Turbulent Energy Budget Research Articles

Turbulent energy budget analysis based on coherent wind lidar observations

Abstract. The turbulent kinetic energy (TKE) budget terms, which collectively are a key physical quantity for describing the generation and dissipation processes of turbulence, are crucial for revealing the essence and characteristics of turbulence. Due to limitations in current observational methods, the generation and dissipation mechanisms of atmospheric turbulent energy are mainly based on ground or tower-based observations, and studies on the budget terms of TKE of vertical structures are lacking. We propose a new method for detecting TKE budget terms based on coherent wind lidar and compare it with data obtained with a three-dimensional ultrasonic anemometer. The results indicate that the error in the buoyancy generation term estimated by the wind lidar is relatively small, less than 0.00014 m2 s−3, which verifies the accuracy and reliability of our method. We explore the generation and dissipation mechanisms of turbulence under different weather conditions, and find that the buoyancy generation term plays a role in dissipating TKE under low-cloud and light-rain conditions. During the day, turbulent transport and the dissipation rate are the main dissipation terms, while buoyancy generation is the main dissipation term at night. The results show that the proposed method can accurately capture the vertical distribution of TKE, the dissipation rate, shear generation, turbulent transport, and buoyancy generation terms in the boundary layer and can comprehensively reflect the influence of each budget term on the vertical structure of turbulent energy. This research provides a new perspective and method for studies of atmospheric turbulence, which can be further applied to fine observations of the vertical structure and dynamics of turbulence.

Performance analysis of various wall treatments of RANS models for prediction of near-wall turbulence transport characteristics of plane wall jet

PurposeThe present study scrutinizes the relative performance of various near-wall treatments coupled with two-equation RANS models to explore the turbulence transport mechanism in terms of the kinetic energy budget in a plane wall jet and the significance of the near-wall molecular and turbulent shear, to select the best combination among the models which reveals wall jet characteristics most efficiently.Design/methodology/approachA two-dimensional steady incompressible plane wall jet in a quiescent surrounding is simulated using ANSYS-Fluent solver. Three near-wall treatments, namely the Standard Wall Function (SWF), Enhanced Wall Treatment (EWT) and Menter-Lechner (ML) treatment coupled with Realisable, RNG and Standard k-e models and also the Standard and Shear-Stress Transport (SST) k-ω models are employed for this investigation.FindingsThe ML treatment slightly overestimated the budget components on an outer scale, whereas the k-ω models strikingly underestimated them. In the buffer layer at the inner scale, the SWF highly over-predicts turbulent production and dissipation and k-ω models over-predict dissipation. Appreciably accurate inner and outer scale k-budgets are observed with the EWT schemes. With a sufficiently resolved near-wall mesh, the Realisable model with EWT exhibits the mean flow, turbulence characteristics and turbulence energy transport even better than the SST k-ω model.Originality/valueThree distinct near-wall strategies are chosen for comparative performance analysis, focusing not only on the mean flow and turbulence characteristics but the turbulence energy budget as well, for finding the best combination, having potential as a viable and low-cost alternative to LES and DNS for wall jet simulation in industrial application.

Thermal convection of viscoelastic fluids in concentric rotating cylinders: Elastic turbulence and kinetic energy budget analysis

Thermal convection of viscoelastic fluids in concentric rotating cylinders: Elastic turbulence and kinetic energy budget analysis

Axial friction coefficient of turbulent spiral Poiseuille flows

Direct numerical simulations of spiral Poiseuille flows in a narrow gap geometry are performed with the aim of identifying the mechanisms governing the dynamics of the axial friction coefficient. The investigation has explored a small portion of the Reynolds number–Taylor number phase space ( $600 \leq Re \leq 5766$ and $1500 \leq Ta \leq 5000$ ), for which reference experimental results are available. The study is focused on the mechanism leading to the enhancement of the axial friction coefficient with the Taylor number when the Reynolds number is kept constant. The analysis of the spatial distribution of the Reynolds stress tensor and of the turbulent energy budget has evidenced the key role of the pressure–strain correlation in the energy transfer from the azimuthal to the axial component. The latter eventually determines the increase of the axial friction coefficient through the enhanced radial mixing of axial momentum. Data have also shown that the flow dynamics is heavily dependent on the $Ta/Re$ ratio, and different regimes develop (ranging from laminar to turbulent), each with peculiar behaviours.

New insights into experimental stratified flows obtained through physics-informed neural networks

We develop a physics-informed neural network (PINN) to significantly augment state-of-the-art experimental data of stratified flows. A fully connected deep neural network is trained using time-resolved experimental data in a salt-stratified inclined duct experiment, consisting of three-component velocity fields and density fields measured simultaneously in three dimensions at Reynolds number $= O(10^3)$ and at Prandtl or Schmidt number $=700$ . The PINN enforces incompressibility, the governing equations for momentum and buoyancy, and the boundary conditions at the duct walls. These physics-constrained, augmented data are output at an increased spatio-temporal resolution and demonstrate five key results: (i) the elimination of measurement noise; (ii) the correction of distortion caused by the scanning measurement technique; (iii) the identification of weak but dynamically important three-dimensional vortices of Holmboe waves; (iv) the revision of turbulent energy budgets and mixing efficiency; and (v) the prediction of the latent pressure field and its role in the observed asymmetric Holmboe wave dynamics. These results mark a significant step forward in furthering the reach of experiments, especially in the context of stratified turbulence, where accurately computing three-dimensional gradients and resolving small scales remain enduring challenges.

Gas Accretion Can Drive Turbulence in Galaxies

The driving of turbulence in galaxies is deeply connected with the physics of feedback, star formation, outflows, accretion, and radial transport in disks. The velocity dispersion of gas in galaxies therefore offers a promising observational window into these processes. However, the relative importance of each of these mechanisms remains controversial. In this work we revisit the possibility that turbulence on galactic scales is driven by the direct impact of accreting gaseous material on the disk. We measure this effect in a disk-like star-forming galaxy in IllustrisTNG, using the high-resolution cosmological magnetohydrodynamical simulation TNG50. We employ Lagrangian tracer particles with a high time cadence of only a few million years to identify accretion and other events. The energies of particles are measured by stacking the events in bins of time around the event. The average effect of each event is measured by fitting explicit models for the kinetic and turbulent energies as a function of time. These measurements are corroborated by cross-correlating the turbulent energy with other time series and searching for signals of causality, i.e., asymmetries across zero time lag. We find that accretion contributes to the large-scale turbulent kinetic energy even if it does not dominate in this ∼5 × 109 M ⊙ stellar mass galaxy. Extrapolating this finding to a range of galaxy masses, we find that there are regimes where energy from direct accretion may dominate the turbulent energy budget, particularly in disk outskirts, galaxies less massive than the Milky Way, and at redshift ∼2.

Application of the exact regularized point particle method (ERPP) to bubble laden turbulent shear flows in the two-way coupling regime

Direct numerical simulations of a bubbly laden homogeneous shear flow have been carried out using the exact regularized point particle method as the inter-phase momentum coupling approach. The aim of this study consists in addressing the modulation of shear turbulence and the bubble clustering geometry in the presence of different inter-phase momentum coupling conditions. Suspensions with different combinations of the void fraction and Kolmogorov-based Stokes number, in the dilute regime, have been addressed. Bubbles suppress the turbulent kinetic energy and turbulent dissipation as well. Turbulent modulation occurs via the direct change of the Reynolds shear stress. In fact, the bubble energy source is proved to be negligible in the scale-by-scale turbulent energy budget. The bubble clustering, in agreement with the literature, occurs in the form of thin elongated structures. The clusters are aligned with the principal strain direction of the mean flow, as usual in shear flows. The bubble clustering and turbulent modification are strictly related: both increase with the Stokes number and are independent of the void fraction. The data show that the turbulent modification is disadvantaged when the bubble distribution is homogeneous (i.e., small Stokes number). Finally, the small-scale bubble clustering is slightly reduced by two-way coupling effects even though the clustering anisotropy still persists at small scales as it occurs for inertial particles.

Mixing in forced stratified turbulence and its dependence on large-scale forcing

We study direct numerical simulations of turbulence arising from the interaction of an initial background shear, a linear background stratification and an external body force. In each simulation the turbulence produced is spatially intermittent, with dissipation rates varying over orders of magnitude in the vertical. We focus analysis on the statistically quasi-steady states achieved by applying large-scale body forcing to the domain, and compare flows forced by internal gravity waves with those forced by vertically uniform vortical modes. By considering the turbulent energy budgets for each simulation, we find that the injection of potential energy from the wave forcing permits a reversal in the sign of the mean buoyancy flux. This change in the sign of the buoyancy flux is associated with large, convective density overturnings, which in turn lead to more efficient mixing in the wave-forced simulations. The inhomogeneous dissipation in each simulation allows us to investigate localised correlations between the kinetic and potential energy dissipation rates. These correlations lead us to the conclusion that an appropriate definition of an instantaneous mixing efficiency, (where and are the volume-averaged turbulent viscous dissipation rate and fluctuation density variance destruction rate respectively) in the wave-forced cases is independent of an appropriately defined local turbulent Froude number, consistent with scalings proposed for low Froude number stratified turbulence.

Turbulence in the stratified boundary layer under ice: observations from Lake Baikal and a new similarity model

Abstract. Seasonal ice cover on lakes and polar seas creates seasonally developing boundary layer at the ice base with specific features: fixed temperature at the solid boundary and stable density stratification beneath. Turbulent transport in the boundary layer determines the ice growth and melting conditions at the ice–water interface, especially in large lakes and marginal seas, where large-scale water circulation can produce highly variable mixing conditions. Since the boundary mixing under ice is difficult to measure, existing models of ice cover dynamics usually neglect or parameterize it in a very simplistic form. We present the first detailed observations on mixing under ice of Lake Baikal, obtained with the help of advanced acoustic methods. The dissipation rate of the turbulent kinetic energy (TKE) was derived from correlations (structure functions) of current velocities within the boundary layer. The range of the dissipation rate variability covered 2 orders of magnitude, demonstrating strongly turbulent conditions. Intensity of mixing was closely connected to the mean speeds of the large-scale under-ice currents. Mixing developed on the background of stable density (temperature) stratification, which affected the vertical structure of the boundary layer. To account for stratification effects, we propose a model of the turbulent energy budget based on the length scale incorporating the dissipation rate and the buoyancy frequency (Dougherty–Ozmidov scaling). The model agrees well with the observations and yields a scaling relationship for the ice–water heat flux as a function of the shear velocity squared. The ice–water heat fluxes in the field were the largest among all reported in lakes (up to 40 W m−2) and scaled well against the proposed relationship. The ultimate finding is that of a strong dependence of the water–ice heat flux on the shear velocity under ice. The result suggests large errors in the heat flux estimations when the traditional “bulk” approach is applied to stratified boundary layers. It also implies that under-ice currents may have much stronger effect on the ice melt than estimated by traditional models.

Double-averaged kinetic energy budgets in flows over mobile granular beds: insights from DNS data analysis

The equations for double-mean, form-induced and spatially averaged turbulent energy budgets are employed to analyse data from direct numerical simulations of turbulent open-channel flows over transitionally rough mobile beds with intermediate flow submergence. Two scenarios were considered related to (i) near-critical bed condition, and (ii) fully mobile bed condition. The bed was composed of a layer of mobile spherical particles moving on the top of one layer of fixed particles of the same size. Data analysis showed the leading energy exchanges between double-mean, form-induced, turbulent flow field contributions as well as particle motions. Above the fixed particles tops, the turbulent flow receives kinetic energy directly from the mean flow as well as from moving bed particles, which in turn also receive energy from the mean flow. For near-critical bed condition, particle aggregations enhanced mean-flow heterogeneity, strengthened turbulent stresses and their effects on the flow, while at increased bed-mobility, energy transport mechanisms became weaker and conversions induced by viscous stresses and pressure became stronger.

Direct numerical simulation of a supersonic turbulent boundary layer subject to adverse pressure gradient induced by external successive compression waves

A freestream Mach 2.9 flat-plate supersonic turbulent boundary layer subject to a “pure” adverse pressure gradient (APG) without the impact of wall curvatures is studied by direct numerical simulation and compared with a benchmark flow with zero pressure gradient. Due to APG, the streamwise velocity shows an increase in the near-wall region and a reduction in the outer boundary layer. The principal strain rate shows a sandwich distribution along the wall-normal direction. The mismatch between the temperature and velocity fluctuations in both the inner and the outer layer is observed. Enhanced LSMs (large-scale motions) and large velocity patches are the typical flow structures in the outer and inner boundary layer subject to APG, respectively. From the analysis of quadrant decomposition, the sweep events dominate in the near-wall region while ejection events dominate the rest of the boundary layer. It is found that the baroclinicity plays a significant role in the formation of the enhanced LSMs in the outer boundary layer and the near-wall velocity patches. The resulting amplified vorticity further drives the interactive motions of the outer fluid and inner fluid. The turbulent kinetic energy and turbulent Mach number profiles are amplified by APG and a second peak is observed in both profiles. Turbulent energy budget analysis demonstrates that both the production and viscous effects are strengthened in the near-wall region while in the outer layer, the production is significantly amplified and balanced by the increased convection and turbulent transport.

Sensitivity of Hurricane Intensity and Structure to Two Types of Planetary Boundary Layer Parameterization Schemes in Idealized HWRF Simulations

ABSTRACT This paper investigates the sensitivity of simulated hurricane intensity and structure to two planetary boundary layer (PBL) schemes in the Hurricane Weather and Research Forecast model including 1) the GFS scheme (control run) that uses the K-profile method to parameterize turbulent fluxes, and 2) the MYJ scheme that is based on turbulent kinetic energy (TKE) budget for turbulent closure. Idealized simulations with these two PBL schemes show that the storm in the TKE run is stronger than that in the control run after three days into simulation. Multi-scale structures are evaluated and compared between the control and the TKE runs prior to the divergence of the model-simulated intensity to elucidate the mechanism underlying such a difference in the intensity between the two runs. It is found that the storm in the TKE run has i) a shallower boundary layer with a stronger PBL inflow, ii) stronger boundary layer convergence closer to the storm center, iii) higher vorticity and inertial stability inside the RMW; iv) stronger and deeper updrafts in regions further inward from the radius of maximum wind (RMW), and v) more convective bursts located near the RMW as compared to the control run. Angular momentum budget analysis suggests that the convergence of angular momentum in the boundary layer is much stronger in the TKE run than in the control run, which is responsible for faster spin-up of the hurricane vortex in the TKE run.

Turbulence structures and statistics of a supersonic turbulent boundary layer subjected to concave surface curvature

Supersonic turbulent flows at Mach 2.7 over concave surfaces for two different radii of curvature were investigated and compared with a flat plate turbulent boundary layer using direct numerical simulations. The streamwise velocity reduces in the outer part of the boundary layer due to compression, while it increases near the wall due to curvature, with a higher shape factor for the concave cases. The near-wall spanwise streak spacing reduces compared to the flat plate, with large-scale streaks and turbulence amplification also observed. Streamwise velocity iso-surfaces and streamlines show the generation of Görtler-like vortices, consistent with significant centrifugal effects. Abundant small vortices are shown to be associated with large baroclinic production of vorticity that is caused by the density and pressure gradients that are associated with concave compression. Profiles of turbulent kinetic energy and turbulent Mach number exhibit a characteristic two-layer structure in the concave boundary layer cases. In the outer layer, turbulence is greatly amplified, whereas a local balance exists in the inner layer. Turbulent energy budget analysis shows that both production and dissipation increase near the concave wall, whereas in the outer part of the boundary layer, the production is increased and ultimately balanced by convection and turbulent transport.

Reynolds Number Dependence of Higher Order Statistics for Round Turbulent Jets Using Large Eddy Simulations

Despite the large repository of experimental and computational studies on the topic of turbulent jets, inconclusive and conflicting estimates prevail in regard to certain terms in the turbulence energy budget and the dependence (or lack of dependence) of these and other flow physics on the jet Reynolds number. No comprehensive study exists which adequately addresses these inconsistencies. The purpose of this study is to resolve these contradictions and ascertain the true dependence of the flow statistics on the jet Reynolds number. This is accomplished through high fidelity Large Eddy Simulations (LES), which are performed for a single isothermal round jet at three different Reynolds numbers, encompassing nearly two orders of magnitude. In each case, results are compared to well-accepted experimental and computational studies, and excellent agreement is found with experimental quantities either directly acquired or computed directly from raw data. A separate discrete eddy simulation of the flow in the nozzle upstream of the jet inlet is performed and is found to be crucial in quantifying the flow physics in the near field (e.g., virtual origin). Results show a definite Reynolds number dependence for nearly all third order terms and this is non-negligible especially for the mean convection and production terms in the turbulent kinetic energy budget.

Flow turbulence topology in regular porous media: From macroscopic to microscopic scale with direct numerical simulation

Microscopic analysis of turbulence topology in a regular porous medium is presented with a series of direct numerical simulation. The regular porous media are comprised of square cylinders in a staggered array. Triply periodic boundary conditions enable efficient investigations in a representative elementary volume. Three flow patterns—channel with sudden contraction, impinging surface, and wake—are observed and studied quantitatively in contrast to the qualitative experimental studies reported in the literature. Among these, shear layers in the channel show the highest turbulence intensity due to a favorable pressure gradient and shed due to an adverse pressure gradient downstream. The turbulent energy budget indicates a strong production rate after the flow contraction and a strong dissipation on both shear and impinging walls. Energy spectra and pre-multiplied spectra detect large scale energetic structures in the shear layer and a breakup of scales in the impinging layer. However, these large scale structures break into less energetic small structures at high Reynolds number conditions. This suggests an absence of coherent structures in densely packed porous media at high Reynolds numbers. Anisotropy analysis with a barycentric map shows that the turbulence in porous media is highly isotropic in the macro-scale, which is not the case in the micro-scale. In the end, proper orthogonal decomposition is employed to distinguish the energy-conserving structures. The results support the pore scale prevalence hypothesis. However, energetic coherent structures are observed in the case with sparsely packed porous media.

Use of DES in mildly separated internal flow: dimples in a turbulent channel

ABSTRACTDetached eddy simulation (DES) is investigated as a means to study an array of shallow dimples with depth to diameter ratios of 1.5% and 5% in a turbulent channel. The DES captures large-scale flow features relatively well, but is unable to predict skin friction accurately due to flow modelling near the wall. The current work instead relies on the accuracy of DES to predict large-scale flow features, as well as its well-documented reliability in predicting flow separation regions to support the proposed mechanism that dimples reduce drag by introducing spanwise flow components near the wall through the addition of streamwise vorticity. Profiles of the turbulent energy budget show the stabilising effect of the dimples on the flow. The presence of flow separation however modulates the net drag reduction. Increasing the Reynolds number can reduce the size of the separated region and experiments show that this increases the overall drag reduction.

Multiphase turbulence mechanisms identification from consistent analysis of direct numerical simulation data

Abstract Direct Numerical Simulation (DNS) serves as an irreplaceable tool to probe the complexities of multiphase flow and identify turbulent mechanisms that elude conventional experimental measurement techniques. The insights unlocked via its careful analysis can be used to guide the formulation and development of turbulence models used in multiphase computational fluid dynamics simulations of nuclear reactor applications. Here, we perform statistical analyses of DNS bubbly flow data generated by Bolotnov (Reτ = 400) and Lu–Tryggvason (Reτ = 150), examining single-point statistics of mean and turbulent liquid properties, turbulent kinetic energy budgets, and two-point correlations in space and time. Deformability of the bubble interface is shown to have a dramatic impact on the liquid turbulent stresses and energy budgets. A reduction in temporal and spatial correlations for the streamwise turbulent stress (uu) is also observed at wall-normal distances of y+ = 15, y/δ = 0.5, and y/δ = 1.0. These observations motivate the need for adaptation of length and time scales for bubble-induced turbulence models and serve as guidelines for future analyses of DNS bubbly flow data.

Physical controls on half‐hourly, daily, and monthly turbulent flux and energy budget over a high‐altitude small lake on the Tibetan Plateau

AbstractPrecise measurements of evaporation and understanding of the physical controls on turbulent heat flux over lakes have fundamental significance for catchment‐scale water balance analysis and local‐scale climate modeling. The observation and simulation of lake‐air turbulent flux processes have been widely carried out, but studies that examine high‐altitude lakes on the Tibetan Plateau are still rare, especially for small lakes. An eddy covariance (EC) system, together with a four‐component radiation sensor and instruments for measuring water temperature profiles, was set up in a small lake within the Nam Co basin in April 2012 for long‐term evaporation and energy budget observations. With the valuable measurements collected during the ice‐free periods in 2012 and 2013, the main conclusions are summarized as follows: First, a bulk aerodynamic transfer model (B model), with parameters optimized for the specific wave pattern in the small lake, could provide reliable and consistent results with EC measurements, and B model simulations are suitable for data interpolation due to inadequate footprint or malfunction of the EC instrument. Second, the total evaporation in this small lake (812 mm) is approximately 200 mm larger than that from adjacent Nam Co (approximately 627 mm) during their ice‐free seasons. Third, wind speed shows significance at temporal scales of half hourly, whereas water vapor and temperature gradients have higher correlations over temporal scales of daily and monthly in lake‐air turbulent heat exchange. Finally, energy stored during April to June is mainly released during September to November, suggesting an energy balance closure value of 0.97.

Global Surface Net-Radiation at 5 km from MODIS Terra

Reliable and fine resolution estimates of surface net-radiation are required for estimating latent and sensible heat fluxes between the land surface and the atmosphere. However, currently, fine resolution estimates of net-radiation are not available and consequently it is challenging to develop multi-year estimates of evapotranspiration at scales that can capture land surface heterogeneity and are relevant for policy and decision-making. We developed and evaluated a global net-radiation product at 5 km and 8-day resolution by combining mutually consistent atmosphere and land data from the Moderate Resolution Imaging Spectroradiometer (MODIS) on board Terra. Comparison with net-radiation measurements from 154 globally distributed sites (414 site-years) from the FLUXNET and Surface Radiation budget network (SURFRAD) showed that the net-radiation product agreed well with measurements across seasons and climate types in the extratropics (Wilmott’s index ranged from 0.74 for boreal to 0.63 for Mediterranean sites). Mean absolute deviation between the MODIS and measured net-radiation ranged from 38.0 ± 1.8 W∙m−2 in boreal to 72.0 ± 4.1 W∙m−2 in the tropical climates. The mean bias was small and constituted only 11%, 0.7%, 8.4%, 4.2%, 13.3%, and 5.4% of the mean absolute error in daytime net-radiation in boreal, Mediterranean, temperate-continental, temperate, semi-arid, and tropical climate, respectively. To assess the accuracy of the broader spatiotemporal patterns, we upscaled error-quantified MODIS net-radiation and compared it with the net-radiation estimates from the coarse spatial (1° × 1°) but high temporal resolution gridded net-radiation product from the Clouds and Earth’s Radiant Energy System (CERES). Our estimates agreed closely with the net-radiation estimates from the CERES. Difference between the two was less than 10 W·m−2 in 94% of the total land area. MODIS net-radiation product will be a valuable resource for the science community studying turbulent fluxes and energy budget at the Earth’s surface.

Reynolds stress distribution and turbulence generated secondary flow in the turbulent three-dimensional wall jet

The lateral half-width of the turbulent three-dimensional wall jet is typically five to eight times larger than the vertical half-width normal to the wall. Although the reason for this behaviour is not fully understood, it is caused by mean secondary flows that develop in the jet due to the presence of the wall. The origin of the secondary flow has been associated previously with both vorticity reorientation and also gradients in the Reynolds stresses, although this has not been directly quantified as yet. The present investigation focuses on a wall jet formed using a circular contoured nozzle with exit Reynolds number of 250 000. Stereoscopic particle image velocimetry measurements are used herein to measure the three-component velocity, thereby allowing access to the full Reynolds stress tensor that contributes to the secondary flow in a turbulent three-dimensional wall jet. Throughout the jet, the Reynolds normal stress ($\overline{u^{2}}$) makes the largest contribution to the Reynolds stress field whereas Reynolds shear stress ($\overline{vw}$) is found to be negligible when compared with other stresses. In particular, the differences in the Reynolds normal stresses ($\overline{v^{2}}-\overline{w^{2}}$) are found to be significantly larger than $\overline{vw}$; these terms are important for the generation of turbulence secondary flow in the wall jet. Above all, the differences in the Reynolds normal stresses are oriented to reinforce the near-wall streamwise vorticity, and thus contribute to the large lateral growth of this flow. The contours of the turbulent kinetic budget indicate that the turbulent energy budget obtained on the jet centreline is different from that obtained off of the jet centreline.