Large-scale Fluid Motions Research Articles

On application of empirical mode decomposition for turbulence analysis in open-channel flows

Large-scale coherent structures are key elements of open-channel flow turbulence, quantification of which remains elusive. In this work, we use empirical mode decomposition (EMD) to break down a velocity time series into different modes, denoted as “intrinsic mode functions” (IMFs). Analysis of velocity auto- and co-spectra indicates that large-scale (LSMs) and very large-scale (VLSMs) fluid motions are sufficiently represented by particular groups of IMFs. A correlation between LSMs and VLSMs, identified by the EMD analysis, was found to generate 7% of the Reynolds shear stresses. However, the EMD analysis of surrogate velocity signals with randomized spectral phases demonstrated that the revealed correlation is actually an artefact of the EMD approach and should not be interpreted physically.

An Inhomogeneous Steady-State Convection of a Vertical Vortex Fluid

An exact solution of the Oberbeck – Boussinesq equations for the description of the steady-state Bénard – Rayleigh convection in an infinitely extensive horizontal layer is presented. This exact solution describes the large-scale motion of a vertical vortex flow outside the field of the Coriolis force. The large-scale fluid flow is considered in the approximation of a thin layer with nondeformable (flat) boundaries. This assumption allows us to describe the large-scale fluid motion as shear motion. Two velocity vector components, called horizontal components, are taken into account. Consequently, the third component of the velocity vector (the vertical velocity) is zero. The shear flow of the vertical vortex flow is described by linear forms from the horizontal coordinates for velocity, temperature and pressure fields. The topology of the steady flow of a viscous incompressible fluid is defined by coefficients of linear forms which have a dependence on the vertical (transverse) coordinate. The functions unknown in advance are exactly defined from the system of ordinary differential equations of order fifteen. The coefficients of the forms are polynomials. The spectral properties of the polynomials in the domain of definition of the solution are investigated. The analysis of distribution of the zeroes of hydrodynamical fields has allowed a definition of the stratification of the physical fields. The paper presents a detailed study of the existence of steady reverse flows in the convective fluid flow of Bénard – Rayleigh – Couette type.

Role of Advective Inertia in Active Nematic Turbulence

Suspensions of active agents with nematic interactions exhibit complex spatiotemporal dynamics such as mesoscale turbulence. Since the Reynolds number of microscopic flows is very small on the scale of individual agents, inertial effects are typically excluded in continuum theories of active nematic turbulence. Whether active stresses can collectively excite inertial flows is currently unclear. To address this question, we investigate a two-dimensional continuum theory for active nematic turbulence. In particular, we compare mesoscale turbulence with and without the effects of advective inertia. We find that inertial effects can influence the flow already close to the onset of the turbulent state and, moreover, give rise to large-scale fluid motion for strong active driving. A detailed analysis of the kinetic energy budget reveals an energy transfer to large scales mediated by inertial advection. While this transfer is small in comparison to energy injection and dissipation, its effects accumulate over time. The inclusion of friction, which is typically present in experiments, can compensate for this effect. The findings suggest that the inclusion of inertia and friction may be necessary for dynamically consistent theories of active nematic turbulence.

Effects of large-scale advection and small-scale turbulent diffusion on vertical phytoplankton dynamics.

Turbulence has been recognized as a factor of paramount importance for the survival or extinction of sinking phytoplankton species. However, dealing with its multiscale nature in models of coupled fluid and biological dynamics is a formidable challenge. Advection by coherent structures, such as those related to winter convection and Langmuir circulation, is also recognized to play a role in the survival and localization of phytoplankton. In this work we revisit a theoretically appealing model for phytoplankton vertical dynamics, and numerically investigate how large-scale fluid motions affect the survival conditions and the spatial distribution of the biological population. For this purpose, and to work with realistic parameter values, we adopt a kinematic flow field to account for the different spatial and temporal scales of turbulent motions. The dynamics of the population density are described by an advection-reaction-diffusion model with a spatially heterogeneous growth term proportional to sunlight availability. We explore the role of fluid transport by progressively increasing the complexity of the flow in terms of spatial and temporal scales. We find that, due to the large-scale circulation, phytoplankton accumulates in downwelling regions and its growth is reduced, confirming previous indications in slightly different conditions. We then explain the observed phenomenology in terms of a plankton filament model. Moreover, by contrasting the results in our different flow cases, we show that the large-scale coherent structures have an overwhelming importance. Indeed, we find that smaller-scale motions only quite weakly affect the dynamics, without altering the general mechanism identified. Such results are relevant for parametrizations in numerical models of phytoplankton life cycles in realistic oceanic flow conditions.

Dependence of small-scale energetics on large scales in turbulent flows

In a turbulent flow, small- and large-scale fluid motions are coupled. In this work, we investigate the small-scale response to large-scale fluctuations in turbulent flows and discuss the implications on large eddy simulation (LES) wall modelling. The interscale interaction in wall-bounded flows was previously parameterized in the predictive inner–outer (PIO) model, where the amplitude of the small scales responds linearly to the large-scale fluctuations. While this assumed linearity is valid in the viscous sublayer, it is an insufficient approximation of the true interscale interaction in wall-normal distances within the buffer layer and above. Within these regions, a piecewise linear response function (piecewise with respect to large-scale fluctuations being positive or negative) appears to be more appropriate. In addition to proposing a new response function, we relate the amplitude modulation process to the Townsend attached eddy hypothesis. This connection allows us to make theoretical predictions on the model parameters within the PIO model. We use these parameters to apply the PIO model to wall-modelled LES. Further, we present empirical evidence of amplitude modulation in isotropic turbulence. The evidence suggests that the existence of nonlinear interscale interactions in the form of amplitude modulation does not rely on the presence of a non-penetrating boundary, but on the presence of a range of viscosity-dominated scales and a range of inertial-dominated scales.

A multifractal model for the momentum transfer process in wall-bounded flows

The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation , where l is the filtering length scale. According to the multifractal formalism, and in the log-region, where Re τ is the friction Reynolds number, p is a real number, L is an outer length scale and ζ p is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at Re τ = 4200.

Turbulence characteristics and vortical structures in combined-convection boundary layers along a heated vertical flat plate

Time-developing direct numerical simulations are performed for the combined-convection boundary layers created by imposing aiding and opposing freestreams to the pure natural-convection boundary layer in air along a heated vertical flat plate to clarify their structural characteristics. The numerical results reveal that with a slight increase in freestream velocity, the transition region moves downstream for aiding flow and upstream for opposing flow. This fact correlates well with the existing experimental results showing that the transition delays for aiding flow and quickens for opposing flow in the practical space-developing boundary layer. Thereby, for aiding flow, turbulence characteristics indicate the behavior proceeding to the laminarization of the boundary layer. On the other hand, for opposing flow, the large scale fluid motions are apparent and become larger than those for the pure natural-convection boundary layer with increasing freestream velocity. For the occurrence of such fluid motions, the budgets of turbulent energy and two-point spatial correlations in the turbulent combined-convection boundary layers are also examined. Consequently, it is found in the spatial correlations that the turbulence structures are mainly controlled by fluid motions in the outer region of the boundary layer.

東北地方太平洋沖地震津波の広域沿岸挙動に関する研究

Large scale fluid motion due to the 2011 Tohoku Tsunami was investigated by decomposing the water surface elevation computed by the linear wave theory through spectrum analysis. Dominant periods of nearshore fluid motion are extracted from the water surface elevation at the depth of 10m. The power spectra and phases at the alongshore points are compared. From these results, cross-shore and alongshore long-period oscillations are described in Sendai Bay, which appear to be consistent with the large runup height especially at the center and the both ends of the Sendai Bay. It appears that the long-period motion with period of 80 minutes propagates southward alongshore as edge waves. Standing alongshore wave motion which is not consistent with the dispersion relationship of edge wave is also detected.

Investigations of Mixing Time Scales in a Baffled Circular Tank with a Surface Aerator

Abstract The oxygen transfer rate is a parameter that characterizes the gas-liquid mass transfer in surface aerators. Gas-liquid transfer mech-anisms in surface aeration tanks depend on two different extreme lengths of time; namely, macromixing and micromixing. Small scale mixing close to the molecular level is referred to as micromixing; whereas, macromixing refers to mixing on a large scale. Using experi-mental data and numerical simulations, macro- and micro-scale parameters describing the two extreme time scales were investigated. A scale up equation to simulate the oxygen transfer rate with micromixing times was developed in geometrically similar baffled surface aerators. Keywords: Energy dissipation, Macromixing, Micromixing, Oxygen transfer rate, Surface aerators, Theoretical power per unit volume 1. Introduction Surface aeration is an important operation in chemical and other processing industries. Surface aeration is defined as the aeration or oxygen transfer that takes place at the gas-liquid surface when the liquid is agitated. The objective of studying aeration process was to interpret the laboratory result for the development of a field installation. This requires a geometrical similarity condition; that is to say the field installation should be built on a definite geometric ratio to that of the laboratory setup. Under a geometric similarity condition, an effective scale-up mandates an awareness of the relative importance of various process parameters at different levels of scrutiny.Inside a surface aeration tank, different scales of mixing are present, with regions where one of the scales of mixing will pre-vail, i.e., either macromixing or micromixing. Macromixing is mixing driven by the largest scales of motion in the fluid. Mi-cromixing prevails near the impeller; where small eddies define the velocity gradients surrounding the bubbles. According to Kolmogorov’s theory, the power per unit volume determines the energy and size of the turbulent eddies, which has traditionally been used in the design and scale up of equipment [1-4].Macromixing prevails adjacent to the micromixing region, which determines the internal homogenization, movement of bubbles across the reactor and flow pattern when the turbulent eddies are tank-sized. The contribution of the surface aeration of a tank, as well as the effect of the geometry of the impeller and the tank to the mass transfer the depend on this scale of mixing [1, 4-8].Unlike macromixing, which is associated with large-scale fluid motions that can be monitored directly through physical property measurements, micromixing deals with diffusive mix-ing at the molecular level, for which only indirect methods are available. Despite the availability of much literature on the mix-ing length scale, mixing scale behavior of surface aerators is typ-ically missing. Recently, Rao and Kumar [9] studied the micro-mixing behaviors of unbaffled surface aerators. However, baffled type surface aeration systems are mostly preferred in the mixing and chemical industry. Baffles are flat vertical strips set radi-ally along the tank wall, which avoid vortex formation. A baffled tank provides a better concentration distribution throughout the tank and; therefore, improved mixing efficiency is achieved. Thus, this study aimed to understand the prevalent mixing scale in baffled circular surface aeration systems and obtain scale-up or simulation equations for different mixing scales.

Positron transport in the interstellar medium

We seek to understand the propagation mechanisms of positrons in the interstellar medium (ISM). This understanding is a key to determine whether the spatial distribution of the annihilation emission observed in our Galaxy reflects the spatial distribution of positron sources and, therefore, makes it possible to place constraints on the origin of positrons. We review the different processes that are likely to affect the transport of positrons in the ISM. These processes fall into three broad categories: scattering off magnetohydrodynamic waves, collisions with particles of the interstellar gas and advection with large-scale fluid motions. We assess the efficiency of each process and describe its impact on the propagation of positrons. We also develop a model of positron propagation, based on Monte-Carlo simulations, which enable us to estimate the distances traveled by positrons in the different phases of the ISM. We find that low-energy (< 10 MeV) positrons generally have negligible interactions with magnetohydrodynamic waves, insofar as these waves are heavily damped. Positron propagation is mainly controlled by collisions with gas particles. Under these circumstances, positrons can travel huge distances (up to 30 kpc/n_H for 1 MeV positrons) along magnetic field lines before annihilating.

Effects of spray targeting on mixture development and emissions formation in late-injection low-temperature heavy-duty diesel combustion

The effects of fuel-spray targeting on mixture development, combustion, and pollutant formation were investigated for a late-injection low-temperature combustion (LTC) operating condition in an optically accessible heavy-duty diesel engine. Equivalence-ratio maps, derived from toluene fuel-tracer fluorescence measurements, quantify the effects of fuel-jet targeting on mixture preparation processes under non-combusting conditions. Planar laser-induced fluorescence of formaldehyde (H 2CO), hydroxyl radical (OH), and polycyclic aromatic hydrocarbons (PAH) provide complementary measurements during the combustion process from fuel-lean to fuel-rich reaction zones. Three different injector nozzles with included angles of 124°, 152° and 160° yield unique jet–wall and jet–jet interactions. The baseline 152° nozzle directs the fuel jet toward the vertical center of the piston bowl-wall, where the jets impinge on the wall and merge with neighboring jets prior to the peak heat-release rate. Fuel-rich jet–jet interaction regions develop between the jets near the floor of the bowl, which is where the majority of soot and/or PAH formation occurs. These fuel-rich jet–jet interactions can be reduced by either a more narrow injection angle (124°) or a wider angle injection (160°), both of which lead to decreased soot formation. However, jet–wall interactions may play an important role for late-cycle bulk flows. With the 160° injection, less bulk-fluid motion in the piston bowl occurs, leading to extensive quenched regions throughout the center of the combustion chamber. By contrast, the 124° injection enhances large-scale fluid motion, transporting hot second-stage ignition regions into the fuel-lean quenched mixtures at the center of the chamber, potentially improving late-cycle oxidation of unburned hydrocarbons (UHC) and carbon monoxide (CO).

Molecular physics of a polymer engineering instability: Experiments and computation

Entangled polymer melts exhibit a variety of flow instabilities that limit production rates in industrial applications. We present both experimental and computational findings, using flow of monodisperse linear polystyrenes in a contraction-expansion geometry, which illustrate the formation and development of one such flow instability. This viscoelastic disturbance is observed at the slit outlet and subsequently produces large-scale fluid motions upstream. A numerical linear stability study using the molecular structure based Rolie-Poly model confirms the instability and identifies important parameters within the model, which gives physical insight into the underlying mechanism. Chain stretch was found to play a critical role in the instability mechanism, which partially explains the effectiveness of introducing a low-molecular weight tail into a polymer blend to increase its processability.

A Revised Prescription for the Tayler‐Spruit Dynamo: Magnetic Angular Momentum Transport in Stars

Angular momentum transport by internal magnetic fields is an important ingredient for stellar interior models. In this paper we critically examine the basic heuristic assumptions in the model of the Tayler-Spruit dynamo, which describes how a pinch-type instability of a toroidal magnetic field in differentially rotating stellar radiative zones may result in large-scale fluid motion. We agree with prior published work both on the existence of the instability and its nearly horizontal geometry for perturbations. However, the approximations in the original Acheson dispersion relation are valid only for small length scales, and we disagree that the dispersion relation can be extrapolated to horizontal length scales of order the radius of the star. We contend that dynamical effects, in particular, angular momentum conservation, limit the maximum horizontal length scale. We therefore present transport coefficients for chemical mixing and angular momentum redistribution by magnetic torques that are significantly different from previous published values. The new magnetic viscosity is reduced by 2-3 orders of magnitude compared to the old one, and we find that magnetic angular momentum transport by this mechanism is very sensitive to gradients in the mean molecular weight. The revised coefficients are more compatible with empirical constraints on the timescale of core-envelope coupling in young stars than the previous ones. However, solar models including only this mechanism possess a rapidly rotating core, in contradiction with helioseismic data. Previous studies had found strong core-envelope coupling, both for solar models and for the cores of massive evolved stars. We conclude that the Tayler-Spruit mechanism may be important for envelope angular momentum transport but that some other process must be responsible for efficient spin-down of stellar cores.

Turbulence characteristics of natural-convection boundary layer in air along a vertical plate heated at high temperatures

Turbulence characteristics of a natural-convection boundary layer in air along a vertical plate heated at high temperatures are experimentally investigated. Two-dimensional velocity vectors and instantaneous temperature in the boundary layer at a wall temperature up to 300 °C are measured using a particle image velocimetry and a cold wire. From the correlation between the local Nusselt number Nu x and the local Grashof number Gr x , it was found that heat transfer rates even for a wall temperature of 300 °C are well expressed by an empirical formula obtained for low wall temperature and the region of transition from laminar to turbulence does not change much with an increase in wall temperature. In addition, the profiles of turbulent quantities measured at a wall temperature of 300 °C resemble those observed at low wall temperatures, and thus the effects of high heat on the turbulent behavior in the boundary layer are quite small. The measured velocity vectors and the higher-order statistics, such as skewness and flatness factors of fluctuating velocities and temperature, also suggest that the structure of large-scale fluid motions in the outer layer of the natural-convection boundary layer, closely connected with turbulence generation, is maintained even under high wall temperature conditions.

2532 Immersed Boundary法による3次元丘風況を対象としたラージ・エディ・シミュレーション(S47-5 自然の流体エネルギー利用技術(風車3),S47 自然の流体エネルギー利用技術)

The large-eddy simulation code with a finite difference method to predict an unsteady three-dimensional wind field was developed in a Cartesian grid system. The immersed boundary method, which enables us to represent the complex geometry in the Cartesian grid system, was used, and the velocity interpolation near the boundary was carried out with a wall model. The mixed-time scale model was adopted for the sub-grid scale stress. According to Kataoka and Mizuno, the inflow boundary conditions were provided by the turbulence computation. Then, the present code was applied to the turbulence simulation of flow fields over a three-dimensional steep hill. Through the calculations, it was confirmed that the present results agreed well with those obtained by wind tunnel experiments, suggesting that the present code is suitable to predict the basic characteristics in the boundary layer over a complex terrain. More detailed results on the turbulent statistics, including higher order moments were also examined, and it was found that the large-scale fluid motions due to the elongated separation region becomes dominant behind the hill.

Formation of large-scale semiorganized structures in turbulent convection.

A new mean-field theory of turbulent convection is developed by considering only the small-scale part of spectra as "turbulence" and the large-scale part, as a "mean flow," which includes both regular and semiorganized motions. The developed theory predicts the convective wind instability in a shear-free turbulent convection. This instability causes formation of large-scale semiorganized fluid motions in the form of cells. Spatial characteristics of these motions, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This study predicts also the existence of the convective shear instability in a sheared turbulent convection. This instability causes formation of large-scale rolls and generation of convective shear waves which have a nonzero hydrodynamic helicity. Increase of shear promotes excitation of the convective shear instability. Applications of the obtained results to the atmospheric turbulent convection and the laboratory experiments on turbulent convection are discussed.

E113 鉛直平板自然対流乱流境界層の大規模構造

The structural characteristics of turbulent natural-convection boundary layer in air along a vertical heated plate have been experimentally investigated. Through the velocity measurement with a particle image velocimetry, the relation between turbulent statistics and large-scale fluid motions in the outer layer of the boundary layer is discussed in detail, especially paying attention to the behavior of Reynolds shear stress, and it is found that the large-scale eddies, which control the structure of the outer layer, contribute largely to the production of turbulent energy. In addition, the change in the maximum velocity location due to flow windings observed in the whole visualized region may lead to the peculiar profile of the Reynolds shear stress.

高温熱駆動乱流境界層のPIV計測

The instantaneous velocity vectors in the thermally driven turbulent boundary layer in air along a vertical plate heated at high temperatures were measured by using a PIV to accumulate experimental data for the velocity field. The effects of PIV parameters on the experimental results were investigated, especially paying attention to the large-scale fluid motions in the outer layer, which play a predominant role in the generation of turbulence. The turbulent statistics revealed that the transverse velocity fluctuation (perpendicular to flat plate) depended on the PIV parameters, while the mean streamwise velocity did not change with the parameters. In addition, it was found that a discontinuous distribution appeared in instantaneous velocity fluctuations measured without the sub-pixel algorithm.

Effects of freestream on turbulent combined-convection boundary layer along a vertical heated plate

A turbulent combined-convection boundary layer, created by imposing an aiding freestream on a turbulent natural-convection boundary layer along a vertical heated plate, was examined with normal hot- and cold-wires and a particle image velocimetry (PIV), with attention to the laminarization process of the boundary layer due to the freestream effects. As the freestream velocity increases, the wall shear stress monotonously increases, whereas the local heat transfer rate suddenly decreases. The reduction in heat transfer rates and the decays in velocity and temperature fluctuations, showing the transition from turbulent to laminar, arise at Grx/ Rex≃3×10 6. With the laminarization of the boundary layer, a similar change in the turbulent quantities appears independently of Grx. For instantaneous velocity vectors obtained with PIV, large-scale fluid motions, which play a predominant role in the generation of turbulence, are frequently observed in the outer layer, while quasi-coherent structures do not exist in the near-wall region. The increasing freestream then restricts large-scale fluid motions in the outer layer, and consequently the generation of turbulence is suppressed and the boundary layer becomes laminar.

Fluid geochemical transect in the Northern Apennines (central-northern Italy): fluid genesis and migration and tectonic implications

Chemical and isotopic characteristics of natural gas and thermal water discharges from the western back-arc Tyrrhenian Sea across the Apennine thrust-belt to the Po Valley and Adriatic coast foredeep basins in the Northern Apennines (central-northern Italy) reveal a large-scale fluid motion in the upper crust, both vertically and horizontally. On the basis of gas compositions, two different domains of rising fluids have been distinguished: (1) CO 2-rich, He-poor, 3He/ 4He-high domain in the western peri-Tyrrhenian extensional sector; (2) CH 4-rich, He-rich, 3He/ 4He-low domain in the eastern Adriatic compressional sector. Such gases, rising from various depths, are crossed by a huge lateral N 2-rich water flow, in the peri-Tyrrhenian sector, of Ca–SO 4(HCO 3) meteoric-derived waters that move in a regional wide aquifer hosted in a quite thick Mesozoic carbonate series. Morphologically, the CO 2 vents consist of mud basins with high gas-rate emission, where the rising fluids move upwards through diatremes. On the other hand, CH 4 emissions seep out from typical mud volcanoes with a reduced gas flow-rate, where the fluid motion is likely related to saline diapir extrusions, and the methane is mostly carried to the surface by the associated mud. The two rising mechanisms described locate southwest and northeast of the Apennine watershed respectively. From a seismic point of view the CH 4 domain in the thrust-belt and foredeep areas is characterized by a large number of earthquakes, indirectly pointing to a different rheological behavior of the terrains with respect to the more internal peri-Tyrrhenian area. Owing to the quite high thermal gradient of the latter, the boundary of the brittle–ductile crust in the peri-Tyrrhenian sector can be located at a <10 km shallow depth. Although the presence of several post-orogenic basins would suggest widespread extensional tectonics in all areas west of the Apennine watershed, those located in the easternmost part display gas vents with typical crustal 3He/ 4He ratios. As this ratio is very sensitive to deep fluids rising from the mantle, we hypothesize that such basins at the foot of the Apennines are not due to tensive stress, as suggested by their morphological shape. They are piggy-back (thrust-top) basins developed and evolved in a still acting compressive tectonic regime.