Turbulent Advection Research Articles

Flow Field in a Skimming Flow Over a Vertical Drop Without End-Sill

ABSTRACTThe flow structure in the shear layer and in the recirculation zone of a skimming flow downstream of a vertical drop without end-sill measured using high speed particle image velocimetry (HSPIV) and flow visualization method is presented. The interface between the sliding jet and the recirculation zone (zone below sliding jet) was enhanced through non-ventilation condition between the drop structure and the jet. The flow field measured through HSPIV was used to represent the characteristics of mean streamwise velocity in the shear layer and mean horizontal velocity in the recirculation zone. With the growth of shear layer as the jet slides down over the recirculation zone, the momentum exchange from the sliding jet into the recirculation zone via the shear layer increases along with energy loss. Hence, it was observed that the amount of energy dissipated in the skimming flow at the drop structure without ventilation is greater than that with ventilation by an average value of 50% forYc/H≥ 0.2 (whereYc= critical depth andH= drop height). However, the flow structure in the recirculation zone is found to be analogous to that of turbulent plane wall jet. The nonlinear regression analysis is used to fit the regressed velocity profiles to the measured HSPIV mean velocity distributions. Further, the appropriate characteristic velocity and length scales are selected to attain the unique similarity profiles both in the shear layer and in the recirculation zone of the skimming flow. The selection of the characteristic scales is also discussed. The similarity profiles are well comparable with those of napped flow without end-sill and with ventilation as well as of skimming flow with end-sill and without ventilation. It is interesting to observe that, the proposed similarity profiles for the shear layer also map the data of backward-facing step flow and cavity shear flow. In addition, the turbulence characteristics in the shear layer, including turbulence intensities, turbulent kinetic energy, viscous and Reynolds shear stresses, and turbulence energy-budget balance, are illustrated in detail. From the variation of turbulence production it is observed that near the drop structure the energy exchange is from the chaotic recirculation zone to the sliding-jet flow, while in the later part it is reversed. Furthermore, the analysis of turbulence energy-budget balance indicates very significant role of turbulence production, pressure diffusion and turbulence diffusion as compared with turbulence advection that has very minor role in turbulence energy-budget balance for the central part of the shear layer.

Comparing Lagrangian and Eulerian models for CO<sub>2</sub> transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

Abstract. We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the Eulerian-based Weather Research Forecasting (WRF) model and the Lagrangian-based Stochastic Time-Inverted Lagrangian Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (Eulerian vs. Lagrangian) on models' spatial resolution is further investigated. A case study using airborne measurements during which two models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and Lagrangian time-scale in STILT is needed to achieve a better match between the Eulerian and the Lagrangian transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data.

Global variation of the dust-to-gas ratio in evolving protoplanetary discs

Recent theories suggest planetesimal formation via streaming and/or gravitational instabilities may be triggered by localized enhancements in the dust-to-gas ratio, and one hypothesis is that sufficient enhancements may be produced in the pile-up of small solid particles inspiralling under aerodynamic drag from the large mass reservoir in the outer disc. Studies of particle pile-up in static gas discs have provided partial support for this hypothesis. Here, we study the radial and temporal evolution of the dust-to-gas ratio in turbulent discs, that evolve under the action of viscosity and photoevaporation. We find that particle pile-ups do not generically occur within evolving discs, particularly if the introduction of large grains is restricted to the inner, dense regions of a disc. Instead, radial drift results in depletion of solids from the outer disc, while the inner disc maintains a dust-to-gas ratio that is within a factor of ~2 of the initial value. We attribute this result to the short time-scales for turbulent diffusion and radial advection (with the mean gas flow) in the inner disc. We show that the qualitative evolution of the dust-to-gas ratio depends only weakly upon the parameters of the disc model (the disc mass, size, viscosity, and value of the Schmidt number), and discuss the implications for planetesimal formation via collective instabilities. Our results suggest that in discs where there is a significant level of midplane turbulence and accretion, planetesimal formation would need to be possible in the absence of large-scale enhancements. Instead, trapping and concentration of particles within local turbulent structures may be required as a first stage of planetesimal formation.

Towards a geometrical classification of statistical conservation laws in turbulent advection

The paper revisits the compressible Kraichnan model of turbulent advection in order to derive explicit quantitative relations between scaling exponents and Lagrangian particle configuration geometry.

Observed ENSO teleconnections to Southern Ocean SST anomalies diagnosed from a surface mixed layer heat budget

This study examines the mechanisms that govern the El Niño Southern Oscillation (ENSO) teleconnections to variability in extratropical Southern Hemisphere sea surface temperature (SST) anomalies using several observational and reanalysis products. During the warm season, turbulent heat fluxes and heat advection by Ekman currents contribute equally to ENSO‐related SST variability throughout the Southern Ocean, while shortwave radiation has a larger contribution in the subtropics. A comparison of the ocean mixed layer heat budget between multiple re‐analysis products reveals that the relative contributions of the turbulent, radiative and Ekman heat fluxes to ENSO‐related SST anomalies is consistent between the NCEP, ERA‐40 and OAFlux/ISCCP products, but discrepancies exist with regard to the structure and amplitude of the turbulent heat fluxes and, to a lesser extent, the shortwave radiation. However, a comparison between the tendencies in SST and flux‐derived temperatures reveals minimal residuals, suggesting that the ENSO‐signal in the SST field can be resolved by turbulent, Ekman, and radiative heat fluxes, particularly in the ERA‐40 products.

Interactions among pressure, density, vorticity and their gradients in compressible turbulent channel flows

The interactions among pressure, density, vorticity and their gradients in compressible turbulent channel flows (TCF) are studied using direct numerical simulations (DNS). DNS of three isothermal-wall TCF for Mach number Ma = 0.2, 0.7, and 1.5, respectively are performed using a discontinuous Galerkin method (DGM). The Reynolds numbers of these three cases are ≈2800, based on the bulk velocity, bulk density, half channel width and dynamic viscosity at the wall. A high cross-correlation between density and spanwise vorticity occurs at y+≈4, which is coincident with the peak mean spanwise baroclinicity. The relationship between the spanwise baroclinicity and the correlation is analysed. The difference between the evolution of density and spanwise vorticity very near the wall is discussed. The transport equation for the mean product of density and vorticity fluctuations 〈ρ′ω′i〉 is presented and the distributions of terms in the 〈ρ′ω′z〉 transport equation indicate that the minima and maxima of the profiles are located around y+≈5. The connection between pressure gradients and vorticity fluxes for compressible turbulent flows with variable viscosity has been formulated and verified. High correlations (0.7–1.0) between pressure gradient and vorticity flux are found very close to the wall (y+<5). The correlation coefficients are significantly influenced by Ma and viscosity in this region. Turbulence advection plays an important role in destroying the high correlations between pressure gradient and vorticity flux in the region away from the wall (y+ > 5).

Semi-linear diffusion in and in Hilbert spaces, a FeynmanWiener path integral study

We present a proof for the existence and uniqueness of weak solutions for a cut-off and non-cut-off model of non-linear diffusion equation in finite-dimensional space useful for modeling flows on porous medium with saturation, turbulent advection, etc. and subject to deterministic or stochastic (white noise) stirrings. In order to achieve such goal, we use the powerful results of compacity on functional L p spaces (the AubinLion Theorem). We use such results to write a path-integral solution for this problem. Additionally, we present the rigorous functional integral solutions for the linear diffusion and wave equations defined in infinite-dimensional spaces (separable Hilbert spaces). These further results are presented in order to be useful to understand Polymer cylindrical surfaces probability distributions and functionals on String theory.

A Simple Reaction Time Scale for Under-Resolved Fire Dynamics

A reaction time scale model is developed for use in the eddy dissipation concept (fast chemistry limit) closure of the mean chemical source term in large-eddy simulation of fires. The novel aspect of the model is to consider a scaling regime for coarse mesh resolution based on buoyant acceleration. The model computes local time scales for diffusion, turbulent advection, and buoyant acceleration and takes the minimum of these as the local mixing time. The new model is implemented in the Fire Dynamics Simulator (FDS) and tested by comparing flame height predictions to the Heskestad correlation.

The Mathematics of Atmospheric Dispersion Modeling

The Gaussian plume model is a standard approach for studying the transport of airborne contaminants due to turbulent diffusion and advection by the wind. This paper reviews the assumptions underlying the model, its derivation from the advection-diffusion equation, and the key properties of the plume solution. The results are then applied to solving an inverse problem in which emission source rates are determined from a given set of ground-level contaminant measurements. This source identification problem can be formulated as an overdetermined linear system of equations that is most easily solved using the method of least squares. Various generalizations of this problem are discussed, and we illustrate our results with an application to the study of zinc emissions from a smelting operation.

Mean and Turbulence Properties of a Neutrally Buoyant Round Jet in a Wave Environment

An experimental study of a turbulent round jet discharged into a regular wave field is presented. The particle image velocimetry (PIV) technique was employed to measure instantaneous velocity fields of the flow. Quantitative mean and turbulence properties were obtained using ensemble- and phase-averaged methods. Both the jet potential core region and self-similar region were measured. Three different wave heights were used to examine the effect of wave steepness on the jet properties. Measurements were also taken at three different phases to examine the wave phase effect. Experimental results demonstrate that the mean jet width, turbulence intensity, and Reynolds stress increased significantly when the jet was acted on by the waves. In addition, the jet mean kinetic energy decreased whereas the turbulent kinetic energy increased when the jet was under the waves, indicating an increase in turbulence. The wave phase has an insignificant effect on the both the mean and turbulence properties. The turbulent kinetic energy budget in the self-similar region at different wave conditions was also examined. It was found that the turbulent production, advection, and dissipation terms all increase with the increase of the wave height.

A passive scalar-like model for rain applicable up to storm scale

Analysis of the data collected during the AMMA (African Monsoon Multidisciplinary Analyses) campaign shows that rain storms typical of the African monsoon have multifractal properties, and can be modelled by fractionally integrated multiplicative cascades. The originality of the present study lies in the application of a constraint, which results in the interior only of storms being investigated, such that the multifractal analysis is not affected by the presence of numerous zero values. The model is validated in the time domain by means of disdrometer measurements, and in the spatial domain with co-localized meteorological radar rain maps. The non-conservation parameter obtained in the spatial domain is found to be consistent with the assumption that the rain rate follows a passive scalar-like scaling law up to the scale of storms, including corrections due to fluxes intermittencies. Comparison of the value of this parameter with that obtained in the temporal domain indicates the presence of a space–time anisotropy, which could be explained by turbulent advection.

Submerged wall jets subjected to injection and suction from the wall

This paper presents an experimental study on turbulent flow characteristics in submerged plane wall jets subjected to injection (upward seepage) and suction (downward seepage) from the wall. The vertical distributions of time-averaged velocity components, turbulence intensity components and Reynolds shear stress at different horizontal distances are presented. The horizontal distributions of wall shear stress determined from the Reynolds shear stress profiles are also furnished. The flow field exhibits a decay of the jet velocity over a horizontal distance. The wall shear stress and the rate of decay of the jet velocity increase in the presence of injection and decrease with suction. Based on the two-dimensional Reynolds-averaged Navier–Stokes equations of a steady turbulent flow, the velocity and Reynolds shear stress distributions in the fully developed zone subjected to no seepage, injection and suction are theoretically computed. The response of the turbulent flow characteristics to injection and suction is analysed from the point of view of similarity characteristics, growth of the length scale and decay of the velocity and turbulence characteristics scales. The significant observation is that the velocity, Reynolds shear stress and turbulence intensities in the fully developed zone are reasonably similar under both injection and suction on applying the appropriate scaling laws. An analysis of the third-order moments of velocity fluctuations reveals that the inner layer of the jet is associated with the arrival of low-speed fluid streaks causing an effect of retardation. On the other hand, the upper layer of the jet is associated with the arrival of high-speed fluid streaks causing an effect of acceleration. Injection influences the near-wall distributions of the third-order moments by increasing the upward turbulent advection of the streamwise Reynolds normal stress. In contrast, suction influences the near-wall distributions of the third-order moments by increasing the downward turbulent advection of the streamwise Reynolds normal stress. Also, injection and suction change the vertical turbulent flux of the vertical Reynolds normal stress in a similar way. The streamwise turbulent energy flux travels towards the jet origin within the jet layer, while it travels away from the origin within the inner layer of the circulatory flow. The turbulent energy budget suggests that the turbulent and pressure energy diffusions oppose each other, and the turbulent dissipation lags the turbulent production. The quadrant analysis of velocity fluctuations reveals that the inward and outward interactions are the primary contributions to the Reynolds shear stress production in the inner and outer layers of the jet, respectively. However, injection induces feeble ejections in the vicinity of the wall.

Asymptotic analysis of transition to turbulence and chaotic advection in shear zonal flows on a beta-plane

The generation of narrow-band Rossby wave packets and the modulated vortex chains induced by them in a weakly-dissipative zonal flow on the beta-plane with a velocity profile in the form of a shear layer is studied. The analysis is performed within the framework of the asymptotic approach based on the distinguishing a thin critical layer inside of which the vortex chains are formed. The evolution equations, describing the simultaneous development of a wave packet envelope and vorticity perturbations in a nonlinear critical layer, are derived for a weakly supercritical flow. A transition to the complex dynamics of a wave packet (low-mode turbulence) is studied within the framework of a numerical solution of the derived equations and its mechanism is revealed. The onset of chaotic advection and anomalous diffusion of passive scalar in the critical layer is considered, and the exponent of the diffusion law is calculated.

Small-scale kinematic dynamo and non-dynamo in inertial-range turbulence

We investigate the Lagrangian mechanism of the kinematic ‘fluctuation’ magnetic dynamo in a turbulent plasma flow at small magnetic Prandtl numbers. The combined effect of turbulent advection and plasma resistivity is to carry infinitely many field lines to each space point, with the resultant magnetic field at that point given by the average over all the individual line vectors. As a consequence of the roughness of the advecting velocity, this remains true even in the limit of zero resistivity. We show that the presence of the dynamo effect requires sufficient angular correlation of the passive line vectors that arrive simultaneously at the same space point. We illustrate this in detail for the Kazantsev–Kraichnan model of the kinematic dynamo with a Gaussian advecting velocity that is spatially rough and white noise in time. In the regime where dynamo action fails, we also obtain the precise rate of decay of the magnetic energy. These exact results for the model are obtained by a generalization of the ‘slow-mode expansion’ of Bernard, Gawȩdzki and Kupiainen to non-Hermitian evolution. Much of our analysis applies also to magnetohydrodynamic turbulence.

Sufficient noise and turbulence can induce phytoplankton patchiness

Phytoplankton patchiness ubiquitously obser- ved in marine ecosystems is a simple phy- sical phenomenon. Only two factors are required for its formation: one is persistent variations of inhomogeneous distributions in the phytopl- ankton population and the other is turbulent stirring by eddies. It is not necessary to assume continuous oscillations such as limit cycles for realization of the first factor. Instead, a certain amount of noise is enough. Random fluctua-tions by environmental noise and turbulent ad-vection by eddies seem to be common in open oceans. Based on these hypotheses, we pro-pose seemingly the simplest method to simulate patchiness formation that can create realistic images. Sufficient noise and turbulence can induce patchiness formation even though the system lies on the stable equilibrium conditions. We tentatively adopt the two-component model with nutrients and phytoplankton, however, the choice of the mathematical model is not essen-tial. The simulation method proposed in this study can be applied to whatever model with stable equilibrium states including one-com-ponent ones.

Understanding and modeling the physical processes that govern the melting of snow cover in a tropical mountain environment in Ecuador

The ISBA/CROCUS coupled ground‐snow model developed for the Alps and subsequently adapted to the outer tropical conditions of Bolivia has been applied to a full set of meteorological data recorded at 4860 m above sea level on a moraine area in Ecuador (Antizana 15 glacier, 0°28′S; 78°09′W) between 16 June 2005 and 30 June 2006 to determine the physical processes involved in the melting and disappearance of transient snow cover in nonglaciated areas of the inner tropics. Although less accurate than in Bolivia, the model is still able to simulate snow behavior over nonglaciated natural surfaces, as long as the modeled turbulent fluxes over bare ground are reduced and a suitable function is included to represent the partitioning of the surface between bare soil and snow cover. The main difference between the two tropical sites is the wind velocity, which is more than 3 times higher at the Antizana site than at the Bolivian site, leading to a nonuniform spatial distribution of snow over nonglaciated areas that is hard to describe with a simple snow partitioning function. Net solar radiation dominates the surface energy balance and is responsible for the energy stored in snow‐free areas (albedo = 0.05) and transferred horizontally to adjacent snow patches by conduction within the upper soil layers and by turbulent advection. These processes can prevent the snow cover from lasting more than a few hours or a few days. Sporadically, and at any time of the year, this inner tropical site, much wetter than the outer tropics, experiences heavy snowfalls, covering all the moraine area, and thus limiting horizontal transfers and inducing a significant time lag between precipitation events and runoff.

NUMERICAL SIMULATIONS OF A ROTATING RED GIANT STAR. I. THREE-DIMENSIONAL MODELS OF TURBULENT CONVECTION AND ASSOCIATED MEAN FLOWS

With the development of one-dimensional stellar evolution codes including rotation and the increasing number of observational data for stars of various evolutionary stages, it becomes more and more possible to follow the evolution of the rotation profile and angular momentum distribution in stars. In this context, understanding the interplay between rotation and convection in the very extended envelopes of giant stars is very important considering that all low- and intermediate-mass stars become red giants after the central hydrogen burning phase. In this paper, we analyze the interplay between rotation and convection in the envelope of red giant stars using three-dimensional numerical experiments. We make use of the Anelastic Spherical Harmonics code to simulate the inner 50% of the envelope of a low-mass star on the red giant branch. We discuss the organization and dynamics of convection, and put a special emphasis on the distribution of angular momentum in such a rotating extended envelope. To do so, we explore two directions of the parameter space, namely, the bulk rotation rate and the Reynolds number with a series of four simulations. We find that turbulent convection in red giant stars is dynamically rich, and that it is particularly sensitive to the rotation rate of the star. Reynolds stresses and meridional circulation establish various differential rotation profiles (either cylindrical or shellular) depending on the convective Rossby number of the simulations, but they all agree that the radial shear is large. Temperature fluctuations are found to be large and in the slowly rotating cases, a dominant ? = 1 temperature dipole influences the convective motions. Both baroclinic effects and turbulent advection are strong in all cases and mostly oppose one another.

Statistical properties of turbulence: An overview

We present an introductory overview of several challenging problems in the statistical characterisation of turbulence. We provide examples from fluid turbulence in three and two dimensions, from the turbulent advection of passive scalars, turbulence in the one-dimensional Burgers equation, and fluid turbulence in the presence of polymer additives.

Influence of turbulent advection on a phytoplankton ecosystem with nonuniform carrying capacity

In this work we study a plankton ecosystem model in a turbulent flow. The plankton model we consider contains logistic growth with a spatially varying background carrying capacity and the flow dynamics are generated using the two-dimensional (2D) Navier-Stokes equations. We characterize the system in terms of a dimensionless parameter, gamma identical with TB/TF, which is the ratio of the ecosystem biological time scales TB and the flow time scales TF. We integrate this system numerically for different values of gamma until the mean plankton reaches a statistically stationary state and examine how the steady-state mean and variance of plankton depends on gamma. Overall we find that advection in the presence of a nonuniform background carrying capacity can lead to very different plankton distributions depending on the time scale ratio gamma. For small gamma the plankton distribution is very similar to the background carrying capacity field and has a mean concentration close to the mean carrying capacity. As gamma increases the plankton concentration is more influenced by the advection processes. In the largest gamma cases there is a homogenization of the plankton concentration and the mean plankton concentration approaches the harmonic mean, <1/K>(-1). We derive asymptotic approximations for the cases of small and large gamma. We also look at the dependence of the power spectra exponent, beta, on gamma where the power spectrum of plankton is proportional to k(-beta). We find that the power spectra exponent closely obeys beta=1+2/gamma as predicted by earlier studies using simple models of chaotic advection.

Effects of turbulent mixing on the nonequilibrium critical behaviour

We study the effects of turbulent mixing on the critical behaviour of a nonequilibrium system near its second-order phase transition between the absorbing and fluctuating states. The model describes the spreading of an agent (e.g., infectious disease) in a reaction-diffusion system and belongs to the universality class of the directed bond percolation process, also known as the simple epidemic process, and is equivalent to the Reggeon field theory. The turbulent advecting velocity field is modelled by the Obukhov–Kraichnan's rapid-change ensemble: Gaussian statistics with the correlation function ⟨vv⟩ ∝ δ(t − t′)k−d−ξ, where k is the wave number, and 0 < ξ < 2 is a free parameter. Using the field theoretic renormalization group we show that, depending on the relation between the exponent ξ and the spatial dimension d, the system reveals different types of large-scale, long-time asymptotic behaviour, associated with four possible fixed points of the renormalization group equations. In addition to known regimes (ordinary diffusion, ordinary directed percolation process and passively advected scalar field), the existence of a new nonequilibrium universality class is established, and the corresponding critical dimensions are calculated to the first order of the double expansion in ξ and ε = 4 − d (one-loop approximation). It turns out, however, that the most realistic values ξ = 4/3 (Kolmogorov's fully developed turbulence) and d = 2 or 3 correspond to the case of a passive scalar field, when the nonlinearity of the Reggeon model is irrelevant, and the spreading of the agent is completely determined by the turbulent transfer.