Terms In Turbulent Kinetic Energy Budget Research Articles

Impact of Momentum Perturbation on Convective Boundary Layer Turbulence

AbstractMesoscale‐to‐microscale coupling is an important tool for conducting turbulence‐resolving multiscale simulations of realistic atmospheric flows, which are crucial for applications ranging from wind energy to wildfire spread studies. Different techniques are used to facilitate the development of realistic turbulence in the large‐eddy simulation (LES) domain while minimizing computational cost. Here, we explore the impact of a simple and computationally efficient Stochastic Cell Perturbation method using momentum perturbation (SCPM‐M) to accelerate turbulence generation in boundary‐coupled LES simulations using the Weather Research and Forecasting model. We simulate a convective boundary layer (CBL) to characterize the production and dissipation of turbulent kinetic energy (TKE) and the variation of TKE budget terms. Furthermore, we evaluate the impact of applying momentum perturbations of three magnitudes below, up to, and above the CBL on the TKE budget terms. Momentum perturbations greatly reduce the fetch associated with turbulence generation. When applied to half the vertical extent of the boundary layer, momentum perturbations produce an adequate amount of turbulence. However, when applied above the CBL, additional structures are generated at the top of the CBL, near the inversion layer. The magnitudes of the TKE budgets produced by SCPM‐M when applied at varying heights and with different perturbation amplitudes are always higher near the surface and inversion layer than those produced by No‐SCPM, as are their contributions to the TKE. This study provides a better understanding of how SCPM‐M reduces computational costs and how different budget terms contribute to TKE in a boundary‐coupled LES simulation.

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.

Features of turbulence during wildland fires in forested and grassland environments

Fire-induced turbulence and the feedback into the fire, following ambient changes, differ for forested (sub-canopy) and grassland environments. Here, we synthesize observations from multiple experimental surface fires: two sub-canopy backing fires, one sub-canopy heading fire, and a grassland heading fire. We identify and compare the most essential coherent structures and processes of each case from the turbulent momentum fluxes and turbulent kinetic energy (TKE) budget terms. In the sub-canopy burns, turbulent eddies are strongest near the canopy top: high streamwise turbulent flux accompanies low cross-stream turbulent flux and vice versa. In the grassland fire, both streamwise and cross-stream eddies strengthen simultaneously until a certain height, informing a vertical length scale for the fire-influence. Moreover, the forward sweep from streamwise eddies assists in the fire spread by pushing hot gases towards unburnt fuel. In the sub-canopy fires, shear production and buoyancy production are more substantial near the canopy top for more intense fires, while their magnitudes decrease with decreasing fire intensity. At mid-canopy-height scales, buoyancy production dominates shear production, becoming the key mechanism for vertical transport of TKE. In the grassland fire, shear production dominates buoyancy production near the surface and is insignificant beyond a certain height relative to the flame length, while buoyancy production increases with height, becoming substantial further away from the surface. Turbulent transport terms are also active in both environments. For intense sub-canopy fires, there is a loss in TKE due to its expulsion to the boundary layer aloft via the transport term, compensated by a reversal process: TKE influx via the transport term. In the grassland fire, the transport term mimics this behavior until a certain height. The insights into the relative significance of the respective turbulent fluxes and TKE budget terms in each environment can help simplify the complex system of equations governing fire physics.

The Effect of Advection on the Three Dimensional Distribution of Turbulent Kinetic Energy and Its Generation in Idealized Tropical Cyclone Simulations

AbstractThe distribution of turbulent kinetic energy (TKE) and its budget terms is estimated in simulated tropical cyclones (TCs) of various intensities. Each simulated TC is subject to storm motion, wind shear, and oceanic coupling. Different storm intensities are achieved through different ocean profiles in the model initialization. For each oceanic profile, the atmospheric simulations are performed with and without TKE advection. In all simulations, the TKE is maximized at low levels (i.e., below 1 km) and ∼0.5 km radially inward of the azimuthal‐mean radius of maximum wind speed at 1‐km height. As in a previous study, the axisymmetric TKE decreases with height in the eyewall, but more abruptly in simulations without TKE advection. The largest TKE budget terms are shear generation and dissipation, though variability in vertical turbulent transport and buoyancy production affect the change in the azimuthal‐mean TKE distribution. The general relationships between the TKE budget terms are consistent across different radii, regardless of storm intensity. In terms of the asymmetric distribution in the eyewall, TKE is maximized in the front‐left quadrant where the sea surface temperature (SST) is highest and is minimized in the rear‐right quadrant where the SST is the lowest. In the category‐5 simulation, the height of the TKE maximum varies significantly in the eyewall between quadrants and is between ∼400 m in the rear‐right quadrant and ∼1,000 m in the front‐left quadrant. When TKE advection is included in the simulations, the maximum eyewall TKE values are downwind compared to the simulations without TKE advection.

One-dimensional turbulence modeling of compressible flows. I. Conservative Eulerian formulation and application to supersonic channel flow

Accurate but economical modeling of supersonic turbulent boundary layers is a standing challenge due to the intricate entanglement of temperature, density, and velocity fluctuations on top of the mean-field variation. Application of the van Driest transformation may describe well the mean state but cannot provide detailed flow information. This lack-in modeling coarse and fine-scale variability is addressed by the present study using a stochastic one-dimensional turbulence (ODT) model. ODT is a simulation methodology that represents the evolution of turbulent flow in a low-dimensional stochastic way. In this study, ODT is extended to fully compressible flows. An Eulerian framework and a conservative form of the governing equations serve as the basis of the compressible ODT model. Computational methods for statistical properties based on ODT realizations are also extended to compressible flows, and a comprehensive way of turbulent kinetic energy budget calculation based on compressible ODT is put forward for the first time. Two canonical direct numerical simulation cases of supersonic isothermal-wall channel flow at Mach numbers 1.5 and 3.0 with bulk Reynolds numbers 3000 and 4880, respectively, are used to validate the extended model. A rigorous numerical validation is presented, including the first-order mean statistics, the second-order root mean square statistics, and higher-order turbulent fluctuation statistics. In ODT results, both mean and root mean square profiles are accurately captured in the near-wall region. Near-wall temperature spectra reveal that temperature fluctuations are amplified at all turbulent scales as the effects of compressibility increase. This phenomenon is caused by intensified viscous heating at a higher Mach number, which is indicated by the steeper profiles of viscous turbulent kinetic energy budget terms in the very near-wall region. The low computational cost and predictive capabilities of ODT suggest that it is a promising approach for detailed modeling of highly turbulent compressible boundary layers. Furthermore, it is found that the ODT model requires a Mach-number-dependent increase in a viscous penalty parameter Z in wall-bounded turbulent flows to enable accurate capture of the buffer layer.

Turbulence structure in a very sharp thermally stratified open-channel meander

Direct numerical simulation (DNS) results for turbulent open-channel flow through an idealized sine-generated meander with and without an internal heat source that models radiative heating from above are used to analyze the effect of a very sharp meander configuration and thermal stratification on the turbulence structure in the channel with friction Reynolds number Reτ=200. Spatial distributions of temperature, mean velocities, vorticity, mean-flow kinetic energy, and turbulent kinetic energy (TKE) are presented. In both cases, the cross-sectional motion is characterized by three circulation cells: a center-region cell and two weaker outer bank and inner bank cells. However, there is also a small cell observed near the corner of the channel bed inner bank at the channel outlet and the channel bed outer bank at the channel inlet. The tri-cellular cross-stream motions control the distributions of temperature and kinetic energy. In the stratified case, two separated shear layers (SSLs) are found: the first one is formed before the bend apex, and the second one is observed in the wake after the bend apex. In the neutral case, only the first SSL is observed. Turbulent amplification can be seen in both cases; however, in the stratified case, the second SSL stretches out to the channel outlet and is introduced back to the channel inlet by an anti-symmetric periodic boundary condition and then follows the outer bank line. The two SSLs converge in the region before the bend apex and amplify the turbulence more strongly there than in the neutral case. The turbulence kinetic energy budget terms for the stratified case are analyzed to determine the characteristics of production, dissipation and transport of TKE in thermally stratified meandering flow.

Amplification of turbulence by sharp meanders on thermally stratified open channel flow

In order to unravel the effects of meander bends on the mechanism by which the turbulence kinetic energy (TKE) is produced, redistributed and dissipated in a thermally stratified curved open-channel flow, Direct Numerical Simulation (DNS) was carried out through an idealized sharp meander with and without an internal heat source. The heat source models radiative heating from above and varies with height due to progressive absorption. In both cases, we find a pronounced local increase in TKE starting in the region approximately 25% of the distance through the bend. Here a local extremum of TKE is found near the channel bed at the inner bank and close to the free surface at the outer bank. This grows to a more generalised increase in turbulence that starts at a location approximately 35% of the distance through the bend and peaks at the meander apex before gradually weakening in the downstream part of the bend. However, while only showing a marked increase in the mid-depth region near the inner bank in the neutral case, turbulence is amplified more strongly in the stratified case with the high TKE values spread out across the whole channel width. This is due to the two observed separated shear layers converging in the bend apex in this case. There is only one SSL observed in the neutral case. An investigation of the TKE budget terms for the stratified case at the turbulence amplification location was undertaken to elucidate the mechanisms leading to the production, dissipation and transport of TKE in these regions.

Macroscopic turbulent kinetic energy budget in flow through a wall-bounded compact bank of cylinders

The flow in devices, such as heat exchangers, can be idealized as turbulent flow past an array of regularly spaced obstacles. Engineering calculations in such devices are easily handled if the flow can be represented by its volume-average quantities. This paper reports an investigation into the volume-averaged flowfield in a regular array of cylinders of finite height in crossflow at two Reynolds numbers (ReD). The investigation is based on scale-resolving computations and is thus the first to analyze the true form of the macroscopic turbulent kinetic energy (TKE) conservation law in the presence of macroscopic shear. Volume-averaging is performed parallel to the end walls in order to obtain profiles of macroscopic flow quantities. In inner coordinates, the macroscopic velocity profiles are similar to the canonical turbulent channel flow profiles, but with different values of the von Kármán constant and log-law y-intercept. The volume-averaged TKE is defined so as to include contributions from both the macroscopic and microscopic components of the flow. While the macroscopic TKE profile is very different to that of channel flow, the macroscopic TKE budget terms are remarkably similar. One notable exception is that the production rate stays large throughout the domain rather than attenuating rapidly after a near-wall peak. An extension to a widely used macroscopic turbulence model is proposed, which enables it to match the volume-averaged TKE production rate predicted by the large eddy simulations.

Turbulent flow characteristics over an abrupt step change in bed roughness

Turbulent flow characteristics over an abrupt step change in bed roughness from smooth to rough are studied measuring the flow field by a Particle Image Velocimetry (PIV) system. The smooth and rough beds are referred to as the upstream and downstream beds, respectively. The velocity color maps and profiles show that an abrupt step change in bed roughness causes flow retardation in the downstream bed owing to the combined effects of roughness-induced and separated flows. The results of the Reynolds stresses reveal that the profiles in the downstream bed exhibit discriminable bulges, whose size increases with an increase in the streamwise distance. The stress color maps illustrate the creation of a roughness-induced layer that grows over the downstream bed as the streamwise distance increases. The bed shear stress evidences an overshooting behavior immediate downstream of the abrupt step change in bed roughness to reach its peak magnitude. The third-order correlations indicate that the effects of the abrupt step change in bed roughness produce an inrush of rapidly moving fluid streaks in the near-bed flow and arrival of slowly moving fluid streaks in the away-bed flow. Regarding the turbulent kinetic energy (TKE) budget, the enhanced magnitudes of the TKE budget terms within the roughness-induced layer are prevalent. The TKE dissipation rate lags the production rate, and the negative TKE diffusion rate implies an addition in the TKE production. Bursting analysis endorses that the sweeps govern the near-bed flow on the downstream bed and the ejections prevail far from the bed.

Direct numerical simulation of supersonic flow and acoustics over a compression ramp

We present direct numerical simulations of the shock wave boundary layer interaction (SBLI) at Mach number 2.9 over a 24° ramp. We study both the numerical accuracy and flow physics. Two classes of spatial reconstruction schemes are employed: the monotonic upstream-centered scheme for conservation laws and the Weighted Essentially Non-Oscillatory (WENO) scheme, of accuracy ranging from 2nd- to 11th-order. Using the canonical Taylor–Green vortex test-case, a simple and computationally inexpensive rescaling of the candidate stencil values—within the context of the high-order WENO scheme—is proposed for reducing the numerical dissipation, particularly in under-resolved simulations. For the compression ramp case, higher-order schemes are shown to capture the size of the SBLI separation zone more accurately, a consequence of resolving much finer turbulence structures. For second- and fifth-order schemes, the energy of the unresolved small scale turbulence shifts the cascade of the turbulence kinetic energy (TKE) spectrum, thus resulting in more energetic large scale turbulent structures. Consequently, the λ-shock foot shifts further downstream, leading to a smaller separation bubble size. Nonetheless, other statistical quantities, such as the turbulence anisotropy invariant map and the turbulence kinetic energy budget terms, show little dependence on the type and order of the spatial reconstruction scheme. Finally, using the more accurate ninth-order WENO results, it is reasoned that the interaction of the λ-shock with the post-shock relaxation region drives the low-frequency oscillation of the λ-shock.

Dynamics of Subsiding Shells in Actively Growing Clouds with Vertical Updrafts

Abstract The dynamics of a subsiding shell at the edges of actively growing shallow cumulus clouds with updrafts is analyzed using direct numerical simulation. The actively growing clouds have a fixed in-cloud buoyancy and velocity. Turbulent mixing and evaporative cooling at the cloud edges generate a subsiding shell that grows with time. A self-similar regime is observed for first- and second-order moments when normalized with respective maximum values. Internal scales derived from integral properties of the flow problem are identified. A self-similarity analysis using these scales reveals that contrary to classical self-similar flows, the turbulent kinetic energy budget terms and velocity moments scale according to the buoyancy and not with the mean velocity. The shell thickness is observed to increase linearly with time. The buoyancy scale remains time invariant and is set by the initial cloud–environment thermodynamics. The shell accelerates ballistically with a magnitude set by the saturation value of the buoyancy of the cloud–environment mixture. In this regime, the shell is buoyancy driven and independent of the in-cloud velocity. Relations are obtained for predicting the shell thickness and minimum velocities by linking the internal scales with external flow parameters. The values thus calculated are consistent with the thickness and velocities observed in typical shallow cumulus clouds. The entrainment coefficient is a function of the initial state of the cloud and the environment, and is shown to be on the same order of magnitude as fractional entrainment rates calculated for large-scale models.

Stability and Sea State as Limiting Conditions for TKE Dissipation and Dissipative Heating

Abstract This study analyzes high-resolution ship data collected in the Gulf of Mexico during the Lagrangian Submesoscale Experiment (LASER) from January to February 2016 to produce the first reported measurements of dissipative heating in the explicitly nonhurricane atmospheric surface layer. Although typically computed from theory as a function of wind speed cubed, the dissipative heating directly estimated via the turbulent kinetic energy (TKE) dissipation rate is also presented. The dissipative heating magnitude agreed with a previous study that estimated the dissipative heating in the hurricane boundary layer using in situ aircraft data. Our observations that the 10-m neutral drag coefficient parameterized using TKE dissipation rate approaches zero slope as wind increases suggests that TKE dissipation and dissipative heating are constrained to a physical limit. Both surface-layer stability and sea state were observed to be important conditions influencing dissipative heating, with the stability determined via TKE budget terms and the sea state determined via wave steepness and age using direct shipboard measurements. Momentum and enthalpy fluxes used in the TKE budget are determined using the eddy-correlation method. It is found that the TKE dissipation rate and the dissipative heating are largest in a nonneutral atmospheric surface layer with a sea surface comprising steep wind sea and slow swell waves at a given surface wind speed, whereas the ratio of dissipative heating to enthalpy fluxes is largest in near-neutral stability where the turbulent vertical velocities are near zero.

Turbulence kinetic energy budget and conditional sampling of momentum, scalar, and intermittency fluxes in thermally stratified wind farms

ABSTRACTA description of the turbulence kinetic energy budget is investigated to understand the dynamics and turbulence energy transfer between the atmospheric boundary layer and large wind farms. The turbulence kinetic energy budget terms are a dominant factor in explaining the energy supply process in wind farms. Large eddy simulations are used to generate the thermally stratified wind turbine array boundary layer, where stable and unstable conditions are considered. The wakes represent a sink of mean kinetic energy, and turbulence transport redistributes energy in the wake region. The energy balance between the budget terms is dependent on the physical location in the wind farm. During the unstable scenario, turbulence is driven by the production, transport, and buoyancy terms. Further, the contribution of the turbulence kinetic energy budget terms is reduced with increasing atmospheric stability, especially above the shear layer, where the mechanical production is the dominant term. Pressure diffusion redistributes the turbulent energy from the streamwise direction into the other components of the normal Reynolds stresses. This distinctive feature of the changing thermal stratification is presented through the quadrant analysis. The momentum ejection and sweep frequencies are both comparable and dominant. The scalar flux shows an increase in the contribution of the negative correlation in the quadrants. The quadrant analysis is extended to account for intermittency based on the pointwise Hölder exponents. Positive correlations are dominant in the wake and in higher layers of the domain for both considered cases.

A two-phase mixing layer between parallel gas and liquid streams: multiphase turbulence statistics and influence of interfacial instability

The two-phase mixing layer formed between parallel gas and liquid streams is an important fundamental problem in turbulent multiphase flows. The problem is relevant to many industrial applications and natural phenomena, such as air-blast atomizers in fuel injection systems and breaking waves in the ocean. The velocity difference between the gas and liquid streams triggers an interfacial instability which can be convective or absolute depending on the stream properties and injection parameters. In the present study, a direct numerical simulation of a two-phase gas–liquid mixing layer that lie in the absolute instability regime is conducted. A dominant frequency is observed in the simulation and the numerical result agrees well with the prediction from viscous stability theory. As the interfacial wave plays a critical role in turbulence transition and development, the temporal evolution of turbulent fluctuations (such as the enstrophy) also exhibits a similar frequency. To investigate the statistical response of the multiphase turbulence flow, the simulation has been run for a long physical time so that time-averaging can be performed to yield the statistically converged results for Reynolds stresses and the turbulent kinetic energy (TKE) budget. An extensive mesh refinement study using from 8 million to about 4 billions cells has been performed. The turbulent dissipation is shown to be highly demanding on mesh resolution compared with other terms in TKE budget. The results obtained with the finest mesh are shown to be close to converged results of turbulent dissipation which allow us to obtain estimations of the Kolmogorov and Hinze scales. The estimated Kolmogorov scale is found to be similar to the cell size of the finest mesh used here. The computed Hinze scale is significantly larger than the size of droplets observed and does not seem to be a relevant length scale to describe the smallest size of droplets formed in atomization.

Turbulence kinetic energy budget in the stable boundary layer over a heterogeneous surface

This study presents turbulence kinetic energy (TKE) budget terms above tall, deciduous walnut canopy in the wintertime stable boundary layer (SBL) and makes a comparison to well‐known results of horizontally homogeneous and flat (HHF) terrain. Turbulence measurements performed at five levels above the canopy height (approximately h=18 m) enable the investigation of joint effect of the roughness sublayer (RSL) and the transition layer on the TKE budget terms. Each term of the TKE budget is investigated within the framework of local similarity theory. Kolomogorov's similarity hypothesis assumes local isotropy within the inertial subrange. Thoroughly testing the local isotropy hypothesis for the present dataset results in a ratio of the horizontal spectral densities (Sv/Su) approaching 4/3, while the ratio of the vertical to the longitudinal spectral density (Sw/Su) is less than the canonical value of 4/3 (even less than 1) for all levels indicating anisotropic turbulence even at very small scales above the canopy. As a consequence, estimated values of TKE dissipation rate (ε) from the vertical component are smaller than those obtained from the horizontal velocity components. This finding has a direct influence on the applicability of classical Kansas spectral models valid for HHF terrain as well as on the budget of wind variances. Additionally, the behavior of the non‐dimensional gradient of mean wind speed is tested with regard to conformity to z‐less scaling requirements (i.e. linear dependence on stability). It is confirmed that a stability threshold (such as Rf > 0.25, where Rf is the flux Richardson number) is a stronger determinant of z‐less behavior than the existence of a well‐defined inertial subrange ‐ opposite to observations in the SBL over ideal flat surfaces. Finally, the local equilibrium between the production and destruction of TKE within the RSL and transition layer is analyzed.

Aerothermal Characteristics of Solid and Slitted Pentagonal Rib Turbulators

This work is an experimental study of detailed aerothermal characteristics inside a duct carrying an array of solid and permeable pentagonal ribs with a parallel and inclined slit, mounted on the bottom wall. The rib height-to-hydraulic diameter ratio, the rib pitch-to-height ratio, and the open area ratio fixed during experiments are 0.125%, 12%, and 25%, respectively. The heat transfer coefficient (HTC) distribution is mapped by using transient liquid crystal thermography (LCT), while the detailed flow measurements are performed by using particle image velocimetry (PIV). The primary focus of the study is to assess the influence of inter-rib region flow characteristics on the local heat transfer fields. The heat transfer and friction factor measurements are evaluated along with thermohydraulic performances at different Reynolds numbers, i.e., 26,160, 42,500, and 58,850. Performance indexes show that the pentagonal ribs with the inclined-slit are superior to other configurations from both perspective. Aerothermal features within inter-rib region were elucidated by analyzing the time-averaged streamlines, mean velocities, fluctuation statistics, vorticity, turbulent kinetic energy (TKE) budget terms, and local and spanwise-averaged Nusselt number as well as augmentation Nusselt numbers. Critical flow structures and coherent structures were identified, which illustrate about different flow dynamic processes. The flow emanating out of the inclined-slit pentagonal rib significantly affects the magnitude of streamwise velocity, fluctuation statistics, vorticity, and TKE budget terms at the downstream corner, whereas the dissipation term of TKE budget correlates well with the surface heat transfer distribution.

Spatiotemporal Variability of Turbulence Kinetic Energy Budgets in the Convective Boundary Layer over Both Simple and Complex Terrain

AbstractThe assumption of subgrid-scale (SGS) horizontal homogeneity within a model grid cell, which forms the basis of SGS turbulence closures used by mesoscale models, becomes increasingly tenuous as grid spacing is reduced to a few kilometers or less, such as in many emerging high-resolution applications. Herein, the turbulence kinetic energy (TKE) budget equation is used to study the spatiotemporal variability in two types of terrain—complex [Columbia Basin Wind Energy Study (CBWES) site, northeastern Oregon] and flat [Scaled Wind Farm Technology (SWiFT) site, west Texas]—using the Weather Research and Forecasting (WRF) Model. In each case, six nested domains [three domains each for mesoscale and large-eddy simulation (LES)] are used to downscale the horizontal grid spacing from ~10 km to ~10 m using the WRF Model framework. The model output was used to calculate the values of the TKE budget terms in vertical and horizontal planes as well as the averages of grid cells contained in the four quadrants of the LES domain. The budget terms calculated along the planes and the mean profile of budget terms show larger spatial variability at the CBWES site than at the SWiFT site. The contribution of the horizontal derivative of the shear production term to the total shear production was found to be ≈45% and ≈15% at the CBWES and SWiFT sites, respectively, indicating that the horizontal derivatives applied in the budget equation should not be ignored in mesoscale model parameterizations, especially for cases with complex terrain with <10-km scale.

Mean and turbulence dynamics in unsteady Ekman boundary layers

Unsteady pressure gradients in turbulent flows not only influence the mean, but also affect the higher statistical moments of turbulence. In these flows, it is important to understand if and when turbulence is in quasi-equilibrium with the mean in order to better capture the dynamics and develop effective closure models. Therefore, this study aims to elucidate how turbulence decays or develops relative to a time-varying mean flow, and how the turbulent kinetic energy (TKE) production, transport and dissipation respond to changes in the imposed pressure forcing. The focus is on the neutral unsteady Ekman boundary layer, where pressure-gradient, Coriolis and turbulent friction forces interact, and the analyses are based on a suite of large-eddy simulations with unsteady pressure forcing. The results indicate that the dynamics is primarily controlled by the relative magnitudes of three time scales: the inertial time scale (characterized by Coriolis frequency${\sim}12$ hours at mid-latitudes), the turbulent time scale (${\sim}2$ hours for the largest eddies in the present simulations) and the forcing variability time scale (which is varied to reflect different (sub)meso to synoptic scale dynamics). When the forcing time scale is comparable to the turbulence time scale, the quasi-equilibrium condition becomes invalid due to highly complex interactions between the mean and turbulence, the velocity profiles manifestly depart from the log-law and the normalized TKE budget terms vary strongly in time. However, for longer, and surprisingly for shorter, forcing times, quasi-equilibrium is reasonably maintained. The analyses elucidate the physical mechanisms that trigger these dynamics, and investigate the implications on turbulence closure models.

Turbulence kinetic energy budget during the afternoon transition – Part 1: Observed surface TKE budget and boundary layer description for 10 intensive observation period days

Abstract. The decay of turbulence kinetic energy (TKE) and its budget in the afternoon period from midday until zero-buoyancy flux at the surface is studied in a two-part paper by means of measurements from the Boundary Layer Late Afternoon and Sunset Turbulence (BLLAST) field campaign for 10 intensive observation period days. Here, in Part 1, near-surface measurements from a small tower are used to estimate a TKE budget. The overall boundary layer characteristics and mesoscale situation at the site are also described based upon taller tower measurements, radiosoundings and remote sensing instrumentation. Analysis of the TKE budget during the afternoon transition reveals a variety of different surface layer dynamics in terms of TKE and TKE decay. This is largely attributed to variations in the 8 m wind speed, which is responsible for different amounts of near-surface shear production on different afternoons and variations within some of the afternoon periods. The partitioning of near-surface production into local dissipation and transport in neutral and unstably stratified conditions was investigated. Although variations exist both between and within afternoons, as a rule of thumb, our results suggest that about 50 % of the near-surface production of TKE is compensated for by local dissipation near the surface, leaving about 50 % available for transport. This result indicates that it is important to also consider TKE transport as a factor influencing the near-surface TKE decay rate, which in many earlier studies has mainly been linked with the production terms of TKE by buoyancy and wind shear. We also conclude that the TKE tendency is smaller than the other budget terms, indicating a quasi-stationary evolution of TKE in the afternoon transition. Even though the TKE tendency was observed to be small, a strong correlation to mean buoyancy production of −0.69 was found for the afternoon period. For comparison with previous results, the TKE budget terms are normalized with friction velocity and measurement height and discussed in the framework of Monin–Obukhov similarity theory. Empirically fitted expressions are presented. Alternatively, we also suggest a non-local parametrization of dissipation using a TKE–length scale model which takes into account the boundary layer depth in addition to distance above the ground. The non-local formulation is shown to give a better description of dissipation compared to a local parametrization.

Assessment of spanwise domain size effect on the transitional flow past an airfoil

In most large-eddy and direct numerical simulations of flow past an isolated airfoil, the flow is assumed periodic in the spanwise direction. The size of the spanwise domain is an important geometrical parameter determining whether the turbulent flow is fully developed, and whether the separation and transition patterns are accurately modeled. In the present study, we investigate the incompressible flow past an isolated NACA0012 airfoil at the angle of attack of 5 degrees and Reynolds number 5 × 104. The spanwise domain size Lz, represented by the aspect ratio AR = Lz/C where C is the airfoil chord length, is varied in the range 0.1−0.8. The effect of varying the normalized spanwise domain size AR is examined via direct numerical simulation (DNS) on several aspects of the turbulent flow quantities including the time-averaged and time-dependent behavior as well as the spanwise variation of the selected statistical quantities. DNS results reveal that different aspect ratios result in close predictions of the time-averaged aerodynamic quantities, and the velocity field except for a slight difference in the separation bubble. Smaller aspect ratios tend to underpredict the turbulent fluctuations near the separation point but overpredict them inside the separation bubble. Large differences are observed for multiple statistical quantities near the reattachment point, especially the turbulent kinetic energy budget terms. The leading edge separation is notably three-dimensional for simulation at AR = 0.8, while remaining quasi-2D for smaller aspect ratios. The spanwise two-point correlation coefficient shows significant dependence on the position of the probe and the velocity component analyzed: small aspect ratios do not produce uncorrelated results for all the velocity components. The simulation results demonstrate that examining only a few statistical quantities may result in a misleading conclusion regarding the sufficiency of the spanwise domain size. Reliable metrics to establish the sufficiency of spanwise domain size require thorough analysis of the turbulent statistics, and are necessary for three-dimensional simulation of turbulent flow in similar configurations.