Advection Velocity Research Articles

On the free surface boundary of moving particle semi-implicit method for thermocapillary flow

The moving particle semi-implicit (MPS) method has great potential in dealing with free surface flow due to its Lagrangian nature. In most cases, the free surface boundary is simply served as the pressure boundary condition. In this paper, an improved MPS method is presented for thermocapillary driven free surface flow. A series of surface nodes explicitly represent the free surface boundary. The normal stress on the free surface provides the Dirichlet pressure boundary condition, while the velocity boundary condition, i.e., Marangoni stress, is enforced through the Taylor series expansion and least squares method. Meanwhile, a quasi-Lagrangian formulation is introduced to avoid particle clustering and the corresponding numerical instability by slightly modifying the advection velocity. The upwind scheme is employed for the convection term to obtain accurate and stable results. A novel constraint scheme with the divergence of provisional velocity is developed for the pressure gradient to enhance stability further. The consistency of the derived generalized boundary condition is firstly verified with a simple convergence test. Then, several numerical tests, including square patch rotation, lid-driven and square droplet oscillation, are simulated to show the improvements. Finally, thermocapillary driven flows in an open cavity without and with buoyancy effect are studied. Good agreements are obtained by comparing with reference simulations taken from literature. Heat transfer characteristics are further investigated for different dimensionless numbers, including the Rayleigh number and Marangoni number.<PE-FRONTEND>

Dispersion in doublet-type flows through highly anisotropic porous formations

Steady doublet-type flow takes place in a porous formation, where the log-transform $Y = \ln K$ of the spatially variable hydraulic conductivity $K$ is regarded as a stationary random field of two-point autocorrelation $\rho _Y$ . A passive solute is injected at the source in the porous formation and we aim to quantify the resulting dispersion process between the two lines by means of spatial moments. The latter depend on the distance $\ell$ between the lines, the variance $\sigma ^2_Y$ of $Y$ and the (anisotropy) ratio $\lambda$ between the vertical and the horizontal integral scales of $Y$ . A simple (analytical) solution to this difficult problem is obtained by adopting a few simplifying assumptions: (i) a perturbative solution, which regards $\sigma ^2_Y$ as a small parameter, of the velocity field is sought; (ii) pore-scale dispersion is neglected; and (iii) we deal with a highly anisotropic formation ( $\lambda \lesssim 0.1$ ). We focus on the longitudinal spatial moment, as it is of most importance for the dispersion mechanism. A general expression is derived in terms of a single quadrature, which can be straightforwardly carried out once the shape of $\rho _Y$ is specified. Results permit one to grasp the main features of the dispersion processes as well as to assess the difference with similar mechanisms observed in other non-uniform flows. In particular, the dispersion in a doublet-type flow is observed to be larger than that generated by a single line. This effect is explained by noting that the advective velocity in a doublet, unlike that in source/line flows, is rapidly increasing in the far field owing to the presence there of the singularity. From the standpoint of the applications, it is shown that the solution pertaining to $\lambda \to 0$ (stratified formation) provides an upper bound for the dispersion mechanism. Such a bound can be used as a conservative limit when, in a remediation procedure, one has to select the strength as well as the distance $\ell$ of the doublet. Finally, the present study lends itself as a valuable tool for aquifer tests and to validate more involved numerical codes accounting for complex boundary conditions.

Sweeping Effects Modify Taylor’s Frozen Turbulence Hypothesis for Scalars in the Roughness Sublayer

AbstractTaylor’s frozen turbulence hypothesis (FTH) is investigated in the roughness sublayer of a sloped vineyard canopy using a spatial array of fine‐wire thermocouples and ultrasonic anemometers. The Ellipse Approximation (EA) method is applied to the measured space‐time temperature correlation function to delineate sweeping effects from advection velocity. Sweeping effects are explained primarily by the turbulence kinetic energy. Upon the removal of sweeping effects, the advection velocity is found to be commensurate with the mean velocity.

Multiband nonthermal radiative model of pulsar wind nebulae: Study of the effects of advection and diffusion

Aims. Nonthermal radiation properties of pulsar wind nebulae (PWNe) are studied in the frame of a time-dependent model with particle advection and diffusion. Methods. The dynamical and radiative evolution of a PWN was self-consistently solved in the model. The time-dependent lepton (electrons and positrons) equation is described by particle injection, advection, diffusion, adiabatic loss, and radiative loss. Nonthermal emission from a PWN is mainly produced by the relativistic leptons through synchrotron radiation and inverse Compton process. Results. The effect of particle transport including advection and diffusion was analyzed, showing that the particle transport process induces a decrease in the nebula flux, and that the total flux decreases with the increase in advection velocity and diffusion coefficient. Meanwhile, the particle transport processes may play an important role in modifying the spectrum of the emitted radiation at X-ray and TeV wavelengths, but only have slightly effects in radio and GeV bands. We applied our model to the three PWNe Crab nebula, 3C 58, and G54.1+0.3, and observed that the spectral energy distributions of photon emissions from the three PWNe are reproduced well. Our results indicate that (i) the particle cooling processes are dominated by adiabatic loss in lower-energy bands and synchrotron loss dominates for the higher-energy particles; and (ii) the particle transport processes are advection dominated, and a slow diffusion may occur within the Crab nebula, 3C 58, and G54.1+0.3.

Competing thermal and solutal advection decelerates droplet evaporation on heated surfaces

We report the complex evaporation kinetics of saline sessile droplets on surfaces with elevated temperatures. Our previous studies show that on non-heated substrates, saline sessile droplets evaporate faster compared to the water counterparts. In the present study, we discover that on heated surfaces, the saline droplets evaporate slower than the water counterpart, thereby posing a counter-intuitive phenomenon. The reduction in the evaporation rates is directly dependent on the salt concentration and the surface wettability. Natural convection around the droplet and thermal modulation of surface tension is found to be inadequate to explain the mechanisms. Flow visualizations using particle image velocimetry (PIV) reveal that the morphed advection within the saline droplets is a probable reason behind the arrested evaporation. Infrared thermography is employed to map the thermal state of the droplets. A thermo-solutal Marangoni based scaling analysis is put forward and the major governing non-dimensional numbers have been accounted for in the analysis. It is observed that the Marangoni flow and internal advection borne of thermal and solutal gradients are competitive, thereby leading to the overall decay of internal circulation velocity compared to the equivalent pure water case, which reduces the evaporation rates. The theoretically proposed advection velocities conform to the experimental results. This study sheds rich insight on a novel species transport behaviour in saline droplets.

Dynamics of A+B→C reaction fronts under radial advection in a Poiseuille flow.

A+B→C reaction fronts describe a wide variety of natural and engineered dynamics, according to the specific nature of reactants and product. Recent works have shown that the properties of such reaction fronts depend on the system geometry, by focusing on one-dimensional plug flow radial injection. Here, we extend the theoretical formulation to radial deformation in two-dimensional systems. Specifically, we study the effect of a Poiseuille advective velocity profile on A+B→C fronts when A is injected radially into B at a constant flow rate in a confined axisymmetric system consisting of two parallel impermeable plates separated by a thin gap. We analyze the front dynamics by computing the temporal evolution of the average over the gap of the front position, the maximum production rate, and the front width. We further quantify the effects of the nonuniform flow on the total amount of product, as well as on its radial concentration profile. Through analytical and numerical analyses, we identify three distinct temporal regimes, namely (i) the early-time regime where the front dynamics is independent of the reaction, (ii) the transient regime where the front properties result from the interplay of reaction, diffusion that smooths the concentration gradients and advection, which stretches the spatial distribution of the chemicals, and (iii) the long-time regime where Taylor dispersion occurs and the system becomes equivalent to the one-dimensional plug flow case.

Analysis of fabrication and crack-induced porosity migration in mixed oxide fuels for sodium fast reactors by the finite element method

We present an engineering-scale model for the migration of porosity in a fuel pellet experiencing a temperature gradient. The system of coupled pore advection and heat diffusion equations governing the problem is solved by a fixed-point iteration technique. The coupling between porosity and temperature fields is considered via the dependency of pore advection velocity on the local temperature and temperature gradient, and via the dependency of fuel thermal conductivity and of the volumetric power source on the local porosity. We employ the finite element method to discretize the resulting equations. As pure advection solutions obtained by this method are well-known to present spurious spatial oscillations, we introduce stabilization techniques in the pore advection equation. The proposed model is first tested against a benchmark problem representative for the conditions of an uranium-plutonium oxide fuel pellet irradiated in a sodium fast reactor. The results are compared to the those obtained by a model implemented in the BISON fuel performance code. The analysis shows how the results of the newly developed model are in line with those obtained by the reference model, and underlines a superior stability of the solution. The model is then applied to analyze the contribution of as-fabricated and crack-induced porosities in determining the fuel restructuring and in particular the central hole formation. A comparison to experimental data shows the impact of considering crack-induced porosity to predict the extent of the central void.

Improved Domenico solution for three-dimensional contaminant transport

The Domenico solution is a widely used analytical solution in screening tools such as BioScreen, FATE5, BioChlor, ART3D, ArcNLET, Quick-Domenico, etc., to simulate the three-dimensional transport of reactive contaminants in groundwater. While being approximate, this solution presents a convenient closed-form expression for computing plume contaminant concentrations without the need for numerical integration. Previous studies have mathematically shown that the Domenico solution provides correct estimates of contaminant plume concentrations when the value of longitudinal dispersivity is zero. However, under non-zero longitudinal dispersivity values, the errors in the Domenico solution increase, especially at plume locations beyond the advective front. The nature of these errors places severe limitations on the applicability of the Domenico solution in simulating realistic contaminant transport problems. Here, we present a new closed-form solution for three-dimensional (3D) reactive contaminant transport that overcomes this limitation. We introduce the concept of characteristic residence time, which represents the average time taken by a contaminant particle to reach a given (x, y, z) location. We show that along the plume centerline, the characteristic residence time exhibits three features, (i) initial linear response with a slope equal to the inverse of advection velocity, (ii) final saturation response with a maximum value of simulation time (iii) transition between the initial and final responses at the region surrounding the advective front, with sharper transitions at lower longitudinal dispersivities and smoother transitions at higher longitudinal dispersivities. We calibrate the Ramberg-Osgood function to fit the behavior of the characteristic residence time along the plume centerline and use this to develop a new and improved closed-form approximation for the Domenico solution. Without any additional computational effort, our new and improved solution better approximates the solute concentrations of a three-dimensional contaminant plume under realistic values of longitudinal dispersivity. Our improved solution closely matches the exact analytical solution, especially at plume locations beyond the advective front, where the Domenico solution performs poorly. Existing screening tools can be readily be retrofitted with the new and improved solution to provide more accurate estimates for plume concentrations.

Global existence for the two-dimensional Kuramoto-Sivashinsky equation with advection

We study the Kuramoto-Sivashinsky equation (KSE) in scalar form on the two-dimensional torus with and without advection by an incompressible vector field. We prove local existence of mild solutions for arbitrary data in L 2. We then study the issue of global existence. We prove global existence for the KSE in the presence of advection for arbitrary data, provided the advecting velocity field v satisfies certain conditions that ensure the dissipation time of the associated hyperdiffusion-advection equation is sufficiently small. In the absence of advection, global existence can be shown only if the linearized operator does not admit any growing mode and for sufficiently small initial data.

Measurement of kinetic constant of protein binding using microfluidics and particle diffusometry

Protein-protein interaction is widely used in biological science and biomedical engineering research Moreira et al. (2007). Accurate measurement of binding kinetics is essential for understanding protein-protein interactions. Current gold standard assays, such as surface plasmon resonance (SPR), bio-layer interferometry (BLI) and quartz crystal microbalance (QCM), can generate precise and real-time kinetics data. However, these methods usually require expensive instruments housed in core facilities and high-level expertise, which is not convenient for most labs to implement. We developed a new method based on microfluidics and particle diffusometry (PD) to measure protein binding kinetics, which only needs very general lab equipment including a fluorescent microscope to take photos, a syringe pump to inject solutions, capillary tubing, a simple chip made on a glass slide and a computer to process images. To measure the binding rate of a protein pair, both proteins are conjugated with beads of different sizes, respectively. The bead solutions are diluted to appropriate concentrations and injected into a Y-junction channel by a syringe pump. In the microchannel, the two kinds of beads will meet at the interface and bind due to surface protein interactions. Therefore, the size of the beads in solution gradually increases and the Brownian motion will be less and less drastic until the reaction is saturated. Taking photos recording this dynamic process, the apparent change in size of the beads can be measured by particle diffusometry and used for extracting binding kinetics. Particle diffusometry is a correlation-based and non-intrusive optical detection method to analyze properties of fluid and particle such as viscosity, temperature and particle diameter Chamarthy et al. (2009); Clayton et al. (2016, 2017b,a); Hohreiter et al. (2002). It was initially developed to determine errors caused by thermal noise in particle image velocimetry (PIV). PD always analyzes image pairs. A single image of a particle laden flow is first used to do auto-correlation, correlating with itself, which will generate a high and sharp peak. Then it is cross-correlated with a successive image with a known time interval ∆t. Because particles slightly deviate away from the initial positions after time ∆t, due to Brownian motion, the correlation peak is lower and broader than that of auto-correlation. Auto- and cross-correlation peaks are fit into Gaussian function to find peak widths, by which the particle size can be computed as long as the viscosity and temperature do not change. Processing the image sets of the protein-conjugated particles’ binding process, we acquire the relation of particle size and time, which can be used to solve protein binding kinetics. An equation of protein interaction and particle volume is derived to work out association rate from particle diameter data acquired by PD. In this study, we measured streptavidin-biotin binding rate. Streptavidin is conjugated with 20nm beads and biotin is immobilized onto 200nm beads. Proteins on the two kinds of beads bind rapidly after mixing in the main channel. It is necessary to choose a narrow area at the interface of particle streams that diffusion does not limit the reaction. Since the liquid is flowing, there is both Brownian motion and advection in particle images. We used EDPIV, a software package developed by Prof. Steven Wereley’s lab, to measure advection velocity. When doing PD analysis, images are shifted following the PIV data to catch up with the flow. The photos are taken at the center layer in the middle of the channel, where there is no velocity gradient. Measuring a series of photo sets along the main channel at several points with known distances to each other, the relation of complex bead size and time can be acquired. Solving for the association constant, the measured value is 1.74 × 107M−1s−1, which is close to that of current gold standard assays. This novel PD-based method is accurate and requires only general lab facilities, making protein binding kinetics measurements accessible and practical for biological and biomedical labs.

A computational study of a new design configuration for a turbulence tunnel

A new kind of turbulence tunnel, the pure coherent shear source turbulence tunnel, proposed to produce high Reynolds number, approximately homogeneous isotropic turbulence is studied computationally. The Reynolds-averaged Navier–Stokes equations, along with the standard k − ϵ model for closure, are solved in the computations. The tunnel design studied here consists of a duct of square cross section with a plane at one end consisting of an array of round jets and suction vents. This plane, referred to as the momentum source plane (MSP), also a zero net-mass flux plane, forces the flow into the tunnel. The flow field inside consists of an advection-dominated region where the jets merge to form a combined flow, and an advection-free near-homogeneous turbulence region. Turbulence statistics in the advection-dominated and advection-free regions of the flow field, and the effect of parameters associated with the forcing that affects these statistics are studied. A plateau of turbulence statistics with rms of fluctuations as high as 0.8 times the mean advective velocity scale for the tunnel section, U T , is obtained in a region with negligible mean advection. The effect of geometrical configuration at the MSP on the turbulence quantities in the advection free region is studied. The Reynolds number based on Taylor length scale of the turbulence produced is estimated to be of the order of 350 in a tunnel of size 0.5 × 0.5 m2.

A high-order semi-Lagrangian method for the consistent Monte-Carlo solution of stochastic Lagrangian drift–diffusion models coupled with Eulerian discontinuous spectral element method

The explicit semi-Lagrangian method for solution of Lagrangian transport equations as developed in Natarajan and Jacobs (2020) is adopted for the solution of stochastic differential equations that is consistent with Discontinuous Spectral Element Method (DSEM) approximations of Eulerian conservation laws. The method extends the favorable properties of DSEM that include its high-order accuracy, its local and boundary fitted properties and its high performance on parallel platforms for the concurrent Monte-Carlo, semi-Lagrangian and Eulerian solution of a class of time-dependent problems that can be described by coupled Eulerian–Lagrangian formulations. Such formulations include the probabilistic models used for the simulation of chemically reacting turbulent flows or particle-laden flows. Consistent with an explicit, DSEM discretization, the semi-Lagrangian method seeds particles at Gauss quadrature collocation nodes within a spectral element. The particles are integrated explicitly in time according to a drift velocity and a Wiener increment forcing and form the nodal basis for an advected interpolant. This interpolant is mapped back in a semi-Lagrangian fashion to the Gauss quadrature points through a least squares fit using constraints for element boundary values. Stochastic Monte-Carlo samples are averaged element-wise on the quadrature nodes. The stable explicit time step Wiener increment is sufficiently small to prevent particles from leaving the element’s bounds. The semi-Lagrangian method is hence local and parallel and does not have the grid complexity, and parallelization challenges of the commonly used Lagrangian particle solvers in particle-mesh methods for solution of Eulerian–Lagrangian formulations. Formal proof is presented that the semi-Lagrangian algorithm evolves the solution according to the Eulerian Fokker–Planck equation. Numerical tests in one and two dimensions for drift–diffusion problems show that the method converges exponentially for constant and non-constant advection and diffusion velocities.

Buoyancy of post‐fertilised Dissostichus mawsoni eggs and implications for early life history

AbstractGametes from gravid Antarctic toothfish (Dissostichus mawsoni) were combined in vitro and buoyancy measurements were made on fertilised eggs during early development. Eggs were strongly positively buoyant, indicating that they would ascend quickly in the water column and reside near or in association with the underside of sea ice, which covers most of the spawning habitat during winter. An association with sea ice may provide: protection from the turbulence of ice‐free surface waters, a mechanism that modifies the velocity of advection by surface currents, and a habitat with a concentrated planktonic food source during spring months. An association with sea ice would also create spatial differences in egg advection patterns for eggs produced spanning a large geographic area. The effects of climate change on sea ice formation and melting patterns, or fishery‐induced changes in the spatial density of adults could then influence juvenile advection patterns and influence survival.

Rapid Formation of Jupiter and Wide-orbit Exoplanets in Disks with Pressure Bumps

Abstract The formation of gas-giant planets within the lifetime of a protoplanetary disk is challenging especially far from a star. A promising model for the rapid formation of giant-planet cores is pebble accretion in which gas drag during encounters leads to high accretion rates. Most models of pebble accretion consider disks with a monotonic, radial pressure profile. This causes a continuous inward flux of pebbles and inefficient growth. Here we examine planet formation in a disk with multiple, intrinsic pressure bumps. In the outer disk, pebbles become trapped near these bumps allowing rapid growth under suitable conditions. In the inner disk, pebble traps may not exist because the inward gas advection velocity is too high. Pebbles here are rapidly removed. In the outer disk, growth is very sensitive to the initial planet mass and the strength of turbulence. This is because turbulent density fluctuations raise planetary eccentricities, increasing the planet-pebble relative velocity. Planetary seeds above a distance-dependent critical mass grow to a Jupiter mass in 0.5–3 Myr out to at least 60 au in a 0.03 solar-mass disk. Smaller bodies remain near their initial mass, leading to a sharp dichotomy in growth outcomes. For turbulent α = 1e-4, the critical masses are 1e-4M ⊕ and 1e-3M ⊕ at 9 and 75 au, respectively. Pressure bumps in disks may explain the large mass difference between the giant planets and Kuiper Belt objects, and also the existence of wide-orbit planets in some systems.

Pegmatitic granite fluid compositions and thermochronometry in the Seridó Belt, Borborema Province, Brazil: Insights from trace element advection-diffusion-partitioning halos in host schist and gneiss

At the Seridó Belt pegmatitic province, fluid advection from dykes and sills led to trace element diffusion and partitioning in biotite, producing sub metric concentration halos in host mica schist and gneiss. We analyzed trace element concentration vs. distance profiles in the host rock of pegmatitic granite intrusions showing enrichments in Li, F, Cl, Zn, Rb, Nb, Sn, Cs, Ta, U and depletions in Sr and Ba. We estimated fluid temperatures in the range 600 to 700 °C using methods of Ti in biotite, F-OH in biotite-apatite and Tschermak component in biotite-muscovite. We analytically modeled thermal profiles around pegmatitic planar intrusions and found that cooling by thermal flats in the first meters into the host rock is reached in 100 years for a 10 m thick sill. The model constraints sustained heat flow during pegmatitic melt emplacement into a colder host rock. The measured trace element profiles were fitted with solutions of differential equations modeling advection-diffusion-partitioning in porous media under isothermal and cooling conditions. Each trace element profile is equally fitted by values of pegmatitic fluid concentration vs. fluid flux duration plotting as a straight line. We obtained a theorical framework combining pegmatitic fluid trace element composition, fluid flux duration and velocity, rock/fluid trace element partition coefficient, and cooling rate. Using published fluid inclusion trace element composition, we obtained fluid flux duration between tens of years to several centuries for the studied profiles. In the case of low temperature fluid flux at 450 °C the modeled flux duration is increased by less than one order of magnitude. The results allow us to interpret the trace element halos as sub millennial hot isothermal fluid influx from the pegmatites into their host rock. Trace element partitioning from the fluid into host rock falls mostly within the range of 0.01 to 25 and decreases in the order Nb, Cu, Rb, Zn-Li, Cs-Sn. The model constraints fluid advection velocity between 1 × 10−11 m/s and 1 × 10−9 m/s, typical of regional metamorphism to shear focused fluid flow regimes. The trace element enrichment of biotite along the profiles reproduces the observed pattern for whole rock, indicating that biotite is their main sink during pegmatitic fluid influx. Using experimental F in biotite diffusivity we obtained a minimal planar diffusion distance, or the effective porosity, between 7 and 15 μm for the total F re-homogenization of metamorphic biotite by pegmatitic fluid. As shown from others fluid-present petrogenetic systems, the trace element contents of biotite in host rock at the contact with pegmatitic intrusions can be a potential tool for the assessment of their rare metal potential.

The half-order energy balance equation – Part 1: The homogeneous HEBE and long memories

Abstract. The original Budyko–Sellers type of 1D energy balance models (EBMs) consider the Earth system averaged over long times and apply the continuum mechanics heat equation. When these and the more phenomenological box models are extended to include time-varying anomalies, they have a key weakness: neither model explicitly nor realistically treats the conductive–radiative surface boundary condition that is necessary for a correct treatment of energy storage. In this first of a two-part series, I apply standard Laplace and Fourier techniques to the continuum mechanics heat equation, solving it with the correct radiative–conductive boundary conditions and obtaining an equation directly for the surface temperature anomalies in terms of the anomalous forcing. Although classical, this equation is half-ordered and not integer-ordered: the half-order energy balance equation (HEBE). A quite general consequence is that although Newton's law of cooling holds, the heat flux across surfaces is proportional to a half-ordered (not first-ordered) time derivative of the surface temperature. This implies that the surface heat flux has a long memory, that it depends on the entire previous history of the forcing, and that the temperature–heat flux relationship is no longer instantaneous. I then consider the case in which the Earth is periodically forced. The classical case is diurnal heat forcing; I extend this to annual conductive–radiative forcing and show that the surface thermal impedance is a complex valued quantity equal to the (complex) climate sensitivity. Using a simple semi-empirical model of the forcing, I show how the HEBE can account for the phase lag between the summer maximum forcing and maximum surface temperature Earth response. In Part 2, I extend all these results to spatially inhomogeneous forcing and to the full horizontally inhomogeneous problem with spatially varying specific heats, diffusivities, advection velocities, and climate sensitivities. I consider the consequences for macroweather (monthly, seasonal, interannual) forecasting and climate projections.

Thallium Isotope Fractionation During Magma Degassing: Evidence From Experiments and Kamchatka Arc Lavas

AbstractThallium (Tl) isotope ratios are an emerging tool that can be used to trace crustal recycling processes in arc lavas and ocean island basalts (OIBs). Thallium is a highly volatile metal that is enriched in volcanic fumaroles, but it is unknown whether degassing of Tl from subaerial lavas has a significant effect on their residual Tl isotope compositions. Here, we present Tl isotope and concentration data from degassing experiments that are best explained by Rayleigh kinetic isotope fractionation during Tl loss. Our data closely follow predicted isotope fractionation models in which TlCl is the primary degassed species and where Tl loss is controlled by diffusion and natural convection, consistent with the slow gas advection velocity utilized during our experiments. We calculate that degassing into air should be associated with a net Tl isotope fractionation factor of αnet = 0.99969 for diffusion and natural gas convection (low gas velocities) and αnet = 0.99955 for diffusion and forced gas convection (high gas velocities). We also show that lavas from three volcanoes in the Kamchatka arc exhibit Tl isotope and concentration patterns that plot in between the two different gas convection regimes, implying that degassing played an important role in controlling the observed Tl isotope compositions in these three volcanoes. Literature inspection of Tl isotope data for subaerial lavas reveals that the majority of these appear only minorly affected by degassing, although a few samples from both OIBs and arc volcanoes can be identified that likely experienced some Tl degassing.

Thermal Submesoscale Motions in the Nocturnal Stable Boundary Layer. Part 1: Detection and Mean Statistics

Submesoscale motions within the stable boundary layer were detected during the Shallow Cold Pool Experiment conducted in the Colorado plains, Colorado, U.S.A. in 2012. The submesoscale motion consisted of two air layers creating a well-defined front with a sharp temperature gradient, and further-on referred to as a thermal submesofront (TSF). The semi-stationary TSFs and their advective velocities are detected and determined by the fibre-optic distributed-sensing (FODS) technique. An objective detection algorithm utilizing FODS measurements is able to detect the TSF boundary, which enables a detailed investigation of its spatio–temporal statistics. The novel approach in data processing is to conditionally average any parameter depending on the distance between a TSF boundary and the measurement location. By doing this, a spatially-distributed feature like TSFs can be characterized by point observations and processes at the TSF boundary can be investigated. At the TSF boundary, the air layers converge, creating an updraft, strong static stability, and vigorous mixing. Further, the TSF advective velocity of TSFs is an order of magnitude lower than the mean wind speed. Despite being gentle, the topography plays an important role in TSF formation. Details on generating mechanisms and implications of TSFs on the stable boundary layer are discussed in Part 2.

Flow patterns and free-surface dynamics in hydraulic jump on pebbled rough bed

Some basic characteristics of a classic hydraulic jump flow over a pebbled rough bed, as well as on a smooth bed as a reference, are presented in this experimental study. For the experiments, an inflow Froude number Fr1from 1.54 to 4.94 and inflow Reynolds number Re1from 42 000 to 230 000 were considered. Visual observations and measurements suggested some differences between the formation of a hydraulic jump on rough and smooth bed configurations, including different air entrainment processes, larger vortical structures in the roller length and stronger backward flow in the upper layer. Furthermore, the jump roller and aerated flow lengths were shorter on a pebbled rough bed than on a smooth bed, while the dimensionless advection velocity of large vortices was the same for both bed types. The instantaneous jump toe perimeter showed the largest variation at the largest Fr1and was generally larger on rough bed than on smooth bed. Larger oscillations of the free-surface profile were observed on smooth bed, highlighting that roughness resulted in smaller free-surface oscillations, suggesting the higher rate of energy dissipation.

A Comparative Study from Spectral Analyses of High-Order Methods with Non-Constant Advection Velocities

The response of numerical methods to flow properties dynamic changes is a key ingredient of numerical modeling calibration. In this context, a range of spectral analyses and canonical fluid mechanics problems are explored to compare the responses of the high-order spectral difference scheme and of the flux reconstruction methods. Spatial eigen-analysis (Hu et al. in J Comput Phys 151(2):921–946, 1999; Hu and Atkins in J Comput Phys 182(2):516–545, 2002), based on spatially evolving oscillations, is used to get useful insights for problems with inflow/outflow boundary conditions (i.e., non-periodic), while non-modal analysis (Fernandez et al. in Comput Methods Appl Mech Eng 346:43–62, 2019. https://doi.org/10.1016/j.cma.2018.11.027 ) focusses on the short-term dynamics of the discretised system. These two approaches are also extended to the general scalar conservation law with non-constant advection velocity. All these tools are used to obtain more insight about the expected behavior of the mentioned numerical methods for typical engineering applications. On this regard, despite the lack of a mathematical proof of stability in the non-linear case, the selected numerical schemes, for which an extensive literature is available for applications to Euler and Navier–Stokes equations, will be assumed to be stable. Findings are then verified considering one-dimensional linear advection, and two- and three-dimensional flows modeled with the compressible Euler equations. Implications in the accurate control of numerical dissipation for turbulent flows is also addressed. Within the context of high-order methods, this work complement the former temporal spectral analyses of the discontinuous Galerkin approach discretising the linear advection equation.