Effective Turbulent Diffusivity Research Articles

The Transition Layer and Remnant Transition Layer of the Western Arctic Ocean: Stratification, Vertical Diffusivity, and Pacific Summer Water Heat Fluxes

AbstractThe exchange of heat and other tracers between the ocean interior and sea ice cover depends on vertical diffusion through the thin and strongly stratified Arctic Ocean transition layer and remnant transition layer. Ice‐Tethered Profiler observations during 2004–2021 were used to characterize and investigate the active and remnant transition layers in the Beaufort Gyre region. Transition layers evolved seasonally, with the deepest, densest, and warmest transition layers observed in spring. In a composite view, the summer mixed layer shoaled over a timescale of approximately 2 weeks, leaving behind a remnant transition layer whose stratification had already begun to weaken. The stratification maximum of the remnant transition layer continued to weaken and broaden throughout the summer, including changes associated with storm events. The weakening stratification was used to estimate an effective vertical turbulent diffusivity which ranged from 10−8 to 10−6 m2/s for individual ITP records; a value of 6 × 10−7 m2/s is representative of the Beaufort Gyre region. Vertical heat fluxes through the active and remnant transition layers were estimated over 90‐day timescales. Springtime vertical heat fluxes increased from 0.3 ± 0.3 W/m2 during 2006–2011 to 1.1 ± 0.7 W/m2 during 2017–2021. Summertime vertical heat fluxes through the remnant transition layer were somewhat less, but also increased interannually. Vertical gradients of density during spring and summer, and so diffusion of density through the active and remnant transition layers, did not increase interannually. Pacific Summer Water warming has increased ocean to ice heat fluxes, which may continue to become more significant in the future.

Experimental study of turbulent thermal diffusion of particles in an inhomogeneous forced convective turbulence

We investigate experimentally the phenomenon of turbulent thermal diffusion of micrometer-size solid particles in an inhomogeneous convective turbulence forced by one vertically oriented oscillating grid in an air flow. This effect causes the formation of large-scale inhomogeneities in particle spatial distributions in a temperature-stratified turbulence. We perform detailed comparisons of the experimental results with those obtained in our previous experiments with an inhomogeneous and anisotropic stably stratified turbulence produced by a one oscillating grid in the air flow. Since the buoyancy increases the turbulent kinetic energy for convective turbulence and decreases it for stably stratified turbulence, the measured turbulent velocities for convective turbulence are larger than those for stably stratified turbulence. This tendency is also seen in the measured vertical integral turbulent length scales. Measurements of temperature and particle number density spatial distributions show that particles are accumulated in the vicinity of the minimum of the mean temperature due to the phenomenon of turbulent thermal diffusion. This effect is observed in both convective and stably stratified turbulence, where we find the effective turbulent thermal diffusion coefficient for micrometer-size particles. The obtained experimental results are in agreement with theoretical predictions.

Turbulent dispersion of a passive scalar in a smooth-wall turbulent boundary layer

The scalar dispersion of a ground-level point-source plume in a smooth-wall turbulent boundary layer is experimentally investigated using simultaneous particle image velocimetry and planar laser-induced fluorescence techniques. In the near-source region, the viscous sublayer is observed to trap dye, while in the far field, the half-width, vertical profiles and peak decay of the mean concentration and concentration variance exhibit self-similar behaviour and collapse with empirical relations. Full two-dimensional maps of the turbulent scalar fluxes show a net transport direction of upward and towards the incoming flow, with the vertical profiles collapsing well with Weibull-type exponential functions and the decay of peaks following power laws. Using the first-order gradient transport to model the turbulent scalar fluxes, maps of the anisotropic turbulent diffusivity tensor and an effective turbulent diffusivity coefficient are calculated. The streamwise and wall-normal turbulent scalar fluxes are driven dominantly by the wall-normal concentration gradient. The turbulent Schmidt number, relating the turbulent diffusivity and the turbulent (eddy) viscosity calculated using the Boussinesq hypothesis, varies with wall-normal position with values of the order of unity in the logarithmic layer.

Helical correction to turbulent magnetic diffusivity.

The effect of helicity in magnetohydrodynamic turbulence on the effective turbulent magnetic diffusion is considered here. The helical correction to turbulent diffusivity is analytically calculated with the use of the renormalization group approach. In agreement with previous numerical findings, this correction is shown to be negative and proportional to the second power of the magnetic Reynolds number, when the latter is small. In addition, the helical correction to turbulent diffusivity is found to obey a power-law-type dependence on the wave number of the most energetic turbulent eddies, k_{ℓ}, of the form k_{ℓ}^{-10/3}.

Turbulent dispersion of breath by the wind

The pioneering work of Taylor on the turbulent dispersion of aerosols is one century old and provides an interesting way to introduce both diffusive processes and turbulence at an undergraduate level. Low mass particles transported by a turbulent flow exhibit a Brownian-like motion over time scales larger than the velocity correlation time. Aerosols and gases are, therefore, subjected to an effective turbulent diffusion at large length scales. However, the case of a source of pollutant much smaller than the integral scale is not completely understood. Here, we present experimental results obtained by undergraduate students in the context of the COVID-19 pandemic. The dispersion of a fog of oil droplets by a turbulent flow is studied in a wind tunnel designed for pedagogical purposes. It shows a ballistic-like regime at short distance, followed by Taylor's diffusive-like regime, suggesting that scale-free diffusion by the turbulent cascade process is bypassed. Measurements show that the dispersion of CO2 emitted when breathing in a natural, indoor air flow is not isotropic but rather along the flow axis. The transverse spread is ballistic-like, leading to the concentration decaying as the inverse-squared distance to the mouth. The experiment helps students understand the role of fluctuations in diffusive processes and in turbulence. A Langevin equation governing aerosol dispersion based on a single correlation time allows us to model the airborne transmission risk of pathogens, indoors and outdoors. The results obtained in this study have been used to provide public health policy recommendations to prevent transmission in shopping malls.

Experimental study of turbulent thermal diffusion of particles in inhomogeneous and anisotropic turbulence

We experimentally studied the turbulent thermal diffusion of small particles in inhomogeneous and anisotropic stably stratified turbulence produced by one oscillating grid in the air flow. The velocity fields have been measured using Particle Image Velocimetry (PIV). We have determined various turbulence characteristics: the mean and turbulent velocities, two-point correlation functions of the velocity field, and an integral scale of turbulence from the measured velocity fields. The temperature field has been measured with a temperature probe equipped with 12 E thermocouples. Spatial distributions of micrometer-sized particles have been determined by a PIV system using the effect of the Mie light scattering by particles in the flow. The experiments have demonstrated that particles are accumulated at the minimum of mean fluid temperature due to the phenomenon of turbulent thermal diffusion. Using measured spatial distributions of particles and temperature fields, we have determined the effective turbulent thermal diffusion coefficient of particles in inhomogeneous temperature-stratified turbulence. This experimental study has clearly detected the phenomenon of turbulent thermal diffusion in inhomogeneous turbulence.

Global heat balance and heat uptake in potential temperature coordinates

The representation of ocean heat uptake in Simple Climate Models used for policy advice on climate change mitigation strategies is often based on variants of the one-dimensional Vertical Advection/Diffusion equation (VAD) for some averaged form of potential temperature. In such models, the effective advection and turbulent diffusion are usually tuned to emulate the behaviour of a given target climate model. However, because the statistical nature of such a “behavioural” calibration usually obscures the exact dependence of the effective diffusion and advection on the actual physical processes responsible for ocean heat uptake, it is difficult to understand its limitations and how to go about improving VADs. This paper proposes a physical calibration of the VAD that aims to provide explicit traceability of effective diffusion and advection to the processes responsible for ocean heat uptake. This construction relies on the coarse-graining of the full three-dimensional advection diffusion for potential temperature using potential temperature coordinates. The main advantage of this formulation is that the temporal evolution of the reference temperature profile is entirely due to the competition between effective diffusivity that is always positive definite, and the water mass transformation taking place at the surface, as in classical water mass analyses literature. These quantities are evaluated in numerical simulations of present day climate and global warming experiments. In this framework, the heat uptake in the global warming experiment is attributed to the increase of surface heat flux at low latitudes, its decrease at high latitudes and to the redistribution of heat toward cold temperatures made by diffusive flux.

Parametrization of irreversible diapycnal diffusivity in salt-fingering turbulence using DNS

Abstract

Turbulence Regulates the Rate of Planetesimal Formation via Gravitational Collapse

Abstract We study how the interaction between the streaming instability (SI) and intrinsic gas-phase turbulence affects planetesimal formation via gravitational collapse in protoplanetary disks. Turbulence impedes the formation of particle clumps by acting as an effective turbulent diffusivity, but it can also promote planetesimal formation by concentrating solids, for example, in zonal flows. We quantify the effect of turbulent diffusivity using numerical simulations of the SI in small local domains, forced with velocity perturbations that establish approximately Kolmogorov-like turbulence. We find that planetesimal formation is suppressed by turbulence once velocity fluctuations exceed ≃ (10−3.5–10−3) . Turbulence whose strength is just below the threshold reduces the rate at which solids are bound into clumps. Our results suggest that the well-established turbulent thickening of the midplane solid layer is the primary mechanism by which turbulence influences planetesimal formation and that planetesimal formation requires a midplane solid-to-gas ratio ϵ ≳ 0.5. We also quantify the initial planetesimal mass function using a new clump-tracking method to determine each planetesimal mass shortly after collapse. For models in which planetesimals form, we show that the mass function is well described by a broken power law, whose parameters are robust to the inclusion and strength of imposed turbulence. Turbulence in protoplanetary disks is likely to substantially exceed the threshold for planetesimal formation at radii where temperatures T ≳ 103 K lead to thermal ionization. Planetesimal formation may therefore be unviable in the inner disk out to 2–3 times the dust sublimation radius.

Mean velocity, spreading and entrainment characteristics of weak bubble plumes in unstratified and stationary water

In this paper we present an experimental and theoretical study of weak bubble plumes in unstratified and stationary water. We define a weak bubble plume as one that spreads slower than the linear rate of a classic plume. This work focuses on the characteristics of the mean flow in the plume, including centreline velocity, plume spreading and entrainment of ambient water. A new theory based on diffusive spreading instead of an entrainment hypothesis is used to describe the lateral spreading of the bubbles and the associated plume. The new theory is supported by the experimental data. With the measured data of liquid volume fluxes and the new theory, we conclude that the weak bubble plume is a decreasing entrainment process, with the entrainment coefficient $\unicode[STIX]{x1D6FC}$ in the weak bubble plume decreasing with height $z$, following $\unicode[STIX]{x1D6FC}\sim z^{-1/2}$, and taking on values much smaller than those in a classic bubble plume. An additional non-dimensional diffusion coefficient, $\hat{E_{t}}\sim E_{t}U_{s}^{2}/B_{0}$, is also needed to describe the evolution of the volume and kinematic momentum fluxes for the mean flow in the weak bubble plume. Here, $E_{t}$ is the effective turbulent diffusion coefficient, $U_{s}$ is the terminal rise velocity of the bubbles, and $B_{0}$ is the kinematic buoyancy flux of the source. Finally, we provide a unified framework for the mean flow characteristics, including volume flux, momentum flux and plume spreading for the classic and weak bubble plumes, which also provides insight on the transition from classic to weak bubble plume behaviour.

Renormalization group analysis of heat transfer in the presence of endothermic and exothermic chemical reactions.

In the present paper, renormalization group methods are used to develop a macroscopic turbulence model for thermal diffusivity in turbulent fluid flow under conditions of endothermic and exothermic chemical reactions in flow. The temperature field is divided into slow (large-scale) and fast (small-scale) modes. With the help of the renormalization procedure, energy equations for the large-scale modes and relations for effective turbulent thermal diffusivity were obtained. It was shown how the type of the chemical reaction affects turbulent thermal diffusivity. In addition, the conditions were identified where effective thermal diffusivity undergoes a sharp growth.

Reconciling turbulent burning velocity with flame surface area in small-scale turbulence

A discrepancy between the enhancement in overall burning rate and the enhancement in flame surface area measured for high-intensity turbulence is addressed. In order to reconcile the two quantities, an additional contribution from the effective turbulent diffusivity is considered. This contribution is expected to arise in sufficiently intense turbulence from eddies smaller than the flamelet thickness. In the present work, the enhancement in diffusivity arising from these eddies is estimated based on a model energy spectrum; individual contributions from all turbulence length scales smaller the flamelet thickness are integrated over the corresponding portion of the spectrum. It is shown that diffusivity enhancement, estimated in this manner, is able to account for the measured discrepancy between the overall burning rate enhancement and flame surface area enhancement. The factor quantifying this discrepancy is formalized as a closed-form function of the Karlovitz number.

Incorporating Surface Convection into a 3D Babcock–Leighton Solar Dynamo Model

Abstract The convective flows observed on the photosphere (e.g., supergranulation, granulation) play a key role in the Babcock–Leighton (BL) process to generate large-scale polar fields from sunspot fields. In most surface flux transport (SFT) and BL dynamo models, the dispersal and migration of surface fields are modeled as an effective turbulent diffusion. Recent SFT models have incorporated explicit, realistic convective flows in order to improve the fidelity of convective transport but, to our knowledge, this has not yet been implemented in previous BL models. We present the first kinematic 3D Flux-Transport/BL model to explicitly incorporate realistic convective flows based on solar observations. Though we describe a means to generalize these flows to 3D, we find that the kinematic small-scale dynamo action they produce disrupts the operation of the cyclic dynamo. The cyclic solution is found by limiting the convective flow to act only on the vertical radial component of the magnetic field. The results obtained are generally in good agreement with the observed surface flux evolution and with non-convective models that have a turbulent diffusivity of the order of 3 × 1012 cm2 s−1 (300 km2 s−1). However, we find that the use of a turbulent diffusivity underestimates the dynamo efficiency, producing weaker mean fields and a shorter cycle than in the convective models. Also, the convective models exhibit bands of mixed polarity in the polar regions that have no counterpart in solar observations, and the poleward migration speed of poloidal flux is determined mainly by the meridional flow and the vertical diffusion.

Drift turbulence, particle transport, and anomalous dissipation at the reconnecting magnetopause

Using fully kinetic 3D simulations, the reconnection dynamics of asymmetric current sheets are examined at the Earth's magnetopause. The plasma parameters are selected to model MMS magnetopause diffusion region crossings with guide fields of 0.1, 0.4, and 1 of the reconnecting magnetosheath field. In each case, strong drift-wave fluctuations are observed in the lower-hybrid frequency range at the steep density gradient across the magnetospheric separatrix. These fluctuations give rise to cross-field electron particle transport. In addition, this turbulent mixing leads to significantly enhanced electron parallel heating in comparison to 2D simulations. We study three different methods of quantifying the anomalous dissipation produced by the drift fluctuations, based on spatial averaging, temporal averaging, and temporal averaging followed by integrating along magnetic field lines. A comparison of different methods reveals complications in identifying and measuring the anomalous dissipation. Nevertheless, the anomalous dissipation from short wavelength drift fluctuations appears weak for each case, and the reconnection rates observed in 3D are nearly the same as in 2D models. The 3D simulations feature a number of interesting new features that are consistent with recent MMS observations, including cold beams of magnetosheath electrons that penetrate into the hotter magnetospheric inflow, the related observation of decreasing temperature in regions of increasing total density, and an effective turbulent diffusion coefficient that agrees with predictions from quasi-linear theory.

Vertically migrating swimmers generate aggregation-scale eddies in a stratified column.

Biologically generated turbulence has been proposed as an important contributor to nutrient transport and ocean mixing1-3. However, to produce non-negligible transport and mixing, such turbulence must produce eddies at scales comparable to the length scales of stratification in the ocean. It has previously been argued that biologically generated turbulence is limited to the scale of the individual animals involved 4 , which would make turbulence created by highly abundant centimetre-scale zooplankton such as krill irrelevant to ocean mixing. Their small size notwithstanding, zooplankton form dense aggregations tens of metres in vertical extent as they undergo diurnal vertical migration over hundreds of metres3,5,6. This behaviour potentially introduces additional length scales-such as the scale of the aggregation-that are of relevance to animal interactions with the surrounding water column. Here we show that the collective vertical migration of centimetre-scale swimmers-as represented by the brine shrimp Artemia salina-generates aggregation-scale eddies that mix a stable density stratification, resulting in an effective turbulent diffusivity up to three orders of magnitude larger than the molecular diffusivity of salt. These observed large-scale mixing eddies are the result of flow in the wakes of the individual organisms coalescing to form a large-scale downward jet during upward swimming, even in the presence of a strong density stratification relative to typical values observed in the ocean. The results illustrate the potential for marine zooplankton to considerably alter the physical and biogeochemical structure of the water column, with potentially widespread effects owing to their high abundance in climatically important regions of the ocean 7 .

A Three dimensional Babcock-Leighton Solar Dynamo Model with Non-axisymmetric Convective Flows

AbstractThe observed convective flows on the photosphere (e.g., supergranulation, granulation) play a key role in the Babcock-Leighton (BL) process to generate large scale polar fields from sunspots fields. In most surface flux transport (SFT) and BL dynamo models, the dispersal and migration of surface fields is modeled as an effective turbulent diffusion. We present the first kinematic 3D FT/BL model to explicitly incorporate realistic convective flows based on solar observations. The results obtained are generally in good agreement with the observed surface flux evolution and with non-convective models that have a turbulent diffusivity on the order of 3 × 1012 cm2 s−1 (300 km2 s−1). However, we find that the use of a turbulent diffusivity underestimates the dynamo efficiency, producing weaker mean fields and shorter cycle.

Magneto-rotational instability in the protolunar disk

We perform the first study of magnetohydrodynamic processes in the protolunar disk (PLD). With the use of published data on the chemical composition of the PLD, along with existing analytical models of the disk structure, we show that the high temperatures that were prevalent in the disk would have led to ionization of Na, K, SiO, Zn and, to a lesser extent, O2. For simplicity, we assume that the disk has a vapor structure. The resulting ionization fractions, together with a relatively weak magnetic field, possibly of planetary origin, would have been sufficient to trigger the magneto-rotational instability, or MRI, as demonstrated by the fact that the Elsasser criterion was met in the PLD: a magnetic field embedded in the flow would have diffused more slowly than the growth rate of the linear perturbations. We calculate the intensity of the resulting magnetohydrodynamic turbulence, as parameterized by the dimensionless ratio α of turbulent stresses to gas pressure, and obtain maximum values α∼10-2 along most of the vertical extent of the disk, and at different orbital radii. This indicates that, under these conditions, turbulent mixing within the PLD due to the MRI was likely capable of transporting isotopic and chemical species efficiently. To test these results in a conservative manner, we carry out a numerical magnetohydrodynamic simulation of a small, rectangular patch of the PLD, located at 4 Earth radii (rE) from the center of the Earth, and assuming once again that the disk is completely gaseous. We use a polytrope-like equation of state. The rectangular patch is threaded initially by a vertical magnetic field with zero net magnetic flux. This field configuration is known to produce relatively weak MRI turbulence in studies of astrophysical accretion disks. We accordingly obtain turbulence with an average intensity α∼7×10-6 over the course of 280 orbital periods (133days at 4rE). Despite this relatively low value of α, the effective turbulent diffusivity D∼1010-1011cm2s−1 of a passive tracer introduced in the flow is large enough to allow the tracer to spread across a radial distance of 10rE in ∼13–129yr, less than the estimated cooling time of the PLD of ∼250yr. Further improvements to our model will need to incorporate the energy balance in the disk, a complete two-phase structure, and a more realistic equation of state.

A novel scalar tracking method for optimising film cooling systems

The purpose of this paper is to outline a novel passive-scalar tracking method for computational fluid dynamics optimisation studies. An example of its utility is in isolating the contributions of individual film cooling holes to overall cooling effectiveness on a heavily film cooled component. To isolate individual cooling contributions, passive (not a physical property of the flow, and therefore non-interacting) scalar variables are associated with the flow at each cooling hole outlet, with the scalar variable diffusivity set equal to the effective turbulent thermal diffusivity to replicate the mixing behaviour of the thermal field. The scalar tracking method is demonstrated by application to the optimisation of a nozzle guide vane endwall film cooling system, allowing a highly optimised system to be designed in three to five computational fluid dynamics simulations, orders of magnitude faster than optimisations performed using automated design space exploration. The test case for the method is an improved design of platform cooling system in which a relatively small quantity of high-momentum coolant is injected upstream of the vanes to reduce the total pressure deficit in near-wall region, followed by additional film cooling in low Mach number regions deeper into the passage. The optimised design uses half the coolant mass flow of a baseline design, while maintaining similar cooling effectiveness levels in critical regions.

EFFECTS OF ANISOTROPIES IN TURBULENT MAGNETIC DIFFUSION IN MEAN-FIELD SOLAR DYNAMO MODELS

We study how anisotropy of turbulent convection affects diffusion of large-scale magnetic fields and the dynamo process on the Sun. The effect of anisotropy is calculated in a mean-field magneto-hydrodynamics framework using the minimal $\tau$-approximation. We examine two types of mean-field dynamo models: the well-known benchmark flux-transport model, and a distributed-dynamo model with the subsurface rotational shear layer. For both models we investigate effects of the double-cell meridional circulation, recently suggested by helioseismology. We introduce a parameter of anisotropy as a ratio of the radial and horizontal intensity of turbulent mixing, to characterize the anisotropy effects. It is found that the anisotropy of turbulent convection affects the distribution of magnetic fields inside the convection zone. The concentration of the magnetic flux near the bottom and top boundaries of the convection zone is greater when the anisotropy is stronger. It is shown that the critical dynamo number and the dynamo period approach to constant values for the large anisotropy parameter. The anisotropy reduces the overlap of the toroidal fields of subsequent cycles in the time-latitude ``butterfly' diagram. If we assume that sunspots are formed in the vicinity of the subsurface shear layer, then the distributed dynamo model with anisotropic diffusivity satisfies the observational constraints from heloseismology results and is consistent with the value of effective turbulent diffusion, estimated from the dynamics of surface magnetic fields.

Estimates of turbulent diffusivities and energy dissipation rates from satellite measurements of spectra of stratospheric refractivity perturbations

Abstract. Approaches for estimations of effective turbulent diffusion and energetic parameters from characteristics of anisotropic and isotropic spectra of perturbations of atmospheric refractivity, density and temperature are developed. The approaches are applied to the data obtained with the GOMOS instrument for measurements of stellar scintillations on-board the Envisat satellite to estimate turbulent Thorpe scales, LT, diffusivities, K, and energy dissipation rates, ϵ, in the stratosphere. At low latitudes, effective values are LT ~ 1–1.1 m, ϵ ~ (1.8–2.4) × 10−5 W kg−1, and K ~ (1.2–1.6) × 10−2 m2 s−1 at altitudes of 30–45 km in September–November 2004, depending on different assumed values of parameters of anisotropic and isotropic spectra. Respective standard deviations of individual values, including all kinds of variability, are δLT ~ 0.6–0.7 m, δϵ ~ (2.3–3.5) × 10−2 W kg−1, and δK ~ (1.7–2.6) × 10−2 m2 s−1. These values correspond to high-resolution balloon measurements of turbulent characteristics in the stratosphere, and to previous satellite stellar scintillation measurements. Distributions of turbulent characteristics at altitudes of 30–45 km in low latitudes have maxima at longitudes corresponding to regions of increased gravity wave dissipation over locations of stronger convection. Correlations between parameters of anisotropic and isotropic spectra are evaluated.