Turbulent Kinetic Energy Dissipation Rate Research Articles

A snapshot of turbulence in the Northeastern Magellan Strait

AbstractFirst-ever measurements of the turbulent kinetic energy (TKE) dissipation rate in the northeastern Strait of Magellan (Segunda Angostura region) taken in March 2019 are reported here. At the time of microstructure measurements, the magnitude of the reversing tidal current ranged between 0.8 and 1.2 ms−1. The probability distribution of the TKE dissipation rate in the water interior above the bottom boundary layer was lognormal with a high median value $${\varepsilon }_{med}^{MS}=1.2\times {10}^{-6}$$ ε med MS = 1.2 × 10 - 6 Wkg−1. Strong vertical shear, $$\left(1-2\right)\times {10}^{-2}$$ 1 - 2 × 10 - 2 s−1, in the weakly stratified water interior ensued a sub-critical gradient Richardson number $$Ri<{10}^{-1}-{10}^{-2}$$ R i < 10 - 1 - 10 - 2 . In the bottom boundary layer (BBL), the vertical shear and the TKE dissipation rate both decreased exponentially with the distance from the seafloor $$\xi$$ ξ , leading to a turbulent regime with an eddy viscosity $${K}_{M}\sim {10}^{-3}$$ K M ∼ 10 - 3 m2/s, which varied with time and location, while being independent of the vertical coordinate in the upper part of BBL (for $$\xi >\sim 2$$ ξ > ∼ 2 meters above the bottom).

Experimental study on the effect of circulating liquid velocity on bubble size distribution and turbulence characteristic in an external loop airlift reactor

AbstractThe influence of circulating liquid velocity on bubble size distribution (BSD) and turbulence characteristics of an external loop airlift reactor was studied in this paper. The instantaneous and time‐averaged velocity in the riser were studied using particle image velocimetry (PIV), and BSDs were measured by digital image analysis technique based on machine learning. Then turbulence kinetic energy (TKE) and energy dissipation rate (EDR) were calculated through the velocity field. The results indicate that as the circulating liquid velocity increased, the peak value of BSD rapidly decreased from nearly 6 mm to approximately 2 mm. The radial velocity of the liquid gradually decreased and changed direction, eventually increasing again. TKE first decreased and then increased. Compared with bubble flow with a BSD peak of 2–6 mm, bubble flow with a BSD peak of 2 mm had larger TKE. The radial movement of bubbles had great influence on the turbulence characteristics. This study demonstrates that selecting an appropriate circulating liquid velocity can reduce the diameter of bubbles while obtaining greater TKE, thereby improving the mass transfer and reaction efficiency in external loop airlift reactors (EL‐ALR).

Ecological inferences on invasive carp survival using hydrodynamics and egg drift models

Bighead carp (Hypophthalmichthys nobilis), silver carp (H. molitrix), black carp (Mylopharyngodon piceus), and grass carp (Ctenopharyngodon idella), are invasive species in North America. However, they hold significant economic importance as food sources in China. The drifting stage of carp eggs has received great attention because egg survival rate is strongly affected by river hydrodynamics. In this study, we explored egg-drift dynamics using computational fluid dynamics (CFD) models to infer potential egg settling zones based on mechanistic criteria from simulated turbulence in the Lower Missouri River. Using an 8-km reach, we simulated flow characteristics with four different discharges, representing 45–3% daily flow exceedance. The CFD results elucidate the highly heterogeneous spatial distribution of flow velocity, flow depth, turbulence kinetic energy (TKE), and the dissipation rate of TKE. The river hydrodynamics were used to determine potential egg settling zones using criteria based on shear velocity, vertical turbulence intensity, and Rouse number. Importantly, we examined the difference between hydrodynamic-inferred settling zones and settling zones predicted using an egg-drift transport model. The results indicate that hydrodynamic inference is useful in determining the ‘potential’ of egg settling, however, egg drifting paths should be taken into account to improve prediction. Our simulation results also indicate that the river turbulence does not surpass the laboratory-identified threshold to pose a threat to carp eggs.

CFD simulation and experimental study of CO2 absorption in a rotating packed bed

The rotating packed bed (RPB), a process intensification equipment, has been widely studied and applied to chemical engineering processes such as gas absorption, nanomaterial preparation, and polymer devolatilization. In this study, we presented a typical RPB model to study the intensification mechanism of high gravity on gas-liquid mass transfer. Based on this, three-dimensional computational fluid dynamics (CFD) simulations and experiments of CO2 physical absorption were conducted to investigate the gas-liquid mass transfer characteristics in the RPB. The predicted and experimental values of CO2 saturation rates of the liquid phase showed good agreement, and the errors were within ± 15 % under various operating conditions. Moreover, detailed flow field and mass transfer information that are difficult to measure experimentally, such as the distribution of CO2 mass fraction in the liquid, liquid holdup, turbulent kinetic energy dissipation rate, and gas-liquid interfacial area, were analyzed by CFD simulation results. These results provide a solid foundation for the further development and application of RPB.

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

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

Prandtl number effects on extreme mixing events in forced stratified turbulence

Relatively strongly stratified turbulent flows tend to self-organise into a ‘layered anisotropic stratified turbulence’ (LAST) regime, characterised by relatively deep and well-mixed density ‘layers’ separated by relatively thin ‘interfaces’ of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study LAST mixing, as it is associated with Reynolds numbers $Re := UL/\nu \gg 1$ and Froude numbers $Fr :=(2{\rm \pi} U)/(L N) \ll 1$ ( $U$ and $L$ being characteristic velocity and length scales, $\nu$ the kinematic viscosity and $N$ the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number $Re_{b} := \epsilon /(\nu N^{2}) \gg 1$ , where $\epsilon$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := \nu /\kappa = {O}(10)$ in thermally stratified water (where $\kappa$ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ( $Fr=0.5, 2$ ) and Prandtl ( $Pr=1, 7$ ) numbers forced so that $Re_{b}=50$ , with resolutions up to $30\,240 \times 30\,240 \times 3780$ . We find that, as $Pr$ increases, emergent ‘interfaces’ become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed ‘layers’. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance $\chi _0$ ) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$ .

Field observations of the wake from a full-scale tidal turbine array

Wake measurements are critical for quantifying the hydrodynamic effects of tidal energy extraction and for designing arrays of tidal turbines. In this investigation field measurements from the wake of PLAT-I, a commercial-scale floating array of four tidal turbines, are presented. Instrumented surface-following drifters are used to measure velocity and turbulence in the wake of PLAT-I while deployed in Grand Passage, an energetic tidal channel in the Bay of Fundy, NS, Canada. Field measurements were obtained when the turbines where fully operational under optimal conditions during spring tides. The collected data are used to construct tridimensional maps of acoustic backscatter, mean velocity, vertical velocity variance and turbulent kinetic energy dissipation rate downstream of the platform at different stages of the tide. The operational turbine array wake was captured for ebb and flood tides. For both ebb and flood, reduced velocities are observed in the upper water column at the depths spanned by the turbine rotors. Vertical profiles of velocity mix quickly during flood tide but velocities remain slower than the undisturbed flow outside of the wake up to 20 effective diameters downstream of the platform. In contrast, during ebb, the velocity deficit persists farther downstream, and the reduced velocity increases slightly. Elevated turbulence levels peak at 2 effective diameters downstream of the turbines and recover to undisturbed flow levels at approximately 10 effective diameters downstream of the platform for both ebb and flood tides. Total energy dissipated through turbulence within the wake is estimated to be less than 10% of the energy extracted for electricity production.

Climatology of turbulent kinetic energy dissipation rate in the middle troposphere using the 205 MHz S–T radar at Kochi, India

Turbulent kinetic energy dissipation rate (ɛ) in the mid-troposphere (5–12 km) using data obtained from the S–T wind profiler radar located at Kochi (10.04°N, 76.33°E) is analyzed for a period of 1595 days, ranging from March 2017 to December 2022, at a vertical resolution of 180 m. The spectral width method was employed for the estimation of ɛ after initial data filtering, and corrections for beam and shear broadening. Monthly variations in ɛ exhibited a marginal decrease with height. The background wind conditions, such as horizontal wind speed, vertical shear of horizontal wind, and wind direction, have minimal impact vertically. It is found that turbulence is more significantly affected by wind speed and wind direction. Westerly winds, despite being infrequent in the mid-troposphere, emerged as the primary contributors to elevated turbulence values. This observation was attributed to the unique topographical characteristics, creating an interplay of land–sea contrast and orography, leading to enhanced turbulence during westerly winds. During the monsoon season, enhanced turbulence is observed throughout the altitude. The presence of the tropical easterly jet was identified as a significant contributor to the increased wind speed and shear observed during the monsoon season and this alignment correlates with an increase in turbulence.

Energetic Stratified Turbulence Generated by Kuroshio–Seamount Interactions in Tokara Strait

Abstract Generating mechanisms and parameterizations for enhanced turbulence in the wake of a seamount in the path of the Kuroshio are investigated. Full-depth profiles of finescale temperature, salinity, horizontal velocity, and microscale thermal-variance dissipation rate up- and downstream of the ∼10-km-wide seamount were measured with EM-APEX profiling floats and ADCP moorings. Energetic turbulent kinetic energy dissipation rates and diapycnal diffusivities above the seamount flanks extend at least 20 km downstream. This extended turbulent wake length is inconsistent with isotropic turbulence, which is expected to decay in less than 100 m based on turbulence decay time of N−1 ∼ 100 s and the 0.5 m s−1 Kuroshio flow speed. Thus, the turbulent wake must be maintained by continuous replenishment which might arise from (i) nonlinear instability of a marginally unstable vortex wake, (ii) anisotropic stratified turbulence with expected downstream decay scales of 10–100 km, and/or (iii) lee-wave critical-layer trapping at the base of the Kuroshio. Three turbulence parameterizations operating on different scales, (i) finescale, (ii) large-eddy, and (iii) reduced-shear, are tested. Average ε vertical profiles are well reproduced by all three parameterizations. Vertical wavenumber spectra for shear and strain are saturated over 10–100 m vertical wavelengths comparable to water depth with spectral levels independent of ε and spectral slopes of −1, indicating that the wake flows are strongly nonlinear. In contrast, vertical divergence spectral levels increase with ε.

Estimating the turbulent kinetic energy dissipation rate from one-dimensional velocity measurements in time

Abstract. The turbulent kinetic energy dissipation rate is one of the most important quantities characterizing turbulence. Experimental studies of a turbulent flow in terms of the energy dissipation rate often rely on one-dimensional measurements of the flow velocity fluctuations in time. In this work, we first use direct numerical simulation of stationary homogeneous isotropic turbulence at Taylor-scale Reynolds numbers 74≤Rλ≤321 to evaluate different methods for inferring the energy dissipation rate from one-dimensional velocity time records. We systematically investigate the influence of the finite turbulence intensity and the misalignment between the mean flow direction and the measurement probe, and we derive analytical expressions for the errors associated with these parameters. We further investigate how statistical averaging for different time windows affects the results as a function of Rλ. The results are then combined with Max Planck Variable Density Turbulence Tunnel hot-wire measurements at 147≤Rλ≤5864 to investigate flow conditions similar to those in the atmospheric boundary layer. Finally, practical guidelines for estimating the energy dissipation rate from one-dimensional atmospheric velocity records are given.

An experimental study of localized flow pattern, strain rate and turbulence kinetic energy dissipation rate of in-line teethed high shear mixer with different rotor and stator structures

The in-line teethed high shear mixers (HSMs) have been widely used in the chemical industry. However, there is still a lack of comprehensive understanding of the hydrodynamics characteristics about the attractive process equipment. In this paper, the effects of rotor and stator structures and rotor speed on flow characteristics of in-line teethed HSM are systematically studied by the particle image velocimetry experiment for the first time. The results show that increasing the rotor speed can significantly increase the strain rate (Sxy) and turbulence kinetic energy dissipation rate (ε). Especially, when the shear gap width is reduced from 1.5 mm to 0.5 mm, the mean ε increases by 96.8 %. Furthermore, two dimensionless correlations are established between the maximum value of the Sxy, ε and rotor and stator geometrical parameters to provide a valuable guidance for the geometrical design and optimization of in-line teethed HSM.

Mixing of North Pacific water masses in the Bali Sea

As part of the Indonesian Throughflow (ITF) from western route, water masses in the Bali Sea are fed by North Pacific water masses. We examined the mixing strength in the Bali Sea which contributes to reducing the core layer S-max of the North Pacific Subtropical Water (NPSW) from 34. 8 – 35 psu in the source region to 34.5 psu in the Bali Sea. Using Thorpe method, we found the mixing strength in the Bali Sea is relatively low. The turbulent kinetic energy dissipation rate (ɛ) of O( 10-11 - 10-6 ) WKg-1 and density turbulent diffusivity (Kρ) are O (10-5 10-3) m-2s-1 were similar to typical open ocean values. However, mixing in the eastern region of the Bali Sea is relatively stronger than in the western region. Based on the critical Ri #, we found the Thorpe scale (LT) under Ri# < 0.25 in the eastern region, which is contrary to other parts. It indicated the turbulent mixing was dominantly caused by shear instability. Shear from the strong outflow of ITF towards the Lombok Strait and the reversal northward current in the lower layer forces a strong turbulent layer.

Dynamic characteristics of two-vent submarine hydrothermal plumes: A case study of Longqi hydrothermal field

Submarine hydrothermal plumes play an important role in the process of material and energy exchange in the deep sea. Due to the influence of complex environmental factors (multiple vents, deep-sea stratified environment) and the limitation of observation capabilities, the dynamic characteristics of submarine hydrothermal plumes have not been fully understood, and it is urgent to study the diffusion and evolution process of submarine hydrothermal plumes by the computational fluid dynamics (CFD) model. In this paper, a CFD model was established to effectively simulate the diffusion and evolution process of two-vent submarine hydrothermal plumes under the deep-sea stratified environment, obtained the three-dimensional plume flow field structure of two-vent submarine hydrothermal plumes, and obtained the spatial distribution of dynamic characteristics parameters such as velocity, turbulent viscosity, turbulent kinetic energy and turbulence dissipation rate of two-vent submarine hydrothermal plumes. The equations for calculating the maximum plume rise height and the neutrally buoyant plume height of a two-vent submarine hydrothermal plume were deduced and established. In addition, a comparative analysis of the single-vent submarine hydrothermal plume revealed the mechanism of the influence of the key characteristics of the two-vent submarine hydrothermal plumes such as the maximum plume rise height. It was applied to analyze the dynamic characteristics of the plume occurred in Longqi hydrothermal field in the southwest Indian Ocean, and the results were verified by the field observation data. The spatial distribution of mass concentration of hydrothermal plume particles was further analyzed, and the difference of mass concentration in different hydrothermal plume structures was compared to study the exchange mechanism of material and energy between submarine hydrothermal plume and surrounding seawater. The results are of guiding significance for the tracing of submarine hydrothermal vents, the study of marine material exchange and energy transport processes, and the exploration and environmental evaluation of submarine polymetallic sulfide resources.

Solid-liquid mixing characteristics in a fractal cut impeller stirred reactor with dense solid loading

The fractal cut impeller (FC impeller) based on fractal iteration of “H” pattern cuts on the impeller blades was introduced in the solid-liquid system with dense solid loading. The solid-liquid mixing characteristics in a stirred tank with pitched blade impeller (PB impeller) and FC impeller were comparatively investigated with experiment and numerical simulation. Results showed that FC impeller exhibited lower power consumption (P) and power number (Np) compared to PB impeller at the same impeller speed. It could be also observed that increasing the fractal iteration number of FC impeller led to a further decrease in P and Np. Meanwhile, FC impeller could reduce the size of impeller tailing vortex, enhance turbulent intensity and turbulent kinetic energy dissipation rate, and improve solid particle suspension quality compared to PB impeller under the constant power consumption, and an increase in fractal iteration number of FC impeller resulted in higher solid particle suspension efficiency. In addition, it was also found that the fractal arrangement of cuts on the impeller blades could increase turbulent intensity, enhance turbulent kinetic energy dissipation rate and facilitate an improvement in solid particle suspension quality as compared to a whole cut on the impeller blades with equal cut area.

Vertical Mixing in The Onshore Region of The Northwestern Maluku Sea, Indonesia

Spatio-temporal dynamics of vertical mixing in the northwestern Maluku Sea were quantified using the Thorpe Method from archived CTD datasets collected during the expedition of Baruna Jaya VIII RCO-LIPI on November 12–13, 2000. The turbulent kinetic energy (TKE) dissipation rate and vertical eddy diffusivity values inspected the variability of mixing properties. Higher values for both parameters were found at the shallower bathymetry, which is less than 1000 m deep. This suggests that the water column is vertically unstable as a result of being often subjected to internal solitary wave (ISW) breaking events. The strong temporal variability observed from the density profile also indicated a strong impact on internal tide activity. There was temporal fluctuation of the TKE dissipation rate as well as vertical eddy diffusivity values following semidiurnal periodicity, with typical variability up to one order of magnitude for both the dissipation and diffusivity. The range of fluctuation is [6.8×10-8 ? 9.3×10-7] W kg-1 and [1.5×10-5 – 5.4×10-3] m2s-1, respectively in the upper 200 m depth. This water generated a high dissipation rate and vertical diffusivity when regularly exposed to internal solitary waves breaking from the Lifamatola Passage.Keywords: mixing properties, CTD data, turbulent kinetic energy, vertical eddy diffusivity

A tri-point correlation method for ocean current estimation and its applications in near-bottom turbulent mixing on the shelf of the Northern South China Sea

We propose a tri-point correlation method to estimate ocean currents using moored temperature observation data. The transit time for two time series of temperature is determined with the cross correlation technique, enabling the formulations of an equation system to determine the current speed and angle. To validate our method, we utilize a high-resolution temperature dataset collected at the shelf bottom of the northern South China Sea and compare the inferred currents with direct measurement results with a current meter. The results demonstrate a high level of agreement between the inferred currents and the directly measured ones. Using this temperature dataset and the synchronously inferred currents, we further estimate near-bottom turbulent mixing, including diapycnal mixing and vertical heat flux. During the observation period, the mean values of the turbulent kinetic energy dissipation rate, turbulent diffusivity, and vertical heat flux are 3.8×10−8 m2/s3,  2.6×10−4 m2/s, and 10.0 W/m2, respectively. These inferred turbulent mixing quantities exhibit a positive correlation with the dynamics of internal waves.

Mixing Processes at the Southwestern Entrance to the Japan/East Sea

Abstract Small-scale processes at the southwestern boundary of the Ulleung Basin (UB) in the Japan/East Sea (JES) were examined using combined ship-based and moored observations along with model output. Model results show baroclinic semidiurnal tides are generated at the shelf break and corresponding slope connecting the Korea/Tsushima Strait with the UB and propagate into the UB with large barotropic-to-baroclinic energy conversion over the slope. Observations show high-frequency internal wave packets and indicate strong velocity shear and energetic turbulence associated with baroclinic tides in the stratified bottom layer. Solitary-like waves with frequencies from 0.2N to 0.5N (buoyancy frequency N) were found at the edge of the shelf break with supercritical flow. For subcritical flow, a hydraulic jump formed over the shelf break with weakly dispersive internal lee waves with frequencies varying from 0.5N to N. These high-frequency lee waves were trapped in the stratified bottom layer, with wave stress similar to the turbulent stress near the bottom. The power loss due to turbulent bottom drag can be an important factor for energy loss associated with the hydraulic jump. Turbulent kinetic energy dissipation rates of ∼10−4 W kg−1 were found. Large downward heat and salt fluxes below the high-salinity core mix warm/salty Tsushima Current Water with cold/low-salinity JES Intermediate Water. Mixing over the shelf break could be very important to the JES circulation since the calculated diapycnal upwelling (1–6 m day−1) at the shelf break and slope is substantially greater than the basin-averaged estimate from chemical tracers and modeling studies. Significant Statement The Japan/East Sea (JES) is a marginal sea, enclosed by Japan, Korea, and Russia. This study describes mixing processes over the shelf break connecting the northern Korea/Tsushima Strait (KTS) with the southern Ulleung Basin (UB), where the warm, high-salinity Kuroshio water carried by the Tsushima Current interacts with southward-flowing subsurface water masses in the JES. Our analysis suggests that the shelf break and slope between the KTS and the UB are vital areas for water-mass exchange in the southern JES. The enhanced mixing at the shelf break may impact water masses and circulation over the entire JES.

Can IR Images of the Water Surface Be Used to Quantify the Energy Spectrum and the Turbulent Kinetic Energy Dissipation Rate?

Near-surface oceanic turbulence plays an important role in the exchange of mass, momentum, and energy between the atmosphere and the ocean. The climate modifying the air-sea CO2 transfer rate varies linearly with the surface turbulent kinetic energy dissipation rate to the 1/4 power in a range of systems with different types of forcing, such as coastal oceans, river estuaries, large tidal freshwater rivers, and oceans. In the first part of this paper, we present a numerical study of the near-surface turbulent kinetic energy spectra deduced from a direct numerical simulation (DNS) compared to turbulent kinetic energy spectra deduced from idealized infrared (IR) images. The DNS temperature fields served as a surrogate for IR images from which we have calculated the underlying kinetic energy spectra. Despite the near-surface flow region being highly anisotropic, we demonstrated that modeled isotropic and homogeneous turbulence spectra can serve as an approximation to observed near-surface spectra within the inertial and dissipation ranges. The second part of this paper validates our numerical observations in a laboratory experiment. In this experiment, we compared the turbulent kinetic energy spectra near the surface, as measured using a submerged shear sensor with the spectra derived from infrared images collected from above the surface. The energy dissipation measured by the shear sensor was found to be within 20% of the dissipation value derived from the IR images. Numerically and experimentally, we have demonstrated that IR-based and remote measurement techniques of the aquatic near surface offer a potentially accurate and non-invasive way to measure near-surface turbulence, which is needed by the community to improve models of oceanic air-sea heat, momentum, and gas fluxes.

Statistical assessment of a Doppler radar model of TKE dissipation rate for low Richardson numbers

Abstract. The potential ability of VHF or UHF Doppler radars to measure turbulence kinetic energy (TKE) dissipation rate ε in the atmosphere is a major asset of these instruments because of the possibility to continuously monitor turbulence in the atmospheric column above the radars. Several models have been proposed over the past decades to relate ε to half the Doppler spectral width σ, corrected for non-turbulent contributions, but their relevance remains unclear. Recently, Luce et al. (2023) tested the performance of a new model expected to be valid for weakly stratified or strongly sheared conditions, i.e., for low Richardson (Ri) numbers. Its simplest expression is εS=CSσ2S, where CS∼0.64 and S=|dV/dz| is the vertical shear of the horizontal wind V. We assessed the relevance of this model with a UHF (1.357 GHz) wind profiler called WPR LQ-7, which is routinely operated at the Shigaraki Middle and Upper Atmosphere (MU) observatory (34.85∘ N, 136.10∘ E) in Japan. For this purpose, we selected turbulence events associated with Kelvin–Helmholtz (KH) billows, because their formation necessarily requires Ri<0.25 somewhere in the flow, a condition a priori favorable to the application of the model. Eleven years of WPR LQ-7 data were used for this objective. The assessment of εS was first based on its consistency with an empirical model εLout=σ3/Lout, where Lout has the dimension of an outer scale of turbulence. It was found to compare well in a KH layer with direct estimates of ε from in situ measurements for Lout≈70 m. Some degree of equivalence between εS and εLout was confirmed by statistical analysis of 192 KH layers found in the height range 0.3–5.0 km indicating that Lout≈LH/0.64, where LH=σ/S is the Hunt scale defined for neutral turbulence. The degree of equivalence is even significantly improved if Lout is not treated as a constant but depends on the depth D of the layer. We found Lout≈0.0875D or equivalently LH∼0.056D, which also means that σ is proportional to the apparent variation in the horizontal velocity (S×D) over the depth of the KH layer. Consequently, εS=0.64σ2S and εLout=σ3/0.0875D would express the same model for KH layers when Ri remains low. For such a condition, we provide a physical interpretation of εLout, which would be qualitatively identical to that for neutral boundary layers.

Three-Dimensional Numerical Analysis and Operational Optimization of High-Efficiency Sedimentation Tank

The high-efficiency sedimentation tank has a wide range of application prospects in industrial wastewater treatment due to its small footprint, strong resistance to shock loads, and high efficiency. However, the complex flow field distribution inside significantly affects the treatment performance of the high-efficiency tank. In this study, a three-dimensional geometric model of the high-efficiency sedimentation tank was constructed based on an engineering prototype. The corresponding solid–liquid two-phase, whole-process computational fluid dynamics (CFD) model for the high-efficiency sedimentation tank was established using the realizable k-ε turbulent model and the multiple reference frame (MRF) method. The internal structures of the flocculation zone, plug-flow zone, and clarification zone were optimized, and then the influence of operational process conditions on the flocculation treatment performance was investigated. The results indicate that, for the given engineering model, the average turbulent kinetic energy k in the flocculation zone exhibits a trend that initially increases and then decreases with the increase in the diameter and height of the draft tube. The optimal hydraulic conditions for the flocculation zone are achieved when the diameter of the draft tube is 2.5 m and the height is 3.5 m. The average turbulent kinetic energy dissipation rate in the plug-flow/clarification zone tends to decrease first and then increase as the height of the water tunnel and water-retaining weir increases. The optimal hydraulic conditions for the plug-flow and clarification zones are achieved when the height of the water tunnel is 1.0 m and the height of the water-retaining weir is 1.6 m. Under optimal operating conditions (dosage of dense media particles: 40 mg/L, stirring rate: 30 rpm, and inlet velocity: 0.72 m/s), satisfactory overall hydraulic conditions can be achieved throughout the entire high-efficiency sedimentation tank. Comparisons between a high-efficiency settling tank and a conventional clarifier for the treatment of circulating water sewage in a practical implementation reveals that the ballasted high-efficiency settling tank has advantages in terms of high hydraulic loading, high removal efficiency of hardness, small footprint, and low doses of flocculant. This research will provide reference values for the design and operation optimization of high-efficiency sedimentation tanks.