Turbulent Kinetic Energy Method Research Articles

Observational Estimates of Turbulence Parameters in the Atmospheric Surface Layer of Landfalling Tropical Cyclones

AbstractThis study analyzes observations collected by multilevel towers to estimate turbulence parameters in the atmospheric surface layer of two landfalling tropical cyclones (TCs). The momentum flux, turbulent kinetic energy (TKE) and dissipation rate increase with the wind speed independent of surface types. However, the momentum flux and TKE are much larger over land than over the coastal ocean at a given wind speed range. The vertical eddy diffusivity is directly estimated using the momentum flux and strain rate, which more quickly increases with the wind speed over a rougher surface. Comparisons of the eddy diffusivity estimated using the direct flux method and that using the friction velocity and height show good agreement. On the other hand, the traditional TKE method overestimates the eddy diffusivity compared to the direct flux method. The scaling coefficients in the TKE method are derived for the two different surface types to better match with the vertical eddy diffusivity based on the direct flux method. Some guidance to improve vertical diffusion parameterizations for TC landfall forecasts in weather simulations are also provided.

A comparison of shear stress estimation methods for a single geobag on a rough bed

There are several methods for estimating bed shear stress in the literature, but comprehensive comparisons among them are limited and under specific conditions. This study compared these methods first on a bare smooth bed, and then for a single geobag on a rough bed in the interest of determining the stability of geobags used in riverbank protection structures. The geobag was filled with cement or sand and tested under different open channel flow conditions. The turbulent kinetic energy method appeared to best represent the local bed shear stress on the geobag when using the newly calibrated proportionality constants. The Reynolds stress method via extrapolation was relatively unaffected by changes to the geobags shape and measurement locations, suggesting this method inadequately represents the local bed shear stress. The Patel method and the universal law of the wall method failed to represent local bed shear stress in the rough bed cases due to instrument limitations and the breakdown of the law of the wall. This study highlights the impact of different methods on the bed shear stress estimation.

A Computationally Efficient Approach to Resolving Vehicle-Induced Turbulence for Near-Road Air Quality

Abstract Near-road air pollution is a worldwide public health concern, especially in urban areas. Vehicle-induced turbulence (VIT) has a major impact on the initial dispersion of traffic-related pollutants on the roadways, affecting their subsequent near-road impact. The current methods for high-fidelity VIT simulations using computational fluid dynamics (CFD) are often computationally expensive or prohibitive. Earlier studies adopted the turbulent kinetic energy (TKE) method, which models VIT as a fixed TKE volume source and produces turbulence uniformly in the computational traffic zones. This paper presents two novel methods, namely the force method and the moving force method, to generate VIT implicitly by injecting a force source into the computational domain instead of physical vehicles in the domain explicitly, thus greatly reducing the computational burden. The simulation results were evaluated against experimental data collected in a field study near a major highway in Las Vegas, NV, which included collocated measurements of traffic and wind speed. The TKE method systematically overestimated the turbulence produced on the highway by converting the drag force completely into turbulence. This indicates that the TKE method, currently being used to implicitly model VIT in CFD simulations, requires major improvements. In comparison, the proposed force and moving force methods performed favorably and were able to capture turbulence anisotropicity and fluid convection. The force method was shown to be a computationally efficient way to simulate VIT with adequate accuracy, while the moving force method has the potential to emulate vehicle motion and its impact on fluid flow.

Study on the Methods to Estimate the Bed Shear Stresses in Yangtze Estuary

High spatial and temporal current resolution velocities were measured by use of an acoustic Doppler velocimeter (ADV) in the tidal bottom layer of North Passage Deep water Navigational Channel (DNC) of Yangtze Estuary in China. And the vertical profiles of mean velocity were measured by using a pulse-coherent acoustic Doppler profiler (PC-ADP). The measured data show the vertical profiles of mean velocity are almost logarithmic. For discussing, the turbulent kinetic energy (TKE) method based on the velocity for ADVs-based is chosen and a new logarithmic profile (LP) method ignoring the influence of complex variation of the parameter Z 0 is suggested to estimate the bed shear stresses respectively. The calculated results show that the bed shear stresses estimated by LP method are larger than the ones estimated by TKE method mostly in Yangtze estuary. At the moment of ebb peak, the maximum error can be about twice occurring and the error of ebb tide is almost greater than the one of flood tide. These phenomena are explained in this study by the deduction of formula for steady and unsteady flow. It is concluded that the vertical logarithmic profile of velocities will be influenced by unsteady flow and there is not the same bed shear stress even if there is the same logarithmic velocity profile in vertical. Generally, this has led to a necessary adjustment of the drag coefficient Cd of steady flow in flow model to avoid overestimating the bed stress for unsteady flow in estuary based on the observed data.

The influence of a deposit body on near-bed shear stress

The probability distribution of the fluctuating velocity in three dimensions and the near-bed shear stress (NBSS) of a channel with a deposit body were studied using mathematical statistics and the turbulent kinetic energy method, respectively. This analysis of the longitudinal and plane distributions of the NBSS under varying discharges, width ratios and lateral slopes will help further understanding of the laws of sediment incipient motion and transport in channels. It was found that the probability distribution of the near-bed vertical fluctuating velocity was closer to a normal distribution than that in the longitudinal and transversal directions. The NBSS did not change much in the upstream sections of the deposit body, but the difference between the left bank (near the deposit body) and the right bank (far away from the deposit body) was obvious in the sections near the deposit body and downstream. A high shear stress area was located in the transition zone between the main flow and the backflow. Introducing the backwater parameter β, an exponential relationship between the relative NBSS and β was determined, which will help in quick estimates of the NBSS in future practical projects.

Comparison of Methods for Bed Shear Stress Estimation in Complex Flow Field of Bend

Bed shear stress is closely related to sediment transport in rivers. Bed shear stress estimation is very difficult, especially for complex flow fields. In this study, complex flow field measurement experiments in a 60° bend with a groyne were performed. The feasibility and reliability of bed shear stress estimations using the log-law method in a complex flow field were analyzed and compared with those associated with the Reynolds, Turbulent Kinetic Energy (TKE), and TKE-w′ methods. The results show that the TKE, Reynolds, and log-law methods produced similar bed shear stress estimates, while the TKE-w′ method produced larger estimates than the other methods. The TKE-w′ method was found to be more suitable for bed shear stress estimation than the TKE method, but the value of its constant C2 needed to be re-estimated. In a complex, strong, three-dimensional flow field, the height of the measurement point (relative or absolute) should be re-estimated when a single point measurement is used to estimate the bed shear stress. The results of this study provide guidance for experimental measurement of bed shear stress in a complex flow field.

Sidewall shear stress distribution effects on cohesive bank erosion in curved channels

A series of experiments were conducted to reveal the effects of the sidewall shear stress distribution (SSSD) on homogeneous cohesive bank erosion processes in a U-shaped flume. The three-dimensional flow velocities were measured in detail and the turbulent kinetic energy method was employed to estimate the SSSD. The experimental results showed that the SSSD changed with the discharge and the point of the maximum shear stress varied within a range of 0·15–0·75 of the relative water depth. The variation of underwater bank topography was found to be consistent with the SSSD and the location of the maximum erosion point was not at the bank toe. The dominant failure mechanisms were observed to be tensile and toppling failures. Furthermore, a simplified bank erosion model (SBEM) was developed with consideration of the SSSD. Compared with the bank stability and toe erosion model, the SBEM can provide a more accurate simulation of bank erosion processes. This study is expected to enrich general understanding of cohesive bank erosion processes in curved channels, which will help to formulate effective strategies for river regulation.

Evaluation of Shallow‐Cumulus Entrainment Rate Retrievals Using Large‐Eddy Simulation

AbstractA complete and quantitative understanding of cumulus entrainment remains elusive, in part due to the difficulty of directly observing cloud entrainment rates. Multiple approaches to ground‐based observational retrieval of bulk fractional entrainment rates (ε) within cumuli have been developed, such as the parcel model by Jensen and Del Genio (JDG, 2006, https://doi.org/10.1175/JCLI3722.1) and Entrainment Rate In Cumulus Algorithm (ERICA) by Wagner et al. (2013, https://doi.org/10.1175/JTECH-D-12-00187.1). In this paper, a new cumulus entrainment retrieval based on a turbulent kinetic energy (TKE) similarity theory is presented. This method estimates ε based on only the environmental and subcloud conditions. By conducting large‐eddy simulations of a range of continental and maritime shallow cumulus convection cases as Observing System Simulations Experiments, the first numerical verification of the three retrieval methods is produced. These simulations consider a broad range of shallow cumulus environments along with variations of the numerical configuration. The diagnosed ε from these simulations is found to be robustly larger in cumuli over the ocean than in cumuli over land. For continental cumuli, the experiments also reveal a diurnal cycle with increasing ε in the late afternoon. These diagnosed ε serve as the “truth” against which the pseudo‐retrieved entrainment rates from several different implementations of each retrieval are verified. Overall, the simpler JDG and TKE retrievals outperform the more sophisticated ERICA method and better capture the sensitivity to continentality. Only the TKE method reproduces the diurnal variations in ε within continental cumuli. The mean error in the ε retrievals are between 20% and 30% for the TKE and JDG methods, but 50% for ERICA.

Bed Shear Stress Estimation Under Wave Conditions Using near-bottom Measurements: Comparison of Methods

Zhang, Q.; Gong, Z.; Zhang, C.K.; Lacy, J.R.; Jaffe, B.E., and Xu, B.B., 2018. Bed Shear Stress Estimation Under Wavy Condition Using near-bottom Measurements: Comparison of Methods. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 241–245. Coconut Creek (Florida), ISSN 0749-0208.Understanding the influence of waves on bed shear stress is critical for predicting morphodynamical behaviours in coastal areas. Near-bed flow was measured on the middle and lower intertidal mudflats along the Jiangsu coast, China, using a three-dimensional acoustic velocimeter that collected a 3.5-cm vertical profile at 1mm resolution and sample rate of 25 Hz. On the lower and middle tidal flats, velocities from ~2.5–6 cmab (cm above bed) and ~0–3 cmab were measured, respectively. Current-induced bed shear stresses were calculated from turbulent kinetic energy (TKE) at the 11th measurement layer (i.e., 5.1 cm below the probe) using wave-turbulence decomposition and from a logarithmic fit to the horizontal mean velocity profile (LP). A wave boundary layer extended from the bed up to 3 cmab when the significant wave height was 0.23 m; when it was present the near-bed mean velocity profile was non-logarithmic. Waves suppress the development of a vertical velocity gradient and lead to an overestimation of bed shear stress when calculated using the log profile assumption. The TKE method is more accurate than the LP method when waves are present and measurements are at least partially within the wave boundary layer. Accurate calculation of current-induced bed shear stress depends on probe height and wave conditions.

The Incipient Motion Features of Sediment from Yangtze Estuary: Annular Flume Experiments

In this study, annular flume experiments are carried out, using the sediment samples collected from Yangtze estuary. The incipient velocity and the incipient shear stress of three different groups of median grain size of sediment are given. The turbulent kinetic energy method (TKE) is used to determine the bed shear stress (τ), by evaluating variations in the suspended sediment concentration (SSC) within the water column. The suspended sediment concentration increases with the increase of the bed shear stress. When the sediment concentration reaches a certain concentration, the rate of change in τ obviously slows down. As the concentration increasing again, the bed shear stress grows rapidly with different growth rate attributed to different grain size. The results of the experiments indicate that SSC and grain size have strong influence on τ.

Examining the Generality of τ0/TKE for Gravel and Cobble Beds with Sand Fill

AbstractTurbulence measurements over rough beds are used for a variety of purposes, including studies of habitat diversity for aquatic organisms, stream restoration efforts, and assessment of drag induced by vegetation. Turbulent kinetic energy (TKE) has been used to estimate bed shear stress by use of a proportionality constant of 0.19–0.21. The TKE method of bed shear stress estimation is less sensitive to flow misalignment relative to Reynolds stress or mean velocity measurements, but it has not been tested across a broad range of hydraulic conditions. In the work reported here, TKE was compared to bed shear stresses for gravel (D50=35 mm) and cobble (D50=156 mm) beds with varying discharges and levels of sand fill (D50=0.3 mm). The ratio of bed shear stress (τ0) with TKE was not strongly affected by mean velocity for either the gravel or cobble beds, but it was affected by bed roughness. The mean of the median values of τ0/TKE across three mean velocities was 0.24 for gravel with no sand in the bed...

Near‐bed shear stress, turbulence production and dissipation in a shallow and narrow tidal channel

AbstractNear‐bed, highly resolved velocity profiles were measured in the lower 0.03 m of the water column using acoustic Doppler profiling velocimeters in narrow tidal channels in a salt marsh. The bed shear stress was estimated from the velocity profiles using three methods: the log‐law, Reynolds stress, and shear stress derived from the turbulent kinetic energy (TKE). Bed shear stresses were largest during ebbing tide, while near‐bed velocities were larger during flooding tide. The Reynolds stress and TKE method gave similar results, while the log‐law method resulted in smaller bed shear stress values during ebbing tide. Shear stresses and turbulent kinetic energy followed a similar trend with the largest peaks during ebbing tide. The maximum turbulent kinetic energy was on the order of 1 × 10− 2 m2/s2. The fluid shear stress during flooding tide was approximately 30% of the fluid shear stress during ebbing tide. The maximum TKE‐derived shear stress was 0.7 N/m2 and 2.7 N/m2 during flooding and ebbing tide, respectively, and occurred around 0.02 m above the bed. Turbulence dissipation was estimated using the frequency spectrum and structure function methods. Turbulence dissipation estimates from both methods were maximum near the bed (~0.01 m). Both the structure function and the frequency spectrum methods resulted in maximum dissipation estimates on the order of 4 × 10− 3 m2/s3. Turbulence production exceeded turbulence dissipation at every phase of the tide, suggesting that advection and vertical diffusion are not negligible. However, turbulence production and dissipation were within a factor of 2 for 77% of the estimates. The turbulence production and dissipation decreased quickly away from the bed, suggesting that measurements higher in the water column cannot be translated directly to turbulence production and dissipation estimates near the bed. Copyright © 2015 John Wiley & Sons, Ltd.

Interaction between flow hydrodynamics and bed roughness in alluvial channel

The present study describes the methods of bed shear stress estimation, numerical estimate of velocity distribution and quadrant events on different hydraulic roughness. Quadrant events of velocity signify the contribution of velocity to generate shear. Experimental data sets of velocities were collected over bed with different hydraulic roughness. In the present work, a turbulent kinetic energy method is anticipated as more reliable to describe the bed shear stress in open channels. These data analysis express that the quadrant events associated with flow is influenced inherently by the bed roughness. Percentage distribution of first and fourth quadrant looks like a wine cup which is wider in the case of hydraulically smooth conditions and getting narrower as the bed roughness increased. It is also a sign of increasing randomness throughout the depth with increased roughness. It is found that at same relative depth for three different roughness conditions, eddy motions are displaying more uncertainty for hydraulically rough condition. Increase in bed roughness augments randomness of Reynolds stress at relative depth 0.05–0.4. The analysis relies on relative depth, which can for imply the local phenomenon and this local phenomenon of velocity on different bed roughness condition was also investigated in this paper.

Wind‐driven nearshore sediment resuspension in a deep lake during winter

AbstractOngoing public concern over declining water quality at Lake Tahoe, California‐Nevada (USA) led to an investigation of wind‐driven nearshore sediment resuspension that combined field measurements and modeling. Field data included: wind speed and direction, vertical profiles of water temperature and currents, nearbed velocity, lakebed sediment characteristics, and suspended sediment concentration and particle size distribution. Bottom shear stress was computed from ADV‐measured nearbed velocity data, adapting a turbulent kinetic energy method to lakes, and partitioned according to its contributions attributed to wind‐waves, mean currents, and random motions. When the total shear stress exceeded the critical shear stress, the contribution to overall shear stress was about 80% from wind‐waves and 10% each from mean currents and random motions. Therefore, wind‐waves were the dominant mechanism resulting in sediment resuspension as corroborated by simultaneous increases in shear stress and total measured sediment concentration. The wind‐wave model STWAVE was successfully modified to simulate wind‐wave‐induced sediment resuspension for viscous‐dominated flow typical in lakes. Previous lake applications of STWAVE have been limited to special instances of fully turbulent flow. To address the validity of expressions for sediment resuspension in lakes, sediment entrainment rates were found to be well represented by a modified 1991 García and Parker formula. Last, in situ measurements of suspended sediment concentration and particle size distribution revealed that the predominance of fine particles (by particle count) that most negatively impact clarity was unchanged by wind‐related sediment resuspension. Therefore, we cannot assume that wind‐driven sediment resuspension contributes to Lake Tahoe's declining nearshore clarity.

Estimating Turbulence and Shear Stress under Regular Waves from ADV Data

The boundary layer flow determines the bottom shear stresses, which is key point for sediment transport and thereby the evolution of coastal morphology. The structure of the bottom boundary layer in coastal seas has been of interest to oceanographers for many years. In the paper Acoustic Doppler velocimeter (ADV) technique is applied to measure the bottom boundary layer under cnoidal waves in a laboratory flume with 40-m-long, 0.5-m-wide, and 0.8-m-deep.. Based on the high frequency turbulence signal collected, statistic parameters of cnoidal wave flow are calculated, compared and analyzed. The turbulent structure over plain bed and sand ripples bed are carefully studied. The turbulence intensity of near-bed velocities changes along depth of several phases in a period is analyzed. Turbulent Kinetic Energy Method (TKE Method) is used to estimate near-bed shear stress on flat and slope.

Measurement of critical shear stress for mud mixtures in the San Jacinto estuary under different wave and current combinations

In situ measurements of the critical shear stress for the onset of erosion were made at three sites in the shallow, microtidal San Jacinto estuary under different hydrodynamic conditions. Sediment at the three sites was composed of a mixture of sand, silt, and clay with the total silt and clay fraction ranging from 45% to 95% of the total mixtures. The measurements were made by deploying an acoustic Doppler velocimeter over a tide cycle to measure mean and turbulent velocity as well as suspended sediment concentration and significant changes in boundary elevation. Six different techniques were used to convert velocity time series to bed shear stress time series. Two of the sites yielded estimates of the critical shear stress condition for erosion of 0.14N/m2 and 0.06N/m2 respectively (which correspond to a Shield's stress value of 0.1), but values were not found in the lowest energy environment. The hydraulics of the region are such that flood currents produce the highest shear stresses and therefore the largest degree of erosion. Deposition largely occurs over the lengthy high-water condition. All six methods for estimating the bed shear stress showed general trend correlation, however, significant variation in the estimated magnitude of the bed shear stress was observed among the methods. Based on theoretical considerations and analysis of the data, it was found that the logarithmic profile method performed best in current dominated regions and that the modified turbulent kinetic energy method performed best in the wave dominated zone.

Turbulence based measurements of wave friction factors under irregular waves on a gravel bed

Very few studies have quantified the wave friction factor, fw, for coarse sediments at field-scale. To address this shortcoming, high-frequency measurements of turbulence obtained within the boundary layer of irregular waves over gravel in the Delta Flume, have been used to calculate values of fw using different evaluation methods. In the field-scale laboratory experiments reported here, three velocimeters were deployed on the seaward side of a 4m-high, 5m-wide and 55m-long gravel barrier subject to a JONSWAP spectrum of waves with significant wave heights ranging from 0.8m to 1.3m, and peak periods of 3.0s to 10s and offshore water depths ranging from 1.75m to 3.75m. The deployment area was essentially flat, with little or no predicted or observed sediment movement under the wave conditions investigated. The turbulent kinetic energy method was found to be the most suitable approach for calculating the bed shear stress, which can be related to fw. Wave friction factor values under the conditions tested here fell in the range 0.01 and 0.27. Although fw predicted by an existing equation agrees well with the mean measured fw value, the application of a new predictor for fw is recommended for improved parameterisation of skin friction over the range of relative roughness values encountered in this study. This approach combines the wave Reynolds number, wave steepness and relative depth to provide a simple expression to assist assessments of coarse sediment transport by waves for uses within a range of practical engineering applications.

Comparison of three different methods for assessing in situ friction velocity: A case study from Loch Etive, Scotland

Three approaches, Eddy Correlation (EC), Turbulent Kinetic Energy (TKE), and Inertial Dissipation (ID) methods, were compared to evaluate their potential for estimation of friction velocity in a Scottish sea loch. As an independent assessment parameter, we used simultaneous O2 recordings of the diffusive boundary layer (DBL) that were compared with theoretical distribution as derived from the respective friction velocity estimates. Friction velocities were calculated based on the three approaches using continuously measured turbulent properties, and values estimated by the TKE method were significantly higher than values of the two other approaches. Time series of calculated friction velocity were subsequently employed as input parameters for nonsteady calculations of the O2 distribution within the DBL. The friction velocity is a controlling factor for the eddy diffusivity distribution immediately above the sediment surface and for the DBL thickness, and friction velocity values of the TKE method derived significantly higher theoretical O2 concentration while the EC and the ID approach provided results that were not significantly different. Overall differences from measured O2 concentration in the DBL were 0.2% for the EC method, 9.8% for the TKE method, and 0.7% for the ID method. The results reveal that the EC method appear to be the best approach for estimating friction velocities though not significantly different from the ID method, whereas the TKE method was unreliable at the ~70 m deep, relatively calm study site. This information is important for future research in similar sounds, fjords, and sea‐lochs.

A Case Study on Shear Velocity Estimation in a Protected Coastal Region

Three approaches; eddy-correlation (EC), turbulent kinetic energy (TKE), and inertial dissipation (ID) methods were compared to evaluate their potential for estimation of shear velocity in a protected coastal region. As an independent assessment parameter we used simultaneous oxygen recordings in the vicinity of the sediment-water interface that were compared with theoretical distribution as derived from the respective shear velocity estimates. Overall differences from measured oxygen concentration were 0.2% for EC method, 9.8% for TKE method, and 0.7% and 4.6% for ID method using vertical and longitudinal velocity components, respectively. The results revealed that the EC method appeared to be the best approach though not significantly different from the ID method using vertical velocity component at the study site.

A simulation study of short-range atmospheric dispersion for hypothetical air-borne effluent releases using different turbulent diffusion methods

Radiological impact due to hypothetical air-borne effluent releases for an upcoming fast reactor (PFBR), at a tropical coastal site in Kalpakkam is studied using the HYSPLIT dispersion model. Short range air dispersion simulations are conducted with HYSPLIT for a weakly forced synoptic condition on 3rd March, 2008 with three turbulent diffusion methods, i.e., standard velocity deformation (A), short range isotropic similarity (B) and turbulent kinetic energy (TKE) (C) schemes to assess their performance in predicting the dose distribution at a local scale. The time varying 3-d meteorological parameters for the case study are predicted using a nested grid meso-scale dynamical atmospheric model MM5. Results indicate that the velocity deformation method gives spatially more complex dose pattern while the short-range similarity and TKE methods provide smoother horizontal dose profiles. The downwind dose in different pathways due to elevated releases is found to be the highest for the method A followed by B and C. For the ground releases, the TKE method produced higher doses than the other two. The difference in the dose values from the three methods is due to the variation in the horizontal and vertical mixing calculation and the assumptions involved in the respective methods. The total dose at the site boundary from different pathways is highest from the TKE method. Values from all the methods are about one to two orders less than the values given by a Gaussian Plume model for similar atmospheric conditions. The total dose estimated from the TKE method is 20.62 mSv at the release location and 1.25 mSv at the site boundary.