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At least 37 records · Page 2

Internal energy balance and aerodynamic heating predictions for hypersonic turbulent boundary layers

The elemental equation governing heat transfer in aerodynamic flows is the internal energy equation. For a boundary layer flow, a double integration of the Reynolds-averaged form of this equation provides an expression of the wall heat flux in terms of the integrated effects, over the boundary layer, of various physical processes: turbulent dissipation, mean dissipation, turbulent heat flux, etc. Recently available direct numerical simulation data for a Mach 11 cold-wall turbulent boundary layer allows a comparison of the exact contributions of these terms in the energy equation to the wall heat flux with their counterparts modeled in the Reynolds-averaged Navier-Stokes (RANS) framework. Various approximations involved in RANS, both closure models as well as approximations involved in adapting incompressible RANS models to a compressible form, are assessed through examination of the internal energy balance. There are a number of potentially problematic assumptions and terms identified through this analysis. Here, the effect of compressibility corrections of the dilatational dissipation type is explored, as is the role of the modeled turbulent dissipation, in the context of wall heat flux predictions. The results indicate several potential avenues for RANS model improvement for hypersonic cold-wall boundary-layer flows.

42 ENGINEERING↗

Budgets for Decadal Variability in Pacific Ocean Heat Content

A slowdown in the rate of surface warming in the early 2000s led to renewed interest in the redistribution of ocean heat content (OHC) and its relationship with internal climate variability. In this work we use the Community Earth System Model version 1 to study the relationship between OHC and the interdecadal Pacific oscillation (IPO), a major mode of decadal sea surface temperature variability in the Pacific Ocean. By comparing the relative contributions of surface heat flux and ocean dynamics to changes in OHC for different phases of the IPO, we try to identify the underlying physical processes involved. Our results suggest that during IPO phase transitions, changes of 0–300-m OHC across the northern extratropical Pacific are positively contributed by both surface heat flux and oceanic heat transport. By contrast, oceanic heat transport appears to drive the OHC changes in equatorial Pacific whereas surface heat flux acts as a damping term. During a positive IPO phase, weakened wind-driven circulation acts to increase the OHC in the equatorial Pacific while the enhanced evaporation acts to damp OHC anomalies. In the Kuroshio–Oyashio Extension region, a dipole anomaly of zonal heat advection amplifies an OHC dipole anomaly that moves eastward, while strong turbulent heat fluxes act to dampen this OHC anomaly. In the northern subtropical Pacific, both the wind-driven evaporation change and the change of zonal heat advection along Kuroshio Extension contribute to the OHC change during phase transition. For the northern subpolar Pacific, both surface heat flux and enhanced meridional advection contribute to the positive OHC anomalies during the positive IPO phase.

54 ENVIRONMENTAL SCIENCES↗

Snow thermal conductivity and conductive flux in the Central Arctic: Estimates from observations and implications for models

During the Arctic winter, the conductive heat flux through the sea ice and snow balances the radiative and turbulent heat fluxes at the surface. Snow on sea ice is a thermal insulator that reduces the magnitude of the conductive flux. The thermal conductivity of snow, that is, how readily energy is conducted, is known to vary significantly in time and space from observations, but most forecast and climate models use a constant value. This work begins with a demonstration of the importance of snow thermal conductivity in a regional coupled forecast model. Varying snow thermal conductivity impacts the magnitudes of all surface fluxes, not just conduction, and their responses to atmospheric forcing. Given the importance of snow thermal conductivity in models, we use observations from sea ice mass balance buoys installed during the Multidisciplinary drifting Observatory for the Study of Arctic Climate expedition to derive the profiles of thermal conductivity, density, and conductive flux. From 13 sites, median snow thermal conductivity ranges from 0.33 W m −1 K −1 to 0.47 W m −1 K −1 with a median from all data of 0.39 W m −1 K −1 from October to February. In terms of surface energy budget closure, estimated conductive fluxes are generally smaller than the net atmospheric flux by as much as 20 W m −2 , but the average residual during winter is −6 W m −2 , which is within the uncertainties. The spatial variability of conductive heat flux is highest during clear and cold time periods. Higher surface temperature, which often occurs during cloudy conditions, and thicker snowpacks reduce temporal and spatial variability. These relationships are compared between observations and the coupled forecast model, emphasizing both the importance and challenge of describing thermodynamic parameters of snow cover for modeling the Arctic as a coupled system.

54 ENVIRONMENTAL SCIENCES↗

Simulations of edge and SOL turbulence in diverted negative and positive triangularity plasmas

Optimizing the performance of magnetic confinement fusion devices is critical to achieving an attractive fusion reactor design. Negative triangularity (NT) scenarios have been shown to achieve excellent levels of energy confinement, while avoiding edge localized modes. Modeling turbulent transport in the edge and SOL is key in understanding the impact of NT on turbulence and extrapolating the results to future devices and regimes. Previous gyrokinetic turbulence studies have reported beneficial effects of NT across a broad range of parameters. However, most simulations have focused on the inner plasma region, neglecting the impact of NT on the outermost edge. In this work, we investigate the effect of NT in edge and scrape-off layer simulations, including the magnetic X-point and separatrix. For the first time, we employ a multi-fidelity approach, combining global, non-linear gyrokinetic simulations with drift-reduced fluid simulations, to gain a deeper understanding of the underlying physics at play. First-principles simulations using the GENE-X code demonstrate that in comparable NT and PT geometries, similar profiles are achieved, while the turbulent heat flux is reduced by more than 50% in NT. Comparisons with results from the drift-reduced fluid turbulence code GRILLIX suggest that the turbulence is driven by trapped electron modes. The parallel heat flux width on the divertor targets is reduced in NT, primarily due to a lower spreading factor S.

GENE-X↗

The two radiative states of the Arctic atmosphere and their impacts on the surface energy budget of sea ice

The surface energy budget (SEB) is a central regulator of Arctic climate and sea ice evolution, yet its processes remain poorly constrained due to sparse observations and complex, coupled surface-atmosphere interactions. This study leverages year-long measurements from the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) to provide the most comprehensive assessment to date of the central Arctic SEB and its modulation by atmospheric variability. Ship- and ice-based observations from October 2019 to September 2020 were used to directly measure or tightly constrain each term of the SEB, leading to exceptional energetic closure with the seasonal snow and ice mass balance. The analysis reveals strong seasonal transitions in atmosphere-surface energy transfer that are modulated by the atmospheric state and constrained by the ability of the surface temperature to respond. Classification of the atmosphere into its two dominant radiative states—the semi-transparent (ST) and opaque (OP)—highlights the central role of synoptic-scale variability in clouds. The ST atmospheric state dominated the long winter ice growth season, with limited cloudiness supporting persistent surface radiative cooling and ice growth. The OP state, associated with liquid-containing or thick ice clouds, became dominant in spring, with the combination of increased solar heating and cloud surface longwave warming driving ice and snow melt. Eddy covariance versus bulk approaches for deriving surface turbulent heat fluxes provide vastly different perspectives on the role of turbulence in modulating the SEB. These results establish a high-quality benchmark dataset for Arctic SEB studies and demonstrate how the balance of atmospheric radiative states exerts a first-order control on the annual evolution of the sea ice. The findings have broad implications for advancing observing technologies, understanding Arctic amplification, improving climate models, and predicting future sea ice change.

54 ENVIRONMENTAL SCIENCES↗

Validation of a comprehensive first-principles-based framework for predicting the performance of future stellarators

This paper presents the validation of the GENE-KNOSOS-Tango framework for recovering both the steady-state plasma profiles in the considered radial domain and selected turbulence trends in a stellarator. This framework couples the gyrokinetic turbulence code GENE, the neoclassical transport code KNOSOS, and the transport solver Tango in a multi-timescale simulation feedback loop. Ion-scale kinetic-electron and electron-scale adiabatic-ion flux-tube simulations were performed to evolve the density and temperature profiles for four OP1.2b W7-X scenarios. The simulated density and temperature profiles showed good agreement with the experimental data using a reasonable set of boundary conditions. Equally important was the reproduction of observed trends for several turbulence properties, such as density fluctuations and turbulent heat diffusivities. Key effects were also touched upon, such as electron-scale turbulence and the neoclassical radial electric field shear. The validation of the GENE-KNOSOS-Tango framework enables credible predictions of physical phenomena in stellarators and reactor performance based on a given set of edge parameters.

Gyrokinetic simulations↗

Numerical simulation of frost formation and heat transfer on fin-and-tube heat exchangers in turbulent cross-flow

Frost formation in fin-and-tube heat exchangers in turbulent cross-flow presents significant challenges in industrial refrigeration applications, affecting heat transfer efficiency and operational reliability. The purpose of this work is to investigate frost deposition and growth on a staggered bank of a fin-and-tube freezer coil under turbulent forced convection conditions. The focus here is on investigating conditions that closely replicate real-world scenarios in large walk-in industrial freezers. Using a direct numerical simulation approach, we examine the flow dynamics and thermal behaviour in the presence of frost, considering turbulent regimes characterized by a Reynolds number in the range 1050 ≤ R e D , avg ≤ 4800 , with the characteristic length being the outer diameter of the tube and the velocity being the bulk fluid velocity between the plates (fins). Computational fluid dynamics simulations are employed to resolve the interactions between turbulent airflow and the frost layer. Our approach incorporates a modified immersed boundary method and a slow-time acceleration technique to address the complex dynamic interface between the continuously evolving frost layer and the flowing air stream. Our findings indicate that frost forms more on the sides of the finned surfaces (plates) and less on the tubes themselves. This article is part of the theme issue ‘Heat and mass transfer in frost and ice’.

Science & Technology - Other Topics↗

Zonally dominated dynamics and Dimits threshold in curvature-driven ITG turbulence

The saturated state of turbulence driven by the ion-temperature-gradient instability is investigated using a two-dimensional long-wavelength fluid model that describes the perturbed electrostatic potential and perturbed ion temperature in a magnetic field with constant curvature (a $Z$ -pinch) and an equilibrium temperature gradient. Numerical simulations reveal a well-defined transition between a finite-amplitude saturated state dominated by strong zonal-flow and zonal temperature perturbations, and a blow-up state that fails to saturate on a box-independent scale. We argue that this transition is equivalent to the Dimits transition from a low-transport to a high-transport state seen in gyrokinetic numerical simulations (Dimits et al. , Phys. Plasmas , vol. 7, 2000, 969). A quasi-static staircase-like structure of the temperature gradient intertwined with zonal flows, which have patch-wise constant shear, emerges near the Dimits threshold. The turbulent heat flux in the low-collisionality near-marginal state is dominated by turbulent bursts, triggered by coherent long-lived structures closely resembling those found in gyrokinetic simulations with imposed equilibrium flow shear (van Wyk et al. , J. Plasma Phys. , vol. 82, 2016, 905820609). The breakup of the low-transport Dimits regime is linked to a competition between the two different sources of poloidal momentum in the system – the Reynolds stress and the advection of the diamagnetic flow by the $\boldsymbol {E}\times \boldsymbol {B}$ flow. By analysing the linear ion-temperature-gradient modes, we obtain a semi-analytic model for the Dimits threshold at large collisionality.

Physics↗

Observations Indicate That Clouds Amplify Mechanisms of Southern Ocean Heat Uptake

Abstract The Southern Ocean has absorbed most of the excess heat associated with anthropogenic greenhouse gas emissions. Since Southern Ocean observations are sparse in certain regions and seasons, much of our knowledge of ocean heat uptake is based on climate model simulations. However, climate models still inadequately represent some properties of Southern Ocean clouds, and they have not identified the mechanisms by which clouds may affect Southern Ocean heat uptake (SOHU). Here, we use the ERA5 and JRA‐55 reanalyses to assess the influence of clouds and other atmospheric processes on SOHU from 1979 to 2020. We find that years with the highest SOHU between 45° and 65°S are dominated by ocean heat uptake anomalies during winter and spring, but not during summer or fall. Winter and spring cloud cover are up to 7% higher when SOHU is up to 5.5 W/m 2 higher than the climatological seasonal mean, with the largest increases in the South Pacific Ocean. Clouds also contain more liquid water. These changes in cloud properties increase downwelling longwave radiation, amplifying ocean heat uptake. Cloud changes are also concomitant with a more stable lower atmosphere, which suppresses turbulent heat fluxes out of the surface. Overall, we find that SOHU is likely not mediated by enhanced surface shortwave absorption over the observational time period. A better understanding of how atmospheric processes impact ocean heat uptake may help improve our understanding of ocean heat uptake mechanisms in the current generation of climate models.

54 ENVIRONMENTAL SCIENCES↗

Two-stage crash process in resistive drift ballooning mode driven ELM crash

We report a two-stage crash process in edge localized mode (ELM) driven by resistive drift-ballooning modes (RDBMs) numerically simulated in a full annular torus domain with a scale-separated four-field reduced MHD (RMHD) model using the BOUT++ framework. In the early nonlinear phase, the small first crash is triggered by linearly unstable RDBMs, and m/n=2/1 magnetic islands are nonlinearly excited by nonlinear coupling of RDBMs as well as their higher harmonics. Here, m is the poloidal mode number, n is the toroidal mode number, the q = 2 rational surface exists near the pressure gradient peak, and q is the safety factor. Simultaneously, middle-n RDBM turbulence develops but is poloidally localized around X-points of the magnetic islands, leading to the small energy loss. The second large crash occurs in the late nonlinear phase. Higher harmonics of m/n=2/1 magnetic islands well develop around the q = 2 surface via nonlinear coupling and make the magnetic field stochastic by magnetic island overlapping. Turbulence heat transport develops at X-points of higher harmonics of m/n=2/1 magnetic islands, resulting in the turbulence spreading in the poloidal direction. The large second crash is triggered when the turbulence covers the whole poloidal region so that the magnetic island generation and magnetic field stochastization before the large crash can be interpreted as ELM precursors. It is concluded that the ELM trigger is attributed to the turbulent spreading in the poloidal direction in synchronization with the magnetic field stochastization and the crash is driven by E × B convection rather than the conventional Rechester–Rosenbluth anomalous electron heat transport.

Seto, H. (ORCID:0000000259278643)↗

Estimating source-sink distributions and fluxes of reactive nitrogen and sulfur within a mixed forest canopy

The vertical source-sink distribution of air pollutants within and above forested canopies is necessary for describing the biological, physical, and chemical processes influencing the soil-vegetation-atmosphere exchange. Here, this study implemented inverse modeling methods to estimate the source-sink and flux profiles of reactive nitrogen (N) and sulfur (S) compounds from measurements of the mean concentration profiles of ammonia (NH 3 ), nitric acid (HNO 3 ), sulfur dioxide (SO 2 ), and particulate ammonium (NH 4 + ), nitrate (NO 3 − ), and sulfate (SO 4 2− ) at a forest site in the southern Appalachian Mountains. Three inverse approaches utilizing different approximations to scalar transport within the canopy were developed and evaluated against sensible heat flux measurements. The Eulerian model (EUL), which incorporates vertical velocity skewness, performed well in reproducing the turbulent heat fluxes and was subsequently used to calculate the chemical source-sink and flux profiles. Above-canopy fluxes of NH 3 were downward, indicating that the forest was a net sink of NH 3 . The soil/litter layer was both a source and a sink for NH 3 but the exchange rate at the forest floor was small. Fluxes of HNO 3 , SO 2 , NO 3 − , NH 4 + , and SO 4 2- were uni-directional (deposition only) between the air and the canopy/ground and increased monotonically from the forest floor to the canopy top. Crown foliage dominated the uptake of reactive N and S during the growing season, accounting for 80–90% of the total canopy-scale flux. Fluxes and canopy-ground partitioning estimated using the resistance-based Surface Tiled Aerosol and Gas Exchange (STAGE) model were generally comparable to EUL. The comparison highlights the need for improved parameterizations of litter exchange and NH 3 compensation points in resistance models for forest ecosystems. The findings here benefit the application of critical loads in forest ecosystems and guide further development of resistance-based exchange models.

54 ENVIRONMENTAL SCIENCES↗

How turbulent transport broadens the heat flux width: local SOL production or edge turbulence spreading?

This paper uses data from limited HL-2A Ohmic-plasma to answer the question of how turbulent transport broadens the heat flux width. A key issue in this study is the determination of the origin of scrape-off layer (SOL) turbulence. We develop the concept of the energy production ratio ${R_a}$, which compares the flux of turbulence energy across the last closed flux surface (LCFS) to the net, integrated energy production in the SOL. The flux of turbulence energy (i.e. spreading) is measured directly, using Langmuir probes. Experimental data is used to evaluate ${R_a}$. Results show that usually ${R_a} > 1$, indicating that SOL turbulence is energized primarily by edge turbulence spreading. The exceptions—cases where ${R_a} < 1$—are those with relatively stronger ${\mathbf{E}} \times {\mathbf{B}}$ shear near the LCFS. The latter inhibits both turbulence spreading and local SOL production, but has greater effects on spreading. High blob fraction in the turbulence correlates with large values of ${R_a}$. The implications for heat flux width physics are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Direct microstability optimization of stellarator devices

Turbulent transport is regarded as one of the key issues in magnetic confinement nuclear fusion, both for tokamaks and stellarators. Here, in this work, we show that a significant decrease in a microstability-based proxy, as opposed to a geometric one, for the turbulent heat flux, namely the quasilinear heat flux, can be obtained in an efficient manner by coupling stellarator optimization with linear gyrokinetic simulations. This is accomplished by computing the quasilinear heat flux at each step of the optimization process, as well as the deviation from quasisymmetry, and minimizing their sum, leading to a balance between neoclassical and the turbulent transport proxy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

On the role of mode resonances in regulating zonal-flow-moderated plasma microturbulence

Abstract The onset of turbulent heat transport at a higher temperature gradient than the critical gradient of linear instability, known as the Dimits shift, is a recurring feature of nonlinear simulations for magnetically confined fusion plasmas. Resonance in the nonlinear coupling between the modes that dominate energy transfer can lead to suppression of turbulence and transport above the linear critical gradient. As an expression of this resonance, gyrokinetic simulations show a quasi-coherent interaction between streamers and sidebands coupled through the zonal flow within the Dimits regime. This mechanism is further confirmed by use of artificial complex frequencies which break the resonance. By incorporating corresponding saturation physics, the standard quasilinear model for rapid head flux prediction is improved, which can now predict reduced heat flux in the Dimits regime. In particular, the triplet correlation time, the lifetime of the nonlinear interaction, is shown to be well-approximated by combinations of linear eigenvalues, and yields good representations of the heat flux variation both in and above the Dimits regime. Thus, a reduced but predictive model for transport near the critical gradient of zonal-flow saturated turbulence now exists.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Sensitivity of Arctic Surface Temperature to Including a Comprehensive Ocean Interior Reflectance to the Ocean Surface Albedo Within the Fully Coupled CESM2

Abstract Almost all current climate models simplify the ocean surface albedo (OSA) by assuming the reflected solar energy without the ocean interior contribution. In this study, an improved ocean surface albedo scheme is incorporated into the Community Earth System Model version 2 (CESM2) to assess the sensitivity of Arctic surface temperature to including ocean interior reflectance to the OSA. Fully coupled CESM2 simulations with and without ocean interior reflectance are subsequently performed, we focus on the analysis of Arctic surface temperature responses. Incorporating ocean interior reflectance increases absorbed solar radiation and warms the ocean, enhancing seasonal heat storage and release across the Arctic Ocean, and increasing sea ice reduction and positive climate feedbacks that elevates Arctic surface temperature. Seasonal variations in air‐surface temperature differences induce changes in turbulent heat flux patterns, concurrently modifying dynamic advection and moisture processes that affect boundary layer humidity and low clouds, especially in winter. Based on partitioning physical processes in the thermodynamic energy equation, surface air warming is induced primarily through positive heating anomalies of vertical advection, latent heat release, and longwave radiative forcing. Through an examination of the surface energy budget, skin temperature warming is driven predominantly by increased downward longwave radiation, positive surface albedo feedback in summer, and increased conductive heat transport from the ocean particularly in winter. Significant effects of ocean interior reflectance on the Arctic Ocean, including sea surface warming and sea ice reduction, justify the importance of ocean interior reflectance in climate models for better understanding of ongoing Arctic climate changes.

Meteorology & Atmospheric Sciences↗

Observations of the Marine Atmospheric Boundary Layer’s Response to a Solar Eclipse

The atmospheric response to the solar eclipse of 8 April 2024 in North America is investigated with a specific focus on the marine atmospheric boundary layer (MABL). We leverage measurements collected during the Third Wind Forecast Improvement Project (WFIP3), including Doppler lidars, sonic anemometers, and thermodynamic profiler data to investigate the atmospheric response across sites that experienced partial eclipse conditions with nearly 90% obscuration. Using these measurements, we examine eclipse-induced changes in key meteorological parameters, such as temperature, wind speed, and turbulent fluxes. Most previous eclipse studies have been conducted over land, whereas this study provides new observations for both coastal and marine environments, offering additional insight into eclipse-driven variability in the MABL. The findings confirm a notable decrease in downwelling shortwave radiation during the eclipse, which results in rapid cooling of surface air. The temperature reduction ranges from $1.2^\circ \text {C}$ to $1.4^\circ \text {C}$ in coastal regions and from $0.3^\circ \text {C}$ to $0.5^\circ \text {C}$ over the ocean. This analysis suggests that the MABL’s higher thermal inertia compared to coastal regions moderates the temperature decrease during the eclipse. Wind speed exhibits a more complex behavior, as it is influenced by both the MABL and preexisting synoptic conditions. Although a reduction in wind speed is observable up to approximately 140 m above ground level (AGL) at more inland sites, at other locations closer to the coast, this reduction is constrained to the lowest 100 m AGL. Turbulence parameters retrieved from sonic anemometers, such as turbulence kinetic energy, turbulent heat flux, and friction velocity, decrease during the eclipse at coastal sites, accompanied by a brief transition of atmospheric stability from unstable to neutral or weakly stable conditions. For the open-ocean sites, the variability in turbulence statistics and atmospheric stability is minimal during the occurrence of the eclipse.

16 TIDAL AND WAVE POWER↗

Scaling patch analysis of turbulent planar plume

Proper scaling in turbulent planar plumes is investigated in this study using a scaling patch approach. Based on the scaled boundary conditions, a proper velocity scale for the mean axial flow is the plume centerline velocity U ref = U ctr , and a proper temperature scale for the temperature excess is Θ ref = T ctr – T ∞ , where T ctr is the plume centerline temperature and T ∞ is the ambient fluid temperature. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity, mean momentum, and mean energy equations, respectively, the following is found: (1) a proper scale for the mean transverse flow is V ref = ( d δ / d x ) U ctr , where d δ / d x is the growth rate of the plume width. (2) A proper scale for the Reynolds shear stress is R vu , ref = U ctr V ref = ( d δ / d x ) U ctr 2 , a mix of the scales for the mean axial and transverse flows. (3) A proper scale for the turbulent heat flux is R v θ , ref = V ref Θ ctr , a mix of the scales for the mean transverse flow and mean temperature excess. The mean transverse flow thus plays a critical role in the scaling of turbulent planar plumes. Approximate functions are developed for the scaled mean transverse flow, Reynolds shear stress, and turbulent temperature flux, and are found to agree favorably with experimental and numerical simulation data. The integral analysis of the mean momentum equation yields a Richardson number Ri, which remains invariant in the axial direction. The Richardson number is defined as Ri = def g β Θ ctr δ t / ( U ctr V ref ) ≈ 1 / 2 , where g is the gravitational acceleration, β is the thermal expansion coefficient, and δ t is the plume half-width based on the mean temperature profile. This Richardson number arises directly from the scaling patch analysis of the mean momentum equation, including both the streamwise and transverse velocity scales.

42 ENGINEERING↗

A Study of the Transition to Turbulence in a Bed of 67 Spherical Pebbles

Packed beds are commonly found in many engineering systems and have been widely studied for decades. A relatively new packed bed system is the Pebble Bed Reactor, a type of generation-IV nuclear reactor. Unlike many of the packed beds encountered in chemical and process engineering applications, Pebble Bed Reactors are larger and operate at significantly higher Reynolds numbers. As a result of these differences, there is a very limited amount of information on the detailed flow physics that exist in these complex geometries. This work seeks to contribute to a growing database of flow data for Pebble Bed Reactor systems by performing Direct Numerical Simulations of the flow in an experimental bed of 67 pebbles for a range of conditions. Simulations are performed at a Prandtl number of 0.66 and Reynolds numbers from 300–600. These Reynolds numbers are chosen to gain additional knowledge on the spatial development of turbulence in these systems. Analysis of the Turbulent Kinetic Energy, turbulence anisotropy, and Turbulent Heat Flux is performed. Results demonstrate significant development of the TKE across the tested range of Reynolds numbers. Examination of both the TKE and THF reveal that development first occurs near the center of the bed and propagates radially as the flow moves further into the bed. Notable regions of negative production of turbulent kinetic energy are observed in regions where flow accelerates around pebble contact points. Furthermore, these regions are found to coincide with regions of 1-component turbulence.Kindly check and confirm, all authors email id is correctly identified.These are correct

Direct numberical simulation↗