Shear-induced Turbulence Research Articles

Experimental investigation of heat transport in inhomogeneous bubbly flow

In this work we study the heat transport in inhomogeneous bubbly flow. The experiments were performed in a rectangular bubble column heated from one side wall and cooled from the other, with millimetric bubbles introduced through one half of the injection section (close to the hot wall or close to the cold wall). We characterise the global heat transport while varying two parameters: the gas volume fraction α=0.4–5.1%, and the Rayleigh number RaH=4×109-2.2×1010. As captured by imaging and characterised using Laser Doppler Anemometry (LDA), different flow regimes occur with increasing gas flow rates. In the generated inhomogeneous bubbly flow there are three main contributions to the mixing: (i) transport by the buoyancy driven recirculation, (ii) bubble induced turbulence (BIT) and (iii) shear-induced turbulence (SIT). The strength of these contributions and their interplay depends on the gas volume fraction which is reflected in the measured heat transport enhancement. We compare our results with the findings for heat transport in homogeneous bubbly flow from Gvozdić et al. (2018). We find that for the lower gas volume fractions (α<4%), inhomogeneous bubbly injection results in better heat transport due to induced large-scale circulation. In contrast, for α>4%, when the contribution of SIT becomes stronger, but so does the competition between all three contributions, the homogeneous injection is more efficient.

Turbulent Transport by Diffusive Stratified Shear Flows: From Local to Global Models. III. A Closure Model

Abstract Being able to account for the missing mixing in stellar radiative zones is a key step toward a better understanding of stellar evolution. Zahn argued that thermally diffusive shear-induced turbulence might be responsible for some of this mixing. In Part I and Part II of this series of papers, we showed that Zahn’s mixing model applies when the properties of the turbulence are local. But we also discovered limitations of the model when this locality condition fails, in particular near the edge of a turbulent region. In this paper, we propose a second-order closure model for the transport of momentum and chemical species by shear-induced turbulence in strongly stratified, thermally diffusive environments (the so-called low Péclet number (LPN) limit), which builds upon the work of Garaud &amp; Ogilvie. Comparison against direct numerical simulations (DNSs) shows that the model is able to predict the vertical profiles of the mean flow and of the stress tensor (including the momentum transport) in diffusive shear flows, often with a reasonably good precision, and at least within a factor of order unity in the worst case scenario. The model is sufficiently simple to be implemented in stellar evolution codes, and all the model constants have been calibrated against DNSs. While significant limitations to its use remain (e.g., it can only be used in the slowly rotating LPN limit), we argue that it is more reliable than most of the astrophysical prescriptions that are used in stellar evolution models today.

Turbulence characteristics of 45° inclined dense jets

In the present study, we performed an extensive laboratory investigation to quantify the turbulence characteristics of 45° inclined dense jets using Particle Image Velocimetry (PIV) over a wide range of Densimetric Froude Number. The objective was to provide benchmark data to guide high resolution turbulence numerical simulations for dense jets in the future. The PIV measurements were sampled at a relatively high frequency of 50 Hz, which enabled the analysis of second order turbulence statistics as well as the turbulence kinetic energy spectrum (including the inertial subrange) along the curvilinear jet trajectory, which has hitherto not been reported. The measurements showed that the spectral profile was flat near the discharge port with the potential core, since the Kelvin–Helmholtz shear-induced turbulence at the jet boundaries had not fully penetrated to the core. The spectral profile then evolved along the trajectory with progressive steepening towards the higher frequencies, and a fully-developed profile appeared beyond the terminal rise with a clearly identifiable inertial subrange for the energy cascade. In parallel, we also performed numerical simulations using the Large Eddy Simulations (LES) approach with the Dynamic Smagorinsky sub-grid model for the specific discharge conditions as in the experiments. The LES approach followed that of Zhang et al. (Environ Fluid Mech 16(1):101–121, 2016, J Hydro Environ Res 15:54–66, 2017) using GCI as the grid convergence criteria. The comparison showed that the time-averaged first order mixing characteristics of the inclined dense jet can be simulated reasonably well comparing to the experimental data. In terms of the turbulence kinetic energy spectrum, the low frequencies of the production range were also well captured by the simulations. However, the simulated transitional spectra towards the inertial subrange decayed substantially faster than the experiments. The discrepancy was attributed to the fact that the grid resolution was not sufficiently fine in the simulations (which were constrained by the available computational resources and time), such that stratified effects remained present inside the sub-grids producing additional turbulence energy that were not represented by the Dynamic Smagorinsky model. Thus, the numerical investigation showed that further improvement in sub-grid models that can incorporate the stratified effects would be desirable in the future for engineering simulations.

Mixing mechanisms in a low-sheared inhomogeneous bubble column

This paper reports an experimental study of the mixing of a passive scalar in a bubble column at high Reynolds number and average gas volume fractions ranging from 2.0% to 7.5%. Starting from a homogeneous bubble column, the bubbly flow is progressively destabilized by imposing a gradient of gas volume fraction at the bottom of the tank. In that way, a single recirculation is produced, which allows to investigate the impact of a large-scale buoyancy-driven flow on the mixing of a passive scalar. It is shown that, as long as the shear-induced turbulence generated by the recirculation is negligible, mixing results from two main mixing mechanisms: the transport by the mean liquid velocity and the mixing induced by the bubbles. While the transport by the liquid recirculation can be accounted for by an advection term, the mixing induced by the bubbles is a diffusive process, the effective diffusivity of which has been measured in a homogeneous bubble column by Alméras et al. (2015). However, once the shear-induced turbulence produced by the shear develops, its role upon the mixing has to be taken into account too.

Methane and carbon dioxide fluxes over a lake: comparison between eddy covariance, floating chambers and boundary layer method

Abstract. Freshwaters bring a notable contribution to the global carbon budget by emitting both carbon dioxide (CO2) and methane (CH4) to the atmosphere. Global estimates of freshwater emissions traditionally use a wind-speed-based gas transfer velocity, kCC (introduced by Cole and Caraco, 1998), for calculating diffusive flux with the boundary layer method (BLM). We compared CH4 and CO2 fluxes from BLM with kCC and two other gas transfer velocities (kTE and kHE), which include the effects of water-side cooling to the gas transfer besides shear-induced turbulence, with simultaneous eddy covariance (EC) and floating chamber (FC) fluxes during a 16-day measurement campaign in September 2014 at Lake Kuivajärvi in Finland. The measurements included both lake stratification and water column mixing periods. Results show that BLM fluxes were mainly lower than EC, with the more recent model kTE giving the best fit with EC fluxes, whereas FC measurements resulted in higher fluxes than simultaneous EC measurements. We highly recommend using up-to-date gas transfer models, instead of kCC, for better flux estimates. BLM CO2 flux measurements had clear differences between daytime and night-time fluxes with all gas transfer models during both stratified and mixing periods, whereas EC measurements did not show a diurnal behaviour in CO2 flux. CH4 flux had higher values in daytime than night-time during lake mixing period according to EC measurements, with highest fluxes detected just before sunset. In addition, we found clear differences in daytime and night-time concentration difference between the air and surface water for both CH4 and CO2. This might lead to biased flux estimates, if only daytime values are used in BLM upscaling and flux measurements in general. FC measurements did not detect spatial variation in either CH4 or CO2 flux over Lake Kuivajärvi. EC measurements, on the other hand, did not show any spatial variation in CH4 fluxes but did show a clear difference between CO2 fluxes from shallower and deeper areas. We highlight that while all flux measurement methods have their pros and cons, it is important to carefully think about the chosen method and measurement interval, as well as their effects on the resulting flux.

Agitation, Mixing, and Transfers Induced by Bubbles

Bubbly flows involve bubbles randomly distributed within a liquid. At large Reynolds number, they experience an agitation that can combine shear-induced turbulence (SIT), large-scale buoyancy-driven flows, and bubble-induced agitation (BIA). The properties of BIA strongly differ from those of SIT. They have been determined from studies of homogeneous swarms of rising bubbles. Regarding the bubbles, agitation is mainly caused by the wake-induced path instability. Regarding the liquid, two contributions must be distinguished. The first one corresponds to the anisotropic flow disturbances generated near the bubbles, principally in the vertical direction. The second one is the almost isotropic turbulence induced by the flow instability through a population of bubbles, which turns out to be the main cause of horizontal fluctuations. Both contributions generate a k−3 spectral subrange and exponential probability density functions. The subsequent issue will be to understand how BIA interacts with SIT.

Role of overturns in optimal mixing in stratified mixing layers

Turbulent mixing plays a major role in enabling the large-scale ocean circulation. The accuracy of mixing rates estimated from observations depends on our understanding of basic fluid mechanical processes underlying the nature of turbulence in a stratified fluid. Several of the key assumptions made in conventional mixing parameterizations have been increasingly scrutinized in recent years, primarily on the basis of adequately high resolution numerical simulations. We add to this evidence by compiling results from a suite of numerical simulations of the turbulence generated through stratified shear instability processes. We study the inherently intermittent and time-dependent nature of wave-induced turbulent life cycles and more specifically the tight coupling between inherently anisotropic scales upon which small-scale isotropic turbulence grows. The anisotropic scales stir and stretch fluid filaments enhancing irreversible diffusive mixing at smaller scales. We show that the characteristics of turbulent mixing depend on the relative time evolution of the Ozmidov length scale$L_{O}$compared to the so-called Thorpe overturning scale$L_{T}$which represents the scale containing available potential energy upon which turbulence feeds and grows. We find that when$L_{T}\sim L_{O}$, the mixing is most active and efficient since stirring by the largest overturns becomes ‘optimal’ in the sense that it is not suppressed by ambient stratification. We argue that the high mixing efficiency associated with this phase, along with observations of$L_{O}/L_{T}\sim 1$in oceanic turbulent patches, together point to the potential for systematically underestimating mixing in the ocean if the role of overturns is neglected. This neglect, arising through the assumption of a clear separation of scales between the background mean flow and small-scale quasi-isotropic turbulence, leads to the exclusion of an highly efficient mixing phase from conventional parameterizations of the vertical transport of density. Such an exclusion may well be significant if the mechanism of shear-induced turbulence is assumed to be representative of at least some turbulent events in the ocean. While our results are based upon simulations of shear instability, we show that they are potentially more generic by making direct comparisons with$L_{T}-L_{O}$data from ocean and lake observations which represent a much wider range of turbulence-inducing physical processes.

Diapycnal mixing in layered stratified plane Couette flow quantified in a tracer-based coordinate

The mixing properties of statically stable density interfaces subject to imposed vertical shear are studied using direct numerical simulations of stratified plane Couette flow. The simulations are designed to investigate possible self-maintaining mechanisms of sharp density interfaces motivated by Phillips’ argument (Deep-Sea Res., vol. 19, 1972, pp. 79–81) by which layers and interfaces can spontaneously form due to vertical variations of diapycnal flux. At the start of each simulation, a sharp density interface with the same initial thickness is introduced at the midplane between two flat, horizontal walls counter-moving at velocities$\pm U_{w}$. Particular attention is paid to the effects of varying Prandtl number$\mathit{Pr}\equiv \unicode[STIX]{x1D708}/\unicode[STIX]{x1D705}$, where$\unicode[STIX]{x1D708}$and$\unicode[STIX]{x1D705}$are the molecular kinematic viscosity and diffusivity respectively, over two orders of magnitude from 0.7, 7 and 70. Varying$\mathit{Pr}$enables the system to access a considerable range of characteristic turbulent Péclet numbers$\mathit{Pe}_{\ast }\equiv {\mathcal{U}}_{\ast }{\mathcal{L}}_{\ast }/\unicode[STIX]{x1D705}$, where${\mathcal{U}}_{\ast }$and${\mathcal{L}}_{\ast }$are characteristic velocity and length scales, respectively, of the motion which acts to ‘scour’ the density interface. The dynamics of the interface varies with the stability of the interface which is characterised by a bulk Richardson number$\mathit{Ri}\,\equiv \,b_{0}h/U_{w}^{2}$, where$b_{0}$is half the initial buoyancy difference across the interface and$h$is the half-height of the channel. Shear-induced turbulence occurs at small$\mathit{Ri}$, whereas internal waves propagating on the interface dominate at large$\mathit{Ri}$. For a highly stable (i.e. large$\mathit{Ri}$) interface at sufficiently large$\mathit{Pe}_{\ast }$, the complex interfacial dynamics allows the interface to remain sharp. This ‘self-sharpening’ is due to the combined effects of the ‘scouring’ induced by the turbulence external to the interface and comparatively weak molecular diffusion across the core region of the interface. The effective diapycnal diffusivity and irreversible buoyancy flux are quantified in the tracer-based reference coordinate proposed by Winters &amp; D’Asaro (J. Fluid Mech., vol. 317, 1996, pp. 179–193) and Nakamura (J. Atmos. Sci., vol. 53, 1996, pp. 1524–1537), which enables a detailed investigation of the self-sharpening process by analysing the local budget of buoyancy gradient in the reference coordinate. We further discuss the dependence of the effective diffusivity and overall mixing efficiency on the characteristic parameters of the flow, such as the buoyancy Reynolds number and the local gradient Richardson number, and highlight the possible role of the molecular properties of fluids on diapycnal mixing.

Limitations of the clump-correlation theories of shear-induced turbulence suppression

The clump theory, primarily constructed by Dupree [Phys. Fluids 15, 334 (1972)] based on the moment approach and then generalized to the correlation theory [Y. Z. Zhang and S. M. Mahajan, Phys. Fluids B 5, 2000 (1993)], has long served as a basis for constructing theories of turbulence suppression by shear flow. In order to reveal the “intrinsic approximation” invoked in the clump-correlation theory, we examine a model based on two dimensional magnetized drift waves. After a rigorous derivation of the exact response function—a key to average the Green function of the system—we show that the Dupree, Zhang-Mahajan approach is recovered as the lowest order approximation in a small dimensionless parameter ϒ which is a triple product of the correlation time, wave number, and fluctuating drift velocity. The clump-correlation theory, thus, constitutes the Gaussian and lowest order non-Markovian process for a homogeneous stationary turbulence. We also provide, especially for the tokamak community, a readily usable formula to evaluate the effectiveness of shear-flow suppression; this formula pertains regardless of the specific model of correlation time.

Internal wave turbulence in the Llobregat prodelta (NW Mediterranean) under stratified conditions: A mechanism for sediment waves generation?

An array of 76 high-resolution temperature sensors at 0.5m intervals between 5 and 42.5m off the bottom was moored near the Barcelona harbor buoy in 81m water depth, between October 2013 and April 2014. The mooring was located just seaward of an extensive sediment wave area developed in the Llobregat River prodelta, with 1m high crests parallel to the coast and 50–100m wavelengths. In the NW-Mediterranean, the thermal stratification reaches its maximum penetration through the water column in autumn until it is broken by winter convection. Such a deep stratification affects large-scale sub-inertial slope currents, which are mostly confined to the upper half of the water column, by the hampered vertical exchange of frictional turbulence, and supports near-bottom internal waves between the inertial and buoyancy frequencies. Observed onshelf propagating frontal bores most likely interact with the sediment waves and contribute to their generation, as they are trailed by considerable shear-induced turbulence and high-frequency internal waves close to the buoyancy frequency that have wavelengths matching those of the sediment waves. The bores are either driven by near-inertial or 3–7day periodic sub-inertial motions just following a brief period of large convective instability at the end of the offshelf flow phase.

TURBULENT TRANSPORT IN A STRONGLY STRATIFIED FORCED SHEAR LAYER WITH THERMAL DIFFUSION

ABSTRACT This work presents numerical results on the transport of heat and chemical species by shear-induced turbulence in strongly stratified, thermally diffusive environments. The shear instabilities driven in this regime are sometimes called “secular” shear instabilities, and can take place when the Richardson number of the flow is large, provided the Péclet number is small. We have identified a set of simple criteria to determine whether these instabilities can take place or not. Generally speaking, we find that they may be relevant whenever the thermal diffusivity of the fluid is very large (typically larger than 1014 cm2 s−1), which is the case in the outer layers of high-mass stars (M ≥ 10 M ⊙), for instance. Using a simple model setup in which the shear is forced by a spatially sinusoidal, constant-amplitude body-force, we have identified several regimes ranging from effectively unstratified to very strongly stratified, each with its own set of dynamical properties. Unless the system is in one of the two extreme regimes (effectively unstratified or completely stable), however, we find that (1) only about 10% of the input power is used toward heat transport, while the remaining 90% is viscously dissipated; (2) that the effective compositional mixing coefficient is well-approximated by the model of Zahn, with D ≃ 0.02κ T /J where κ T is the thermal diffusivity and J is the Richardson number. These results need to be confirmed, however, with simulations in different model setups and at higher effective Reynolds number.

A new characterization of the turbulent diapycnal diffusivities of mass and momentum in the ocean

AbstractThe diapycnal diffusivity of mass supported by turbulent events in the ocean interior plays a fundamental role in controlling the global overturning circulation. The conventional representation of this diffusivity, due to Osborn (1980), assumes a constant mixing efficiency. We replace this methodology by a generalized‐Osborn formula which involves a mixing efficiency that varies nonmonotonically with at least two nondimensional variables. Using these two variables, we propose dynamic parameterizations for mixing efficiency and turbulent Prandtl number (the latter quantifies the ratio of momentum to mass diapycnal diffusivities) based on the first synthesis of an extensive direct numerical simulation of inhomogeneously stratified shear‐induced turbulence. Data from Argo floats are employed to demonstrate the extent of the spatial and statistical variability to be expected in both the diapycnal diffusivities of mass and momentum. We therefore suggest that previous estimates of these important characteristics of the global ocean require reconsideration.

Scalar mixing in bubbly flows: Experimental investigation and diffusivity modelling

Transport properties of scalars, as concentrations of a solute or temperature, are important for scale-up and design of operation units. An appropriate description of convective and diffusive mechanisms is required to predict local concentrations in complex geometries. In the case of gas–liquid bubbly flows, which are present in many chemical- or bio-reactors, effective diffusivity of scalars results from three contributions: molecular diffusion, Shear-Induced Turbulence (S.I.T.), i.e. turbulence induced by gradients of velocity in the continuous phase, and Bubble-Induced Turbulence (B.I.T.), i.e. turbulence generated by interactions of bubble wakes. In a previous work (Alméras et al., 2014, 2015), the diffusion resulting from B.I.T. has been characterized. Based on experiments performed in a homogeneous bubble column, it has been shown that the transport can be modelled by an effective diffusion and a physical modelling has been proposed to predict the diffusion induced by B.I.T. when other contributions are negligible.In the present work, we investigate the transport of a passive scalar in a complex bubbly flow at moderate gas volume fraction (αg≤3%), involving a large-scale flow recirculation responsible for the development of Shear-Induced Turbulence. Experimental mixing times measured by image processing under various operating conditions have been compared to numerical simulations of scalar transport. Simulations have been performed by means of an Eulerian RANS CFD model wherein the diffusion generated by B.I.T. modelled by Alméras et al. (2015) is implemented in addition to the diffusion resulting from the S.I.T.Results show that the diffusion caused by B.I.T. plays a major role in the mixing of scalars in the investigated flows. Neglecting this contribution leads to an important overestimation of the mixing time unless assigning arbitrary low values to the turbulent Schmidt number Sct (<0.3) adapted a posteriori to the simulated cases. On the other hand, considering the scalar diffusivity by B.I.T leads to a good agreement between experiments and CFD simulations, with keeping the Schmidt number in the usual range adopted for mixing in S.I.T. [0.7–1]. The model is generic enough to reproduce the scalar transport for various gas injections, without any further user adaptation.

A dual-scale turbulence model for gas–liquid bubbly flows

A dual-scale turbulence model is applied to simulate cocurrent upward gas–liquid bubbly flows and validated with available experimental data. In the model, liquid phase turbulence is split into shear-induced and bubble-induced turbulence. Single-phase standard k-ε model is used to compute shear-induced turbulence and another transport equation is added to model bubble-induced turbulence. In the latter transport equation, energy loss due to interface drag is the production term, and the characteristic length of bubble-induced turbulence, simply the bubble diameter in this work, is introduced to model the dissipation term. The simulated results agree well with experimental data of the test cases and it is demonstrated that the proposed dual-scale turbulence model outperforms other models. Analysis of the predicted turbulence shows that the main part of turbulent kinetic energy is the bubble-induced one while the shear-induced turbulent viscosity predominates within turbulent viscosity, especially at the pipe center. The underlying reason is the apparently different scales for the two kinds of turbulence production mechanisms: the shear-induced turbulence is on the scale of the whole pipe while the bubble-induced turbulence is on the scale of bubble diameter. Therefore, the model reflects the multi-scale phenomenon involved in gas–liquid bubbly flows.

Small-Scale Precipitation Elements in Midlatitude Cyclones Crossing the California Sierra Nevada

Abstract Radar data in some frontal systems passing over the Sierra Nevada of California show large variance on scales of ~10 km. The most prominent features are a few kilometers in scale and are similar to small-scale precipitation cells embedded in fronts seen over other mountain ranges. Other frontal systems crossing the Sierras are characterized by more uniform air motions. Updrafts in large-variance storms have characteristics of shear-induced turbulence, although buoyant instability may also contribute. Large-variance storms occur under stronger upstream winds and vertically integrated cross- and along-barrier moisture fluxes. Rain gauges indicate that large-variance storms have precipitation greater than smaller-variance storms. Stronger horizontal moisture fluxes may provide greater mean upslope condensation rates; however, it is hypothesized that accelerated microphysical processes are needed to most efficiently convert the condensate into precipitation that falls out on the lower slopes before being carried downstream. Radar data indicate that the turbulence embodied in the cellular motions of the large-variance cases is consistent with microphysical enhancement resulting from updraft elements producing pockets of liquid water conducive to riming and coalescence. In addition, radar spectrum-width data show that the cells contain strong subcell-scale turbulence conducive to particle collisions and aggregation. Polarimetric radar data just below the 0°C level show large raindrops in the cells, consistent with aggregation occurring in cells just above the melting layer. It is hypothesized that such enhanced microphysical processes in large-variance cases hasten the growth and fallout in the regions of maximum condensation over the windward slopes.

Diapycnal diffusivity, turbulent Prandtl number and mixing efficiency in Boussinesq stratified turbulence

In order that it be correctly characterized, irreversible turbulent mixing in stratified fluids must distinguish between adiabatic ‘stirring’ and diabatic ‘mixing’. Such a distinction has been formalized through the definition of a diapycnal diffusivity, $K_{{\it\rho}}$ (Winters &amp; D’Asaro, J. Fluid Mech., vol. 317, 1996, pp. 179–193) and an appropriate mixing efficiency, $\mathscr{E}$ (Caulfield &amp; Peltier, J. Fluid Mech., vol. 413, 2000, pp. 1–47). Equivalent attention has not been paid to the definitions of a corresponding momentum diffusivity $K_{m}$ and hence an appropriately defined turbulent Prandtl number $\mathit{Pr}_{t}=K_{m}/K_{{\it\rho}}$. In this paper, the diascalar framework of Winters &amp; D’Asaro (1996) is first reformulated to obtain an ‘Osborn-like’ formula in which the correct definition of irreversible mixing efficiency $\mathscr{E}$ is shown to replace the flux Richardson number which Osborn (J. Phys. Oceanogr., vol. 10, 1980, pp. 83–89) assumed to characterize this efficiency. We advocate the use of this revised representation for diapycnal diffusivity since the proposed reformulation effectively removes the simplifying assumptions on which the original Osborn formula was based. We similarly propose correspondingly reasonable definitions for $K_{m}$ and $\mathit{Pr}_{t}$ by eliminating the reversible component of the momentum production term. To explore implications of the reformulations for both diapycnal and momentum diffusivity we employ an extensive series of direct numerical simulations (DNS) to investigate the properties of the shear-induced density-stratified turbulence that is engendered through the breaking of a freely evolving Kelvin–Helmholtz wave. The DNS results based on the proposed reformulation of $K_{{\it\rho}}$ are compared with available estimations due to the mixing length model, as well as both the Osborn–Cox and the Osborn models. Estimates based upon the Osborn–Cox formulation are shown to provide the closest approximation to the diapycnal diffusivity delivered by the exact representation. Through compilation of the complete set of DNS results we explore the characteristic dependence of $K_{{\it\rho}}$ on the buoyancy Reynolds number $\mathit{Re}_{b}$ as originally investigated by Shih et al. (J. Fluid Mech., vol. 525, 2005, pp. 193–214) in their idealized study of homogeneous stratified and sheared turbulence, and show that the validity of their results is only further reinforced through analysis of the turbulence produced in the more geophysically relevant Kelvin–Helmholtz wave life-cycle ansatz. In contrast to the results described by Shih et al. (2005) however, we show that, besides $\mathit{Re}_{b}$, a vertically averaged measure of the gradient Richardson number $\mathit{Ri}_{b}$ may equivalently characterize the turbulent mixing at high $\mathit{Re}_{b}$. Based on the dominant driving processes involved in irreversible mixing, we categorize the intermediate (i.e. $\mathit{Re}_{b}=O(10^{1}{-}10^{2})$) and high (i.e. $\mathit{Re}_{b}&gt;O(10^{2})$) range of $\mathit{Re}_{b}$ as ‘buoyancy-dominated’ and ‘shear-dominated’ mixing regimes, which together define a transition value of $\mathit{Ri}_{b}\sim 0.2$. Mixing efficiency varies non-monotonically with both $\mathit{Re}_{b}$ and $\mathit{Ri}_{b}$, with its maximum (on the order of 0.2–0.3) occurring in the ‘buoyancy-dominated’ regime. Unlike $K_{{\it\rho}}$ which is very sensitive to the correct choice of $\mathscr{E}$ (i.e. $K_{{\it\rho}}\propto \mathscr{E}/(1-\mathscr{E})$), we show that $K_{m}$ is almost insensitive to the choice of $\mathscr{E}$ (i.e. $K_{m}\propto 1/(1-\mathscr{E})$) so long as $\mathscr{E}$ is not close to unity, which implies $K_{m}\approx \mathit{Ri}_{b}\mathit{Re}_{b}$ for the entire range of $\mathit{Re}_{b}$. The turbulent Prandtl number is consequently shown to decrease monotonically with $\mathit{Re}_{b}$ and may be (to first order) simply approximated by $\mathit{Re}_{b}$ itself. Assuming $\mathit{Pr}_{t}=1$, or $\mathit{Pr}_{t}=10$ (as is common in large-scale numerical models of the ocean general circulation), is also suggested to be a questionable assumption.

An intercomparison study between RAMS and CRES-Flow-NS models and evaluation with wind tunnel experimental data: Toward improving atmospheric modeling for wind resource assessment

The use of atmospheric models for wind resource assessment in complex terrain is limited by their coarse resolution. Using non-hydrostatic mesoscale models such as RAMS, fine resolution grids and a proper turbulent closure scheme such as the k–ε, it is theoretically possible to describe orographic shear-induced turbulence at microscale level with certain accuracy. In such cases, microscale CFD models modified to represent the interaction of the atmospheric boundary layer with the local orography are proven to show accurate results in idealized cases such as neutral stratification. On the other hand, their limitation in representing real atmospheric interaction between large scale structures and thermal stratification with the flow pattern can introduce significant errors in evaluating wind energy potential. In this work, proper modifications of the RAMS model were performed to simulate 2D wind flow over an isolated hill at high resolution configuration. The results have been compared with the CFD model CRES-Flow-NS and with wind tunnel experimental data. It is found that RAMS is able to reproduce basic flow features with comparable accuracy as the CFD model. This work is part of a major effort to make RAMS a reliable tool for atmospheric flow simulations of various complexity.

Controls for multi-scale temporal variation in ecosystem methane exchange during the growing season of a permanently inundated fen

Wetlands are the largest natural sources for atmospheric methane (CH4). In wetlands with permanent shallow inundation, the seasonal variation of CH4 exchange is mainly controlled by temperature and phenology. In addition, ecosystem CH4 exchange varies considerably on smaller temporal scales such as days or weeks. Several single processes that control CH4 emissions on the local soil–plant–atmosphere continuum are well investigated, but their interaction on ecosystem level is not well understood yet. We applied wavelet analysis to a quasi-continuous eddy covariance CH4 flux time series to describe the temporal variation of ecosystem CH4 exchange within the growing season of a permanently inundated temperate fen. Moreover, we addressed time scale-specific controls and investigated whether their impact changes during the course of the growing season.On large time scales of two weeks to three months, temperature explained most of the variation in ecosystem CH4 exchange. In general, the temperature in the shallow water column had the largest impact as explanatory variable, however, air temperature and soil temperature became increasingly important as explanatory variables when water level dropped slightly up to June. The diurnal variation of ecosystem CH4 exchange shifted during the course of the growing season: During a short time period at the end of April, plant activity (expressed by canopy photosynthesis) caused a diurnal variation of ecosystem CH4 exchange with peak time around noon. In the following weeks, the daily cycle of convective mixing within the water column (expressed by the water temperature gradient) gradually gained importance and caused high night-time CH4 emissions, thereby levelling off the diurnal CH4 emission pattern. Moreover, shear-induced turbulence caused short-term fluctuations of ecosystem CH4 exchange on time scales up to two hours.Our study highlights the need for multi-scale approaches that consider the non-stationarity of the underlying processes to adequately describe the complexity of ecosystem CH4 exchange. Moreover, we show that CH4 release processes such as convective mixing of the water column which have been mainly considered for aquatic ecosystems (see recent exceptions in Godwin et al., 2013; Poindexter and Variano, 2013) might also be of importance in shallowly flooded terrestrial ecosystems.

In-flight turbulence benefits soaring birds

ABSTRACT Birds use atmospheric updrafts to subsidize soaring flight. We observed highly variable soaring flight by Black Vultures (Coragyps atratus) and Turkey Vultures (Cathartes aura) in Virginia, USA, that was inconsistent with published descriptions of terrestrial avian flight. Birds engaging in this behavior regularly deviated vertically and horizontally from linear flight paths. We observed the soaring flight behavior of these 2 species to understand why they soar in this manner and when this behavior occurs. Vultures used this type of soaring mainly at low altitudes (<50 m), along forest edges, and when conditions were poor for thermal development. Because of the tortuous nature of this flight, we describe it as “contorted soaring.” The primary air movement suitable to subsidize flight at this altitude and under these atmospheric conditions is small-scale, shear-induced turbulence, which our results suggest can be an important resource for soaring birds because it permits continuous subsidized flig...

Lithium abundance dispersion in the Pleiades and M 34

Context. K-type stars of similar effective temperatures in clusters younger than about 250 Myr are characterised by a wide dispersion in lithium abundance whose origin is not understood. Aims. The present study addresses this question in light of rotation period measurements recently conducted in the Pleiades and M 34 open clusters. Methods. The study investigates the dependence of lithium abundance with effective temperature distinguishing stars that belong to different rotation sequences in diagrams where measured rotation periods are plotted against B − V colour indices. Results. At any given effective temperature below 5500 K, stars on the fast rotator sequence in the Pleiades and M 34 have significantly higher lithium abundances that stars with same masses and ages located on the slow rotator sequence. Conclusions. This correlation suggests that shear-induced turbulence at the base of the convection zone accelerates the depletion of lithium in rapidly rotating late G- and K-type stars during a brief episode of strong rotational braking by stellar wind in their early evolution on the main sequence. The epoch at which this strong rotational braking occurs does not depend on stellar mass only but also on the rotation history of each individual star. I argue that the large dispersion in surface lithium abundance of K stars in the Pleiades and M 34 could be a consequence of this phenomenon.