Turbulent Kinetic Energy Dissipation Research Articles

Oceanic turbulence parameters recognition based on convolutional neural network

The distortion induced by ocean turbulence has a substantial impact on the propagation of light in water, posing challenges for applications including underwater wireless optical communications and submarine surveys. Obtaining accurate information about the properties of oceanic turbulence (OT), particularly the parameters describing OT, is crucial for addressing these challenges and enhancing the performance of such applications. In this paper, we propose a convolutional neural network (CNN) and validate its ability to recognize OT parameters. The physical quantities of oceanic turbulence collectively influence the formation and strength of turbulence. We recognize the dissipation rate of temperature variance χ T and the turbulent kinetic energy dissipation rate ɛ, taking into account various balance parameter ω, transmission distance z. Furthermore, in order to simultaneously recognize χ T and ɛ, we enhanced the existing network by modifying the output structure, resulting in a dual-output architecture that facilitates concurrent classification of both χ T and ɛ. Our method for classifying turbulence parameters will contribute to the field of underwater wireless optical communication and promote its further development.

A snapshot of turbulence in the Northeastern Magellan Strait

First-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 εmedMS=1.2×10-6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varepsilon }_{med}^{MS}=1.2\ imes {10}^{-6}$$\\end{document} Wkg−1. Strong vertical shear, 1-2×10-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left(1-2\\right)\ imes {10}^{-2}$$\\end{document} s−1, in the weakly stratified water interior ensued a sub-critical gradient Richardson number Ri<10-1-10-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Ri<{10}^{-1}-{10}^{-2}$$\\end{document}. In the bottom boundary layer (BBL), the vertical shear and the TKE dissipation rate both decreased exponentially with the distance from the seafloor ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi$$\\end{document}, leading to a turbulent regime with an eddy viscosity KM∼10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${K}_{M}\\sim {10}^{-3}$$\\end{document} m2/s, which varied with time and location, while being independent of the vertical coordinate in the upper part of BBL (for ξ>∼2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi >\\sim 2$$\\end{document} meters above the bottom).

Investigation on the turbulent structures in combined wave-current boundary layers

The problem of turbulent vortices and vortex dynamics under the influence of ocean waves is a subject of continuing research in the field of wave-current interaction. Thus, this study investigates the evolution of turbulence structures and vortex interactions in combined wave-current boundary layers, where water waves propagate with currents. Experiments were performed in two glass-walled laboratory channels with water depths of 160 and 400 mm. A two-dimensional two-component (2D2C) Particle Image Velocimetry (PIV) system was used to measure the velocities. Periodic variations in turbulence are observed for combined wave-current flows. Pairs of counter-rotating vortices are identified in the outer region when the combined flow is reversed, leading to destructive vortex interactions. This process leads to a reduction in the turbulent kinetic energy (TKE) and TKE production and dissipation during the passage of the wave trough. A conceptual model of hairpin vortices in combined wave-current flows is proposed in this study. The results of this study provide novel insights into the hydrodynamics of combined wave-current flows.

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).

Wave and Roller Transformation Over Barred Bathymetry

AbstractThe cross‐shore transformation of breaking‐wave roller momentum and energy on observed barred surfzone bathymetry is investigated with a two‐phase Reynolds Averaged Navier Stokes model driven with measured incident waves. Modeled wave spectra, wave heights, and wave‐driven increases in the mean water level (setup) agree well with field observations along transects extending from 5‐m water depth to the shoreline. Consistent with prior results the roller forcing contributes 50%–60% to the setup, whereas the advective terms contribute ∼20%, with the contribution of bottom stress largest (up to 20%) for shallow sandbar crest depths. The model simulations suggest that an energy‐flux balance between wave dissipation, roller energy, and roller dissipation is accurate. However, as little as 70% of the modeled wave energy ultimately dissipated by breaking was first transferred from the wave to the roller. Furthermore, of the energy transferred to the roller, 15%–25% is dissipated by turbulence in the water column below the roller, with the majority of energy dissipated in the aerated region or near the roller‐surface interface. The contributions of turbulence to the momentum balance are sensitive to the parameterized turbulent anisotropy, which observations suggest increases with increasing turbulence intensity. Here, modeled turbulent kinetic energy dissipation decreases with increasing depth of the sandbar crest, possibly reflecting a change from plunging (on the steeper offshore slope of the bar) to spilling breakers (over the flatter bar crest and trough). Thus, using a variable roller front slope in the roller‐wave energy flux balance may account for these variations in breaker type.

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.

A Hybrid PIV/Optical Flow Method for Incompressible Turbulent Flows

We present novel velocimetry algorithms based on the hybridization of correlation-based Particle Image Velocimetry (PIV) and a combination of Lucas–Kanade and Liu–Shen optical flow (OpF) methods. An efficient Aparapi/OpenCL implementation of those methods is also provided in the accompanying open-source QuickLabPIV-ng tool enabled with a Graphical User Interface (GUI). Two different options of hybridization were developed and tested: OpF as a last step, after correlation-based PIV, and OpF as a substitute for sub-pixel interpolation. Hybridization increases the spatial resolution of PIV, enabling the characterization of small turbulent scales and the computation of key turbulence parameters such as the rate of dissipation of turbulent kinetic energy. The method was evaluated using both synthetic and real databases, representing flows that exhibit a variety of locally isotropic homogeneous turbulent scales. The proposed hybrid PIV-OpF results in a 3-fold increase in the PIV density for synthetic images. The analysis of power spectral density functions and auto-correlation demonstrated the impact of PIV image quality on the accuracy of the method and its ability to extend the turbulence range. We discuss the challenges posed by optical noise and tracer density in the quality of the vector map density.

Assessment of Laws of the Wall During Flame–Wall Interaction of Premixed Flames Within Turbulent Boundary Layers

The validity of the usual laws of the wall for Favre mean values of the streamwise velocity component and temperature for non-reacting flows has been assessed for turbulent premixed flame-wall interaction using Direct Numerical Simulation (DNS) data. Two different DNS databases corresponding to friction velocity-based Reynolds number of 110 and 180 representing unsteady head-on quenching of statistically planar flames within turbulent boundary layers have been considered. The usual log-law based expressions for the Favre mean values of the streamwise velocity and temperature for the inertial layer have been found to be inadequate at capturing the corresponding variations obtained from DNS data. The underlying assumptions of constant shear stress and the equilibrium of production and dissipation of turbulent kinetic energy underpinning the derivation of the usual log-law for the mean streamwise velocity have been found to be rendered invalid within the usual inertial layer during flame-wall interaction for both cases considered here. The heat flux does not remain constant within the usual inertial layer, and the turbulent flux of temperature exhibits counter-gradient transport within the so-called inertial layer for the cases considered in this work. These render the assumptions behind the derivation of the usual log-law for temperature to be invalid for application to turbulent flame-wall interaction. It has been found that previously proposed empirical modifications to the existing laws of the wall, which account for density and kinematic viscosity variations with temperature, do not significantly improve the agreement with the corresponding DNS data in the inertial layer and the inaccurate approximations for the kinematic viscosity compensated wall normal distance and the density compensated streamwise velocity component contribute to this disagreement. The DNS data has been utilised here to propose new expressions for the kinematic viscosity compensated wall normal distance and the density compensated streamwise velocity component, which upon using in the empirically modified law of wall expressions have been demonstrated to provide reasonable agreement with DNS data.

A simple analytical model for turbulent kinetic energy dissipation for self-similar round turbulent jets

This work presents a simple analytical model for the streamwise and radial variations of turbulent kinetic energy dissipation in an incompressible round turbulent jet. The key assumptions in the model are: similarity in the axial velocity profile with a Gaussian shape, axisymmetric flow and the dominance of radial derivatives of the mean velocity over axial direction derivatives (similar to boundary layer theory). Initially, a simplified eddy-viscosity relation for turbulent stresses is derived using the algebraic stress model by Gatski &amp; Speziale (J. Fluid Mech., vol. 254, 1993, pp. 59–78). Subsequently, with this eddy-viscosity relation, the relation for variations of turbulent kinetic energy dissipation is formulated using the conservation of turbulent kinetic energy. To extract the necessary constants of the model, experimental velocity statistics for round jets are obtained through particle image velocimetry measurements. The experimental results of the mean entrainment coefficient for turbulent jets are also analysed. When comparing the radial variation of turbulent kinetic energy dissipation from the model with experimental results at Reynolds number $1.4\times 10^5$ and numerical results at Reynolds number $1200$ from the available literature, we observe a maximum error of $10\,\%$ and $15\,\%$ , respectively. Finally, using the validated model, we analyse the impact of mean velocity evolution parameters on the behaviour of turbulent kinetic energy dissipation and discuss its potential significance in future studies.

A Combined Experimental and Turbulence-Resolved Modeling Approach for Aeroengine Turbine Rim Seals

Abstract Ingress is the penetration of hot mainstream gas into the rotor–stator wheel-space formed between adjacent disks; a rim seal is installed at the periphery of the wheel-space. Purge flow is bled from the compressor and re-introduced in the turbine to reduce, or in the limit prevent, ingress. This study presents a unique, concomitant experimental and turbulence-resolved numerical investigation of ingress in an aeroengine rim seal, with leakage flow. Experimental modeling is conducted in the University of Bath's 1-stage turbine test facility. Measurements of gas concentration, pressure and swirl were used to assess the performance of the rim seal. A parallel study using improved delayed detached eddy simulations (IDDES) was used to generate time-averaged and time-resolved flow-fields, enabling direct comparison with experimental data. The modeled geometry included realistic features typical of aeroengine architectures, including a contoured stator undershroud and an omega-seal cover plate. Such features were shown to locally distort the flow field, highlighting the limitation when modeling simplified geometry. The circumferential distribution of sealing effectiveness was nonaxisymmetric and synchronized in accordance with the local radial velocity field. Utilization of a detached eddy simulation (DES) turbulent kinetic energy (TKE) dissipation multiplier demonstrated regions where increased turbulence resolution was required to resolve the appropriate scale of turbulent eddies. IDDES computations were found to accurately capture the radial distributions of pressure, swirl and effectiveness, both in the absence and presence of a superposed leakage flow, provided that the mesh was sufficiently refined so as to resolve ≥50% of the energy cascade. The IDDES approach exhibited significantly superior agreement with experiments when compared to previous studies that employed the unsteady Reynolds-averaged Navier–Stokes (URANS) methodology.

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.

Analysis of open channel flow with various layered vegetation using CFD, considering different near-wall treatment methods

PurposeThe purpose of this paper is to investigate the impact of near-wall treatment approaches, which are crucial parameters in predicting the flow characteristics of open channels, and the influence of different vegetation covers in different layers.Design/methodology/approachAnsys Fluent, a computational fluid dynamics software, was used to calculate the flow and turbulence characteristics using a three-dimensional, turbulent (k-e realizable), incompressible and steady-flow assumption, along with various near-wall treatment approaches (standard, scalable, non-equilibrium and enhanced) in the vegetated channel. The numerical study was validated concerning an experimental study conducted in the existing literature.FindingsThe numerical model successfully predicted experimental results with relative error rates below 10%. It was determined that nonequilibrium wall functions exhibited the highest predictive success in experiment Run 1, standard wall functions in experiment Run 2 and enhanced wall treatments in experiment Run 3. This study has found that plant growth significantly alters open channel flow. In the contact zones, the velocities and the eddy viscosity are low, while in the free zones they are high. On the other hand, the turbulence kinetic energy and turbulence eddy dissipation are maximum at the solid–liquid interface, while they are minimum at free zones.Originality/valueThis is the first study, to the best of the author’s knowledge, concerning the performance of different near-wall treatment approaches on the prediction of vegetation-covered open channel flow characteristics. And this study provides valuable insights to improve the hydraulic performance of open-channel systems.

Profiling the molecular destruction rates of temperature and humidity as well as the turbulent kinetic energy dissipation in the convective boundary layer

Abstract. A simultaneous deployment of Doppler, temperature, and water-vapor lidars is able to provide profiles of molecular destruction rates and turbulent kinetic energy (TKE) dissipation in the convective boundary layer (CBL). Horizontal wind profiles and profiles of vertical wind, temperature, and moisture fluctuations are combined, and transversal temporal autocovariance functions (ACFs) are determined for deriving the dissipation and molecular destruction rates. These are fundamental loss terms in the TKE as well as the potential temperature and mixing ratio variance equations. These ACFs are fitted to their theoretical shapes and coefficients in the inertial subrange. Error bars are estimated by a propagation of noise errors. Sophisticated analyses of the ACFs are performed in order to choose the correct range of lags of the fits for fitting their theoretical shapes in the inertial subrange as well as for minimizing systematic errors due to temporal and spatial averaging and micro- and mesoscale circulations. We demonstrate that we achieve very consistent results of the derived profiles of turbulent variables regardless of whether 1 or 10 s time resolutions are used. We also show that the temporal and spatial length scales of the fluctuations in vertical wind, moisture, and potential temperature are similar with a spatial integral scale of ≈160 m at least in the mixed layer (ML). The profiles of the molecular destruction rates show a maximum in the interfacial layer (IL) and reach values of ϵm≃7×10-4 g2 kg−2 s−1 for mixing ratio and ϵθ≃1.6×10-3 K2 s−1 for potential temperature. In contrast, the maximum of the TKE dissipation is reached in the ML and amounts to ≃10-2 m2 s−3. We also demonstrate that the vertical wind ACF coefficient kw∝w′2‾ and the TKE dissipation ϵ∝w′2‾3/2. For the molecular destruction rates, we show that ϵm∝m′2‾w′2‾1/2 and ϵθ∝θ′2‾w′2‾1/2. These equations can be used for parameterizations of ϵ, ϵm, and ϵθ. All noise error bars are derived by error propagation and are small enough to compare the results with previous observations and large-eddy simulations. The results agree well with previous observations but show more detailed structures in the IL. Consequently, the synergy resulting from this new combination of active remote sensors enables the profiling of turbulent variables such as integral scales, variances, TKE dissipation, and the molecular destruction rates as well as deriving relationships between them. The results can be used for the parameterization of turbulent variables, TKE budget analyses, and the verification of large-eddy simulations.

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.

Classical and local similarity in problems of turbulent convection: Extension of Prandtl semi-empirical theory for horizontal layers of water and air mediums

A variant of the local similarity theory is considered, assuming a priori specification of two basic dimensional parameters: the second moment of vertical velocity and the “spectral” Prandtl mixing length. Such selection of basic parameters lets us interpret the algebraic formulas of Prandtl's semiempirical turbulence theory for the coefficients of turbulent heat transfer and kinetic energy dissipation as relationships of the local similarity theory. A priori approximations of the basic parameters are based on known relationships and consider the upper boundary of the convective layer as a solid wall. Within the framework of local similarity theory, approximations for the turbulent moments of buoyancy and vertical velocity of arbitrary order are also proposed. The correspondence of these approximations to experimental data has been established in both air and water mediums, as well as in the results of numerical modeling. Such correspondence allows us to conclude that a wide class of vertical profiles of turbulent moments in a windless convective layer depends only on two basic parameters: the second moment of vertical velocity and the “spectral” Prandtl mixing length. The obtained result indicates the universal nature of the theory of local similarity and is a significant addition to the semiempirical Prandtl theory.

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.