fluid Mech., vol. 690, 2012, p. 148) numerically and theoretically evidenced that two physical mechanisms can act to prevent contact: surface tension and nonlinear advection. However, the advection dominated regime has remained hidden in experiments as liquid–solid contact prevents rebounds being realised at sufficiently large impact velocities. By performing impacts on superheated surfaces, in the so-called dynamical Leidenfrost regime (Tran et al., Phys. Rev. Lett., vol. 108, issue 3, 2012, p. 036101), we enable drop rebound at higher impact velocities, allowing us to reveal this regime. Using high-speed total internal reflection, we measure the minimal gas film thickness under impacting drops, and provide evidence for the transition from the surface tension to the nonlinear inertia dominated regime. We rationalise our measurements through scaling relationships derived by coupling the liquid and gas dynamics, in the presence of evaporation.

Quantifying the physical processes leading to atmospheric hot extremes at a global scale

Heat waves are among the deadliest climate hazards. Yet the relative importance of the physical processes causing their near-surface temperature anomalies (\U0001d447′)—advection of air from climatologically warmer regions, adiabatic warming in subsiding air and diabatic heating—is still a matter of debate. Here we quantify the importance of these processes by evaluating the \U0001d447′ budget along air-parcel backward trajectories. We first show that the extreme near-surface \U0001d447′ during the June 2021 heat wave in western North America was produced primarily by diabatic heating and, to a smaller extent, by adiabatic warming. Systematically decomposing \U0001d447′ during the hottest days of each year (TX1day events) in 1979–2020 globally, we find strong geographical variations with a dominance of advection over mid-latitude oceans, adiabatic warming near mountain ranges and diabatic heating over tropical and subtropical land masses. In many regions, however, TX1day events arise from a combination of these processes. In the global mean, TX1day anomalies form along trajectories over roughly 60 h and 1,000 km, although with large regional variability. This study thus reveals inherently non-local and regionally distinct formation pathways of hot extremes, quantifies the crucial factors determining their magnitude and enables new quantitative ways of climate model evaluation regarding hot extremes.

A novel method to investigate nonlinear advection–diffusion processes

In this study, a new approach called the reversed fixed point iteration method (RFPIM) is implemented to solve a class of fundamental partial differential equations, namely viscous and inviscid Burgers equations. The results confirm that the current method has the potential to effectively solve problems governed by nonlinear PDEs representing the phenomena of advection and diffusion. Derivations reveal that even in challenging situations such as advection dominance, the RFPIM is highly capable of capturing the natural behaviour of the problem under study. Another important finding, depending on the considered problem, is that the RFPIM can allow the use of relatively large time steps. This feature is of great importance in reducing the storage burden and CPU time for the computational society. The observations reveal that the current approach leads to a significant improvement in the understanding of inverse problems and inverse optimal control problems.

The Neural Network shifted-proper orthogonal decomposition: A machine learning approach for non-linear reduction of hyperbolic equations

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate the Kolmogorov N−width decay thereby obtaining smaller linear subspaces with improved accuracy. These methods however must rely on the knowledge of the characteristic speeds in phase space of the solution, limiting their range of applicability to problems with explicit functional form for the advection field. In this work we approach the problem of automatically detecting the correct pre-processing transformation in a statistical learning framework by implementing a deep-learning architecture. The purely data-driven method allowed us to generalise the existing approaches of linear subspace manipulation to non-linear hyperbolic problems with unknown advection fields. The proposed algorithm has been validated against simple test cases to benchmark its performances and later successfully applied to a multiphase simulation.

Where do the fish come from, and where do they go? Seasonal observations of pelagic fishes from echosounder moorings in the Chukchi sea

Recent summer surveys of the Chukchi Sea determined that pelagic fishes were dominated by large numbers of age-0 Arctic cod and walleye pollock, while adult fishes are comparatively scarce. Modeling based on regional currents indicates that these age-0 fishes are likely advected to the north in fall; however, the source and fate of these fishes remains unclear as this region is seasonally ice-covered. To determine the movement and variability of this age-0 gadid population, bottom-moored multifrequency echosounders were deployed at three locations in the northeastern Chukchi Sea from 2017-2019. These observations indicate that the abundance and composition of the pelagic community on the Chukchi Sea shelf is highly variable over seasonal time scales. Fish abundance was very low in winter, increased in May, and reached peak abundance in late summer. Target strength and diel vertical migration of fishes increased in summer, indicating that this is a key period for growth. Age-0 gadids were displaced to the northeast, consistent with the dominant advection on the shelf. Fish speeds and headings were strongly correlated with local currents, providing evidence that these small age-0 fishes are primarily being passively transported and behavior plays a limited role in population distribution.

Bivariant species mixing and pressure drop within a hybrid periodic modulated microslit

In this article, a mathematical study is presented on electroosmotic flow (EOF) of power law fluids driven by an external electric field, where the heterogeneity of a microslit is created by multiple wavy triangular modulated polarized wall hurdles. The primary aim of this paper is to demonstrate and depict the mixing performance that generating more retention time and enhancing the interface area, which is evaluated both analytically and computationally. EOF in microchannels is restricted to low Reynolds numbers with a relatively high viscosity effect, which could predict advection domination in flow mixing due to heterogeneities that can supersede the need of flow turbulence. The numerical experiment is performed for the flow phenomena of this novel alternating microgrooves' patterning to generate an intensively transverse flow field, which represents strong reverse flow due to a higher pressure drop. The geometry modification and potential heterogeneity are the key factors to disturb the flow stream by fluid folding and stretching, leading to significant improvement in mixing efficiency. The numerical computations are performed for the nonlinear coupled Nernst–Planck–Navier Stokes equations using a control volume approach over a staggered grid algorithm to elaborate the performance of the electric potential distribution, the external electric field, the flow field, and the species concentration, which are the major contributors of the mixing efficiency. The evaluated results confirm that surface modulation substantially reduces the mass flow rate, effectively resulting in an increase in the retention time of the flow diffusion, which is justified through analytical testing. The nonlinear coupling effects are found to be more pronounced for shear thickening fluids rather than shear thinning and Newtonian solutions, resulting in a low torque corresponding to equilibrium conditions. To achieve a targeted mixing performance, it is observed that flow behavior indices should be optimized in terms of aversion of flow behavior index, viscous dissipation, and yield stress effect.

Equivalence of DEC and box methods for the diffusion–advection–reaction equation

We show that the discrete exterior calculus (DEC) method can be cast as the earlier box method for the diffusion–advection–reaction problem in the plane. Consequently, error estimates are established, proving that the DEC method is comparable to the finite element method with linear elements. Also a stabilization technique is introduced for dominant advection problems.

Goal-based angular adaptivity for Boltzmann transport in the presence of ray-effects

Boltzmann transport problems often involve heavy streaming, where particles propagate long distance due to the dominance of advection over particle interaction. If an insufficiently refined non-rotationally invariant angular discretisation is used, there are areas of the problem where no particles will propagate. These “ray-effects” are problematic for goal-based error metrics with angular adaptivity, as the metrics in the pre-asymptotic region will be zero/incorrect and angular adaptivity will not occur. In this work we use low-order filtered spherical harmonics, which are rotationally invariant and hence not subject to ray-effects, to “bootstrap” our error metric and enable highly refined anisotropic angular adaptivity with a Haar wavelet angular discretisation. We test this on three simple problems with pure streaming in which traditional error metrics fail. We show our method is robust and produces adapted angular discretisations that match results produced by fixed a priori refinement with either reduced runtime or a constant additional cost even with angular refinement.

Traveling wave solutions and stability behaviours under advection dominance for singularly perturbed advection-diffusion-reaction processes

Abstract In this paper, different traveling wave solutions of the kink type are obtained for significant advection-diffusion-reaction mechanisms such as the singularly perturbed generalized Burgers Huxley and Burgers Fisher equations. To achieve this, a nonlinear transformation and an ansatz method have been utilized. Stability analysis is performed on different types of equations to detect the effects of the coefficients on the stability of the obtained solutions. Particularly under advection dominant cases, the stability of the derived solutions is examined separately. It is observed that especially the coefficient of nonlinearity, and partly one of the reaction coefficients, determine the stability behaviour under advection dominance.

Possible Detection of Magnetic Anomaly During Tsunami Events in Indonesian Regions Using Global Magnetogram Records

Ocean flow generates secondary, weak magnetic signals relative to the main field induced by the Earth spinning motion, where the secondary signals lead to magnetic anomaly. The anomaly were apparently observed as short-lived variation in secondary field components, namely the vertical bz and horizontal components bH , respectively, during tsunami occurrence. In this study, maximum amplitudes associated with these components were determined using theoretical approaches and field records on global magnetogram provided by INTERMAGNET and BCMT. The roles played by a depth ratio of h/L where h and L are the ocean depth and characteristic length, respectively, and a speed ratio of c/cs where c and cs are the speed for linear long wave solution and the complex speed involving ocean diffusion, respectively, are here examined using Indonesian case studies of tsunami with respect to trans-Pacific tsunamis as reference. For cases with advection dominance, it was found that frozen-flux theory can be used to estimate bz and bH, consistent with values provided by the global magnetic institutions. In short, whereas bz is a measure of water surface elevation and hence tsunami height offshore, bH is an indicator for tsunami propagation direction. Detection of magnetic anomaly prior to tsunami arrivals at coastal zones is thus possible, making it crucial for tsunami early warning.

Stably stratified exact coherent structures in shear flow: the effect of Prandtl number

We examine how known unstable equilibria of the Navier-Stokes equations in plane Couette flow adapt to the presence of an imposed stable density difference between the two boundaries for varying values of the Prandtl number $Pr$, the ratio of viscosity to density diffusivity, and fixed moderate Reynolds number, $Re=400$. In the two asymptotic limits $Pr \to 0$ and $Pr \to \infty$, it is found that such solutions exist at arbitrarily high bulk stratification but for different physical reasons. In the $Pr \to 0$ limit, density variations away from a constant stable density gradient become vanishingly small as diffusion of density dominates over advection, allowing equilibria to exist for bulk Richardson number $Ri_b \lesssim O(Re^{-2}Pr^{-1})$. Alternatively, at high Prandtl numbers, density becomes homogenised in the interior by the dominant advection which creates strongly stable stratified boundary layers that recede into the wall as $Pr\to\infty$. In this scenario, the density stratification and the flow essentially decouple, thereby mitigating the effect of increasing $Ri_b$. An asymptotic analysis is presented in the passive scalar regime $Ri_b \lesssim O(Re^{-2})$, which reveals $O(Pr^{-1/3})$-thick stratified boundary layers with $O(Pr^{-2/9})$-wide eruptions, giving rise to density fingers of $O(Pr^{-1/9})$ length and $O(Pr^{-4/9})$ width that invade an otherwise homogeneous interior. Finally, increasing $Re$ to $10^5$ in this regime reveals that interior stably stratified density layers can form away from the boundaries, separating well-mixed regions.

A FEniCS-based model for prediction of boundary layer transition in low-speed aerodynamic flows

In the paper, a finite element model is developed that predicts boundary layer transition in low-speed aerodynamic flows. The model is based on a Reynolds-averaged Navier-Stokes approach, where the incompressible form of the Navier-Stokes equations is solved together with a three-equation eddy-viscosity model utilizing the FEniCS framework. A least-square stabilized Galerkin method is employed in order to prevent numerical oscillations that can arise from dominant advection terms. The proposed FEniCS model is ideal for applications with complex geometries and is tested on high performance computing platforms for parallel processing. The FEniCS model is validated by comparing the skin friction coefficient as well as profiles of velocity and total fluctuation kinetic energy with the benchmark experimental data for transitional boundary layers on a flat plate. The validity of the solver is further examined using experimental measurements reported for a NLF(1)-0416 natural laminar flow airfoil at different angles of attack. The airfoil results are also compared with those obtained using XFOIL, a well-known tool for the design of two-dimensional airfoils. These comparisons suggest that the proposed FEniCS-based model can effectively simulate aerodynamic flow fields that involve laminar-to-turbulent transition.

Modeling Polarized Emission from Black Hole Jets: Application to M87 Core Jet

We combine three-dimensional general-relativistic numerical models of hot, magnetized Advection Dominated Accretion Flows around a supermassive black hole and the corresponding outflows from them with a general relativistic polarized radiative transfer model to produce synthetic radio images and spectra of jet outflows. We apply the model to the underluminous core of M87 galaxy. The assumptions and results of the calculations are discussed in context of millimeter observations of the M87 jet launching zone. Our ab initio polarized emission and rotation measure models allow us to address the constrains on the mass accretion rate onto the M87 supermassive black hole.

Factors affecting atmospheric vertical motions as analyzed with a generalized omega equation and the OpenIFS model

ABSTRACTA statistical analysis of the physical causes of atmospheric vertical motions is conducted using a generalized omega equation and a one-year simulation with the OpenIFS atmospheric model. Using hourly output from the model, the vertical motions associated with vorticity advection, thermal advection, friction, diabatic heating, and an imbalance term are diagnosed. The results show the general dominance of vorticity advection and thermal advection in extratropical latitudes in winter, the increasing importance of diabatic heating towards the tropics, and the significant role of friction in the lowest troposphere. As this study uses notably higher temporal resolution data than previous studies which applied the generalized omega equation, our results reveal that the imbalance term is larger than the earlier results suggested. Moreover, for the first time, we also explicitly demonstrate the seasonal and geographical contrasts in the statistics of vertical motions as calculated with the generalized omega equation. Furthermore, as our analysis covers a full year, significantly longer than any other previous studies, statistically reliable quantitative estimates of the relative importance of the different forcing terms in different locations and seasons can be made. One such important finding is a clear increase in the relative importance of diabatic heating for midtropospheric vertical motions in the Northern Hemisphere midlatitudes from the winter to the summer, particularly over the continents. We also find that, in general, the same processes are important in areas of both rising and sinking motion, although there are some quantitative differences.

Error estimates for transport problems with high Péclet number using a continuous dependence assumption

In this paper we discuss the behavior of stabilized finite element methods for the transient advection–diffusion problem with dominant advection and rough data. We show that provided a certain continuous dependence result holds for the quantity of interest, independent of the Péclet number, this quantity may be computed using a stabilized finite element method in all flow regimes. As an example of a stable quantity we consider the parameterized weak norm introduced in Burman (2014). The same results may not be obtained using a standard Galerkin method. We consider the following stabilized methods: Continuous Interior Penalty (CIP) and Streamline Upwind Petrov–Galerkin (SUPG). The theoretical results are illustrated by computations on a scalar transport equation with no diffusion term, rough data and strongly varying velocity field.

Variability of geostrophic airflow over Poland, 1951-2014

Abstract The paper presents the analysis of the anemological conditions variability over Poland with the usage of geostrophic wind vector as an objective (and homogenous) information concerning the airflow over the area of research. The geostrophic wind vector components are calculated using SLP and air temperature (at sigma 995 level) at selected gridpoints which were subsequently interpolated to a central point thus describing the average flow over the research area. The data originated from NCEP/NCAR Reanalysis and its temporal range was 1951-2014. The analysis covers statistical characteristics of the overall annual cycle as well as trend analysis of the airflow features over Poland: geostrophic wind vector module (V), and its zonal (u) and meridional (v) components. Aside from general statistical characteristics for averages and extremes (quantiles 10% and 90%) GEV distribution was fitted to maximum annual/monthly geostrophic wind speed values which allowed the estimation of return levels for selected return periods. For the period 1951-2014 average geostrophic wind velocity over Poland equals 7.4 ms−1 and the 99% quantile exceeds 21 ms−1. Maximum speed ever recorded equalled 37.6 ms−1. Geostrophic wind vector module (V) and its components (u, v) exhibit clear annual cycle with the highest V values in winter. Positive (westerly) u values dominate in the colder part of the year. In spring the dominance of eastern advection appears and in summer the prevalence of westerly flow is only minimal. There exists a distinctive variability of decadal directional structure and this is clearly visible in the substantial increase in the share of western sector frequencies in 1981-1990 and following decade. Monthly V averages do not exhibit (except October) statistically significant trends whereas in spring and summer months as well as for annual averages of u component trend is significant. There are virtually no significant changes in the v values. GEV analysis allowed the year to be divided into two parts. Warm one with relatively low return levels – for many months not exceeding 20 ms−1 even for 50y return period. On the other hand winter months return level values exceed 30 ms−1 even for relatively short return periods (20y) with upper estimates for 100y return period closing to 40 ms−1.

Jet Magnetically Accelerated from Advection Dominated Accretion Flow

A jet model for the jet power arising from a steady, optically thin, advection dominated accretion flow (ADAF) around a Kerr black hole (BH) is proposed. We investigate the typical numerical solutions of ADAF, and calculate the jet power from an ADAF using a general relativistic version of electronic circuit theory. It is shown that the jet power concentrates in the inner region of the accretion flow, and the higher the degree to which the flow advection-dominated is, the lower the jet power from the ADAF is.

Interpreting the effect of soil texture on transport and removal of nitrate-N in saline coastal tidal flats under steady-state flow condition

Tidal-flats play important roles in oceanic nitrogen (N) cycles. Particularly, N loss in the tidal-flats depends on soil texture and yet the dominant N removal mechanism in relation to soil texture is not clear. Therefore, the objective of this study was to investigate the effect of soil texture on NO3−-N removal and transport in texturally contrasting tidal-flats of the western coast of Korea [Gangwha (GH, silt) and Saemangeum (SMG, loamy sand) sites]. To interpret the experimental results, we compared the time-course patterns of NO3−-N disappearance during incubation under intertidal and subtidal conditions and the patterns of breakthrough curves (BTCs) of NO3−-N with a conservative tracer (Br−) during miscible displacement experiment. Nitrate disappearance by denitrification was negligible for SMG soils, but was 1.6 and 2.3mgNkg−1 soil day−1 under intertidal and subtidal conditions for GH soils, respectively. The BTCs of NO3−-N and Br− were identical and followed Gaussian distributions in SMG tidal-flats, while those obtained for GH tidal-flats were broad and asymmetrical. Calculated Pêclet number of Br− in seawater matrix by fitting the CXTFIT model to the measured BTCs was 45.03 for SMG and 4.93 for GH tidal-flats, indicating dominance of advection over dispersion for the former, and vice versa for the latter. From a mass balance of NO3−-N, nearly all of the added NO3−-N (38.8mg) was recovered in the effluents with a slight unaccounted-for portion (2.8mg) in SMG system, indicating the possibility of an intense off-shore NO3−-N discharge (leaching) from the tidal-flats. In contrast, a considerably large amount (27.0mg) of added NO3−-N was not recovered in GH system but nearly one-third (13.5mg) was recovered in the effluents, suggesting that denitrification dominates over off-shore discharge in NO3−-N removal. Our results showed that the patterns of NO3−-N removal was different depending on soil texture of the tidal-flats and that a dominant mechanism of NO3−-N removal was denitrification in GH tidal-flats and was off-shore discharge in SMG tidal-flats. Therefore, NO3−-N removal characteristics of tidal-flats should be predetermined for site-specific management of waste water N loadings to coastal water systems.