Turbulent Kinetic Energy Flux Research Articles

Turbulent kinetic energy budget of sediment-laden open-channel flows: bedload-induced wall-roughness similarity

New experiments in highly turbulent, steady, subcritical and uniform water open-channel flows have been carried out to measure the mean turbulent kinetic energy (TKE) budget of sediment-laden boundary layer flows with two sizes (dp = 3 mm and 1 mm) of Plexiglas particles $({\rm relative\ density}\ = 1.192)$ . The experiments covered energetic sediment transport conditions (Shields number of $0.35 < \theta < 1.2$ ) ranging from non-capacity to full-capacity flows in bedload-to-suspension-dominated transport modes (suspension number of $0.5 < {w_s}/{u_\ast } < 1.3$ where ${w_s}$ is the settling velocity and $u_*$ is the friction velocity) and for weakly to highly inertial, finite size turbulence-particle conditions (Stokes number of 0.1 < St < 3.5 and dp/η > 10 where $\eta$ is the Kolmogorov length scale). It was shown that the effects of sediments on the TKE budget are very pronounced in all large particle experiments for which a bedload layer of several grain diameter thickness is developed above the channel bed. When compared with the corresponding reference clear-water flows, the TKE shear-production rate for the 3 mm particle flows is strongly reduced in the wall region corresponding to the bedload layer. This turbulence damping is seen to increase with sediment load until full capacity for flows with constant Shields value, as well as with Shields number value. Inside this damped TKE shear-production zone, a distinct peak of maximal turbulence production appears to coincide with the upper edge of the bedload layer delimited by a sharp gradient in mean sediment concentration. This vertically upshifted peak of TKE production is accompanied by an enhanced net downward oriented TKE flux when compared with the reference clear-water flows. The downward diffused TKE is found to act in the bedload layer as a local energy source in reasonable balance with the sediment transport term. The mechanism behind this downward TKE transport was further analysed on the basis of coherent flow structure dynamics controlled by ejection- and sweep-type events. The agreement between the height of downward directed mean TKE flux and the height below which sweep-type events dominate the Reynolds shear-stress contribution over ejections, revealed the leading role played by sweeps in mean TKE transport. This agreement holds for all reference clear-water flows supporting the well-known wall-roughness-induced dominance of the sweep contribution in turbulent, rough clear-water boundary layer flows. Furthermore, for all 3 mm particle flows, the two referred to transition levels were significantly and similarly upshifted to the upper edge of the bedload layer. Only for these sediment-laden flows, the bedload layer thickness is seen to exceed the wall-roughness sublayer of the reference clear-water flows. This supports a strong analogy between wall-roughness effects in clear-water flows and bedload layer effects in sediment-laden flows, on the mean TKE budget induced by a similarly modified coherent flow structure dynamics. The bedload layer-controlled wall roughness is finally confirmed by the good prediction of the wall-roughness parameter ks of the logarithmic velocity distribution. An empirical formulation fitting the presented measurements is presented, valid over the range of Shields number values covered herein.

An observational study on the impact of sea-land breeze and low-level jet on air pollutant transport in the Bohai Bay

Nocturnal pollutant concentrations in Bohai Bay often exhibit significant uneven spatial distribution, even under weak atmospheric circulation and stable boundary layer conditions, posing a serious challenge for air pollution forecasting. This study analyzed the causes of inverse changes in nocturnal pollutant concentrations between inland and coastal areas based on a month-long observation campaign on the meteorology and air pollutants in Bohai Bay. The results indicated that the primary cause was the combined influence of sea-land breeze (SLB) and low-level jet (LLJ) under a weak synoptic pattern. Sea breezes (SB) can transport pollutants from the coast to inland areas. The occurrence of land breezes (LB) and southwest-west LLJ at night can lead to the transport of pollutants inland to the coast. The impacts of LLJ on pollutant transport can be observed in three ways. First, the LLJ enhanced the horizontal ventilation in the boundary layer. The horizontal wind speed in the stable boundary layer increased by 2–6 m/s. Second, the LLJ weakened the stability of the stable boundary layer. A thin layer of instability existed between the surface-based and elevated inversion layers. The height of the inversion layer top increased by approximately 200 m, and the strength of the inversion weakened by at least 1 °C. Finally, the LLJ enhanced atmospheric vertical diffusion. The increased turbulent kinetic energy and upward momentum flux in the lower layer of the boundary layer, as well as the pronounced vertical upward motion between the top of the boundary layer and the altitude of the LLJ, contributed to the vertical dispersion of ground pollutants. Pollutants diffusing to the altitude of the LLJ can be transported horizontally to the coastal areas along the southwest-west LLJ.

Vertical Energy Fluxes Driven by the Interaction Between Wave Groups and Langmuir Turbulence

Abstract Data from an air-sea interaction tower are used to close the turbulent kinetic energy (TKE) budget in the wave-affected surface layer of the upper ocean. Under energetic wind forcing with active wave breaking, the dominant balance is between the dissipation rate of TKE and the downward convergence in vertical energy flux. The downward energy flux is driven by pressure work, and the TKE transport is upward, opposite to the downgradient assumption in most turbulence closure models. The sign and the relative magnitude of these energy fluxes are hypothesized to be driven by an interaction between the vertical velocity of Langmuir circulation (LC) and the kinetic energy and pressure of wave groups, which is the result of small-scale wave-current interaction. Consistent with previous modeling studies, the data suggest that the horizontal velocity anomaly associated with LC refracts wave energy away from downwelling regions and into upwelling regions, resulting in negative covariance between the vertical velocity of LC and the pressure anomaly associated with the wave groups. The asymmetry between downward pressure work and upward TKE flux is explained by the Bernoulli response of the sea surface, which results in groups of waves having a larger pressure anomaly than the corresponding kinetic energy anomaly, consistent with group-bound long wave theory.

Investigation on scouring and turbulence characteristics around T-head spur dike

ABSTRACT In this study, different geometrical configurations of T-head spur dikes, such as spur dike length (l = 6, 9, and 12 cm), wing length (λ = 0.5, 0.75 l, and l), and wing orientation (θ = 60°, 90°, and 120°) are used to investigate the local scour. The T-head spur dike with l = 9 cm, λ = l, and θ = 90° is found as the optimum configuration. The turbulent kinetic energy flux in the vertical direction is positive in the non-scour zone and negative in the scour zone with a higher magnitude, resulting in the transport of turbulent energy towards the bed that leads to scouring. The sweep events dominate against the ejection events in the scour zones, but in the non-scoured zone, it is the opposite. A regression equation was developed to estimate the scour depth around the spur dike, and satisfactory results were obtained.

Time-averaged flow characterisations in a bimodal gravel-bed stream and relative role of sediment depositions on near-bed coherent flow structures

Abstract The present study aims to quantify experimentally the relative role of sediment depositions on near-bed flows and turbulence in a gravel-bed stream. Time-averaged velocity was measured over a sand-filled gravel-bed stream with four cases of sediment depositions and compared with those over a gravel-bed stream without sediment depositions. An acoustic Doppler velocimeter was used to measure the instantaneous velocity of flows. The progressive infilling of void spaces in the gravel-bed stream forms distinct bimodal depositions that alter the mean flows characterised by increasing zero-velocity levels and massive damping in the bed shear stresses. The data plots of turbulent intensity depict enhancement of streamwise turbulent intensity in the near-bed flow region with increasing sand depositions. Moreover, the opposite nature of streamwise and vertical turbulent kinetic energy fluxes in the interfacial sublayer leads to slowing down the time-average Reynolds shear stresses at the vicinity of the gravel-bed surface. At the vicinity of the crest, the ejection and sweep events contributed approximately 86 and 56%, respectively, to the total Reynolds shear stress production in the case of gravel bed under clear-water flow conditions. By contrast, the contributions of turbulent sweep events increased over the sand-filled gravel bed at the same location.

Numerical investigation of mixed-phase turbulence induced by a plunging jet

In nature and engineering applications, water jet plunging acts as a key process causing interface breaking and generating mixed-phase turbulence. In this paper, high-resolution numerical simulations of the plunging of a water jet into a quiescent pool were performed to investigate the statistical properties of mixed-phase turbulence, with a special focus on the closure problem of the Reynolds-averaged equation. We conducted phase-resolved simulations, with the air–water interface captured using a coupled level-set and volume-of-fluid method. Various cases were performed to analyse the effects of the Froude number and Reynolds number. The simulation results showed that the turbulence statistics are insensitive to the Reynolds number under investigation, while the Froude number influences the flow properties significantly. To investigate the closure problem of the mean momentum equation, the turbulent kinetic energy (TKE) and turbulent mass flux (TMF) and their transport equations were analysed further. It was discovered that the balance relationship of the TKE budget terms remained similar to many single-phase turbulent flows. The TMF is an additional unclosed term in mixed-phase turbulence over the single-phase turbulence. Our simulation results showed that the production term in its transport equation was highly correlated to TKE. Based on this finding, a closure model for the production term of TMF was further proposed.

Direct Numerical Simulation of Heat Transfer in a 7-Pin Wire-Wrapped Rod Bundle

The Sodium-Cooled Fast Reactor (SFR) is a promising concept chosen in the Generation IV International Forum as a possible design for pursuing the sustainable use of nuclear energy. Its core consists of multiple hydraulically isolated assemblies, with a tightly packed triangular lattice array of fuel pins enclosed in a hexagonal duct present within each assembly. Helical wire spacers are wrapped along the axis of the rods to maintain a gap between them, inducing a secondary flow, increasing the channel mixing, and enhancing convective heat transfer. In this study, a direct numerical simulation campaign is conducted for a simplified 7-pin wire wrapper geometry, with Reynolds numbers ranging from = 1000 to 10 000 and a Prandtl number of = 0.005, to investigate heat transfer in low-flow conditions. The wire wrapper case is compared to a bare bundle case with seven pins. The results are discussed, and heat transfer predictions are compared between our numerical results and classic correlations. An anisotropy invariant map is obtained for the above-mentioned cases, and turbulent kinetic energy and turbulent heat flux budgets are computed and analyzed. Our findings provide unique insights into the flow behavior within a wire-wrapped bundle.

Higher-order turbulent characteristics of sinuous alluvial river

Sinuous channels with movable banks were examined for flow patterns in laboratory experiments. The velocity, Turbulent kinetic energy (TKE) budget, TKE flux, and bursting events were analyzed to examine the turbulent flow behavior. Quadrant analysis is performed to determine the contribution of bursting events to Reynold shear stress. At the apex of the sinuous channel, quadrant analysis reveals a mixing of events. On the other hand, as the hole size increases, the contribution of events decreases. The TKE (turbulent kinetic energy) flux is greater near the riverbed and diminishes as it approaches the bed surface. The TKE flux is higher at the river bend's exit than at the entry point. Examining the TKE budget, the TKE production and TKE dissipation indicate that TKE dissipation surpasses the production near the riverbed and the surface. These terms are uniformly distributed and decrease as they approach the surface.

Direct Numerical Simulation and Large Eddy Simulation of a 67–Pebble Bed Experiment

An in-depth understanding of the flow physics in packed beds is critical for developing simulation tools for pebble bed reactors. Advances in computing power have now made the full-core pebble-resolved computational fluid dynamics simulation of these systems possible. This work presents validation of the velocity and pressure predictions made by the spectral element code NekRS followed by a study of the turbulent kinetic energy and turbulent heat flux budgets. Two cases with corresponding experiments are considered: a bed of 67 pebbles with Re = 1460 and a bed of 789 pebbles with 324 < Re < 1024. Velocity and pressure drop comparisons are performed with the two cases, respectively. Good agreement is found between the experiments and their respective NekRS simulations. The 67-pebble case was then used to perform a direct numerical simulation to extract the turbulent kinetic energy and turbulent heat flux budget terms. Analysis of the turbulent kinetic energy production revealed large areas of negative production near the bottom surfaces of the pebbles. Further investigation revealed a trend between the average amount of negative turbulent kinetic energy production and the local porosity. These results continue to suggest that inertial effects play a large role in differentiating near-wall flow from bed-interior flow.

Turbulence in a wall-wake flow downstream of two horizontal cylinders

Experimental investigations of flow past two (one above other) horizontal cylinders have been presented in this paper. The experimental data captured over a rough-bed with double cylinders having three different diameters, were used for the analysis. Firstly, general characteristics such as streamwise velocity, Reynolds shear stress and turbulence intensity profiles have been elucidated at different downstream locations from cylinder position; then some advanced analysis such as length scales, turbulent kinetic energy (TKE) fluxes and budget have been investigated to exhibit their variations. Length scale profiles exhibit higher values in near bed; indicating comparatively larger eddies’ downstream of both cylinders. TKE budget profiles indicate highly negative pressure energy diffusion rate together with a sufficient TKE production rate, stabilized by the amplified TKE diffusion and dissipation rates. To determine one of the most prime behaviors of turbulence characteristics, namely TKE dissipation rate more accurately, the concept of structure function has been employed. Primarily velocity gradient method elucidates TKE dissipation rate, then it has been verified by Kolmogorov’s two-thirds law using second order structure function and Kolmogorov’s − 5/3 law using the method of power spectra.

Behavioral patterns of turbulent kinetic energy budget and quadrant analysis for flows over bedform under the influence of downward seepage

Seepage is one of the important factors involved in natural flow conditions, contributing to changes in flow turbulence patterns and morphological changes due to the transport of sediments. This transport of sediment particles influences the development of fluvial bedforms in any river channel. However, previous research on fluvial dynamics has not considered the influence of seepage on the flow field over the fluvial bedforms. The present experimental research aims to explore the behavioral patterns of turbulent kinetic energy, the turbulent kinetic energy (TKE) budget, and quadrant analysis for flows over two-dimensional dune shaped bedforms in the absence and presence of downward seepage. Results from the study illustrate that at the measurement locations on the initial and lee side sections of a dune, the TKE increases with the introduction of downward seepage, leading to an increase in turbulence production near the bed-surface region. The flow energy under both no seepage and seepage conditions contributes mainly to the turbulent production. Turbulence diffusion and dissipation rates have been found to decline in the near-bed region of the initial and lee side sections of the dune. However, turbulent production has been found to be significantly higher in the presence of downward seepage than under the no seepage condition. Similarly, turbulent kinetic energy flux increases in the streamwise direction, while it reduces in the vertical direction at initial sections and lee side sections of the dune under seepage conditions. However, at the middle sections and crest portion of the dune, opposite behavioral patterns are observed for all the aforementioned turbulent entities. Quadrant analysis reveals that the sweep and ejection event increases while inward and outward interaction reduces in the near bed zone. Although the contribution of both sweep and ejection events increases in the presence of downward seepage, sweep events have clear dominance in the near bed region, suggesting the possibility of a higher rate and amount of sediment transportation than under the no seepage condition.

Energy balances for the collision of gravity currents of equal strengths

Collision of two counterflowing gravity currents of equal densities and heights was investigated by means of three-dimensional high-resolution simulations with the goal of understanding the flow structures and energetics in the collision region in more detail. The lifetime of collision is approximately $3 \tilde {H}/\tilde {u}_f$ , where $\tilde {H}$ is the depth of heavy and ambient fluids, and $\tilde {u}_f$ is the front velocity of the approaching gravity currents, and the lifetime of collision can be divided into three phases. During Phase I, $-0.2 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 0.5$ , where $\tilde {t}$ is the time, and $\tilde {t}_c$ is the time instance at which the two colliding gravity currents have fully osculated, geometric distortions of the gravity current fronts result in stretching of pre-existing vorticity in the wall-normal direction inside the fronts, and an array of vertical vortices extending throughout the updraught fluid column develop along the interface separating the two colliding gravity currents. The array of vertical vortices is responsible for the mixing between the heavy fluids of the two colliding gravity currents and for the production of turbulent kinetic energy in the collision region. The presence of the top boundary deflects the updraughts into the horizontal direction, and a number of horizontal streamwise vortices are generated close to the top boundary. During Phase II, $0.5 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 1.2$ , the horizontal streamwise vortices close to the top boundary induce turbulent buoyancy flux and break up into smaller structures. While the production of turbulent kinetic energy weakens, the rate of transfer of energy to turbulent flow due to turbulent buoyancy flux reaches its maximum and becomes the primary supply in the turbulent kinetic energy in Phase II. During Phase III, $1.2 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 2.8$ , the collided fluid slumps away from the collision region, while the production of turbulent kinetic energy, turbulent buoyancy flux and dissipation of energy attenuate. From the point of view of energetics, the production of turbulent kinetic energy and turbulent buoyancy flux transfers energy away from the mean flow to the turbulent flow during the collision. Our study complements previous experimental investigations on the collision of gravity currents in that the flow structures, spatial distribution and temporal evolution of the mean flow and turbulent flow characteristics in the collision region are presented clearly. It is our understanding that such complete information on the energy budgets in the collision region can be difficult to attain in laboratory experiments.

Assessing the Departures from the Energy- and Flux-Budget (EFB) Model in Heterogeneous and Urbanized Environment for Stable Atmospheric Stratification

Turbulence closure schemes, besides their intrinsic theoretical importance, represent a fundamental component in the atmospheric numerical models. Among his numerous and diverse scientific contributions, Prof. Sergej S. Zilitinkevich, with his coauthors, elaborated a turbulence closure model for stably-stratified geophysical flows, the Energy and Flux Budget (EFB) model. This closure has been verified and applied on many different experimental datasets and case studies, for steady state and homogeneous conditions. Having available observational datasets for urban and suburban sites in different cities in Italy, we investigate the deviation of the observations of turbulent kinetic energy and momentum flux from the EFB turbulence closure model in heterogeneous conditions. This allows addressing and interpreting the features that induce such deviation between the model and the observations. The EFB model is then revisited including residual terms that can account for the non-stationarity and heterogeneity of the considered cases. The correction with the residual terms leads to improve the agreement between the theoretical formulations and the observed behaviour for the turbulent kinetic energy shares and for the vertical momentum flux.

Computational Characterization of Unsteadiness and Turbulence in Rotor Hub Wakes

Reynolds stresses and turbulent kinetic energy are studied in the wakes of several helicopter rotor hub geometries in forward flight. Computational fluid dynamics simulations are performed using NASA's OVERFLOW 2.2n Reynoldsaveraged Navier–Stokes solver. The simulations impose flow conditions based on previous and current experimental and numerical studies. Discrete Fourier transforms are used to examine velocity harmonics for several frequencies and compared against available experimental results. Components of the Reynolds stress tensor are computed and examined. Production and transport of the turbulent kinetic energy are examined through the rotor hub wakes at six streamwise coordinates. It was found that the scissor arms, previously found to have a significant effect on rotor hub force harmonics, also had a significant effect on the magnitudes of Reynolds stresses and turbulent kinetic energy. Integrated values of turbulent kinetic energy flux indicate that drag-reducing designs have a direct effect on turbulent kinetic energy levels in the wake.

Suppression of the turbulent kinetic energy and enhancement of the flame-normal Reynolds stress in premixed jet flames at small Lewis numbers

We report the effects of the Lewis number on the turbulent kinetic energy, Reynolds stresses, and scalar fluxes in premixed jet flames with strong mean shear. The direct numerical simulation (DNS) of piloted turbulent premixed jet flames is performed under the same condition except for different Lewis numbers to isolate the Lewis number effects. The turbulence intensity within the mean flame brush is found to decay more rapidly along the axial distance with a smaller Lewis number. This Lewis number dependence results from the coupling of the mean shear and the combustion heat release, where the mean shear is the primary source of turbulence production. We show that, under the strain imposed by the mean shear and turbulence fluctuation, the heat release of premixed jet flames is significantly enhanced at the Lewis number smaller than unity, which is represented by the rising flamelet consumption speed and flame surface area. As a consequence, the mean shear within the flame brush is suppressed at small Lewis numbers via the dilatation effect, and the weakened mean shear production causes the fast turbulence suppression along the axial direction. The enhanced heat release at small Lewis numbers also increases the flame-normal Reynolds stress, and leads to the counter-Boussinesq behavior of the shear Reynolds stress and the counter-gradient transport of scalar fluxes. We model the Lewis number effects on local turbulence and scalar transport using the stretched laminar flame speed and thickness, and achieve overall good estimations of the flame-normal Reynolds stress and scalar transport at small Lewis numbers.

Improvement of the Ocean Mixed Layer Model via Large-Eddy Simulation and Inverse Estimation

Abstract The ocean mixed layer model (OMLM) is improved using the large-eddy simulation (LES) and the inverse estimation method. A comparison of OMLM (Noh model) and LES results reveals that underestimation of the turbulent kinetic energy (TKE) flux in the OMLM causes a negative bias of the mixed layer depth (MLD) during convection, when the wind stress is weak or the latitude is high. It is further found that the entrainment layer thickness is underestimated. The effects of alternative approaches of parameterizations in the OMLM, such as nonlocal mixing, length scales, Prandtl number, and TKE flux, are examined with an aim to reduce the bias. Simultaneous optimizations of empirical constants in the various versions of Noh model with different parameterization options are then carried out via an iterative Green’s function approach with LES data as constraining data. An improved OMLM is obtained, which reflects various new features, including the enhanced TKE flux, and the new model is found to improve the performance in all cases, namely, wind-mixing, surface heating, and surface cooling cases. The effect of the OMLM grid resolution on the optimal empirical constants is also investigated. Significance Statement This work illustrates a novel approach to improve the parameterization of vertical mixing in the upper ocean, which plays an important role in climate and ocean models. The approach utilizes the data from realistic turbulence simulation, called large-eddy simulation, as proxy observation data for upper ocean turbulence to analyze the parameterization, and the statistical method, called inverse estimation, to obtain the optimized empirical constants used in the parameterization. The same approach can be applied to improve other turbulence parameterization, and the new vertical mixing parameterization can be applied to improve climate and ocean models.

Analysis of scale-dependent kinetic and potential energy in sheared, stably stratified turbulence

Budgets of turbulent kinetic energy (TKE) and turbulent potential energy (TPE) at different scales $\ell$ in sheared, stably stratified turbulence are analysed using a filtering approach. Competing effects in the flow are considered, along with the physical mechanisms governing the energy fluxes between scales, and the budgets are used to analyse data from direct numerical simulation at buoyancy Reynolds number $Re_b=O(100)$ . The mean TKE exceeds the TPE by an order of magnitude at the large scales, with the difference reducing as $\ell$ is decreased. At larger scales, buoyancy is never observed to be positive, with buoyancy always converting TKE to TPE. As $\ell$ is decreased, the probability of locally convecting regions increases, though it remains small at scales down to the Ozmidov scale. The TKE and TPE fluxes between scales are both downscale on average, and their instantaneous values are correlated positively, but not strongly so, and this occurs due to the different physical mechanisms that govern these fluxes. Moreover, the contributions to these fluxes arising from the sub-grid fields are shown to be significant, in addition to the filtered scale contributions associated with the processes of strain self-amplification, vortex stretching and density gradient amplification. Probability density functions (PDFs) of the $Q,R$ invariants of the filtered velocity gradient are considered and show that as $\ell$ increases, the sheared-drop shape of the PDF becomes less pronounced and the PDF becomes more symmetric about $R=0$ .

The Redistribution of Air–Sea Momentum and Turbulent Kinetic Energy Fluxes by Ocean Surface Gravity Waves

Abstract The momentum flux to the ocean interior is commonly assumed to be identical to the momentum flux lost from the atmosphere in traditional atmosphere, ocean, and coupled models. However, ocean surface gravity waves (hereafter waves) can alter the magnitude and direction of the ocean-side stress (τoc) from the air-side stress (τa). This is rarely considered in coupled climate and forecast models. Based on a 30-yr wave hindcast, the redistribution of the global wind stress and turbulent kinetic energy (TKE) flux by waves was investigated. Waves play a more important role in the windy oceans in middle and high latitudes than that in the oceans in the tropics (i.e., the central portion of the Pacific and Atlantic Oceans). On average, the relative difference between τoc and τa, γτ, can be up to 6% in middle and high latitudes. The frequency of occurrence of γτ &gt; 9% can be up to 10% in the windy extratropics. The directional difference between τoc and τa exceeds 3.5° in the middle and high latitudes 10% of the time. The difference between τoc and τa becomes more significant closer to the coasts of the continents due to strong wind gradients. The friction velocity-based approach overestimates (underestimates) the breaking-induced TKE flux in the tropics (middle and high latitudes). The findings presented in the current study show that coupled climate and Earth system models would clearly benefit from the inclusion of a wave model. Significance Statement The purpose of this study is to investigate the redistribution of the global wind stress and turbulent kinetic energy flux due to surface waves based on a 30-yr wave hindcast. The mean relative difference of the magnitude between the air-side and ocean-side stress is up to 6% with a 90th percentile of more than 9% in the windy extratropics. Due to strong wind gradients, the redistributive role of waves in the stress becomes more significant closer to coasts. The results indicate that we should consider the redistributive role of waves in the momentum and energy fluxes in climate and Earth system models since they are the key elements in the predictability of weather forecasting models and climate models.

Magneto-thermal instability in galaxy clusters – I. Theory and two-dimensional simulations

ABSTRACT Determining the origin of turbulence in galaxy clusters, and quantifying its transport of heat, is an outstanding problem, with implications for our understanding of their thermodynamic history and structure. As the dilute plasma of the intracluster medium (ICM) is magnetized, heat and momentum travel preferentially along magnetic field lines. This anisotropy triggers a class of buoyancy instabilities that destabilize the ICM, and whose turbulent motions can augment or impede heat transport. We focus on the magneto-thermal instability (MTI), which may be active in the periphery of galaxy clusters. We aim to take a fresh look at the problem and construct a general theory that explains the MTI saturation mechanism and provides scalings and estimates for the turbulent kinetic energy, magnetic energy, and heat flux. We simulate MTI turbulence with a Boussinesq code, snoopy, which, in contrast to previous work, allows us to perform an extensive sampling of the parameter space. In two dimensions the saturation mechanism involves an inverse cascade that carries kinetic energy from the short MTI injection scales to larger scales, where it is arrested by the stable entropy stratification; at a characteristic ‘buoyancy scale’, the energy is dumped into large-scale g-modes, which subsequently dissipate. Consequently, the entropy stratification sets an upper limit on the size and strength of turbulent eddies. Meanwhile, the MTI conveys a substantial fraction of heat, despite the tangled geometry of the magnetic field. In a companion paper, these results are extended to three-dimensional flows, and compared to observations of real clusters.

Analysis of turbulence generation and dissipation in shear layers of methane–oxygen diffusion flames using direct numerical simulations

A turbulent methane–oxygen diffusion flame is studied using a direct numerical simulation setup. The operating regime and turbulence characteristics are chosen to resemble those of a modern methane rocket combustor. Local flame characteristics and dimensionless numbers are defined and evaluated, and their relationship with the turbulent kinetic energy transport budget is studied. Positive net turbulence generation is observed in the reaction shear layer. It is found that the underlying mechanisms for these results are similar to those encountered in premixed flames, with pressure terms acting as the primary turbulent kinetic energy sources. Models for predicting turbulent transport through mean pressure gradients, fluctuating pressure gradients, and turbulent flux of turbulent kinetic energy are adapted. The accuracy of the proposed formulations is assessed, and the involved challenges are discussed.