Estimates Of Dissipation Rate Research Articles

Correction to: Estimate of turbulent energy dissipation rate using free-fall and CTD-attached fast-response thermistors in weak ocean turbulence

Correction to: Estimate of turbulent energy dissipation rate using free-fall and CTD-attached fast-response thermistors in weak ocean turbulence

Turbulent kinetic energy dissipation rate in the lower troposphere using the 205 MHz radar at Kochi, India

The Stratosphere–Troposphere (S–T) radar at Kochi (10.04° N, 76.33° E), India is the first radar operating at 205 MHz. At this location, the atmospheric background parameters such as atmospheric wind, temperature, and humidity show distinct changes from monsoon to winter season in the lower atmosphere. The general wind patterns differ significantly during different seasons, giving rise to differences in the characteristics of atmospheric turbulence parameters. S–T radar estimates of the Turbulence Kinetic Energy dissipation rate (ɛ) from ∼0.35–5 km for 722 days (2017–2019) are presented in this study to explain the seasonal variability of turbulence in terms of the background atmospheric conditions. Doppler spectral width measurements made by the S–T Radar are utilized to estimate ɛ. Non-turbulent contributions to the spectral broadening are calculated and separated from the observed spectral width before estimating ɛ. Turbulence in the planetary boundary layer is stronger and it generally decreases with height. Turbulence is highest during the monsoon season and lowest during winter. Under strong wind conditions, turbulence is stronger, and it is highly variable under weak wind conditions. Stronger turbulence is observed during monsoon season and is associated with higher wind speeds.

Thermodynamically consistent strain hardening variable/driving force, inelastic stored energy and self-heating in dynamic plasticity

Accounting for self-heating and subsequent thermal softening in dynamic plasticity requires an accurate estimation of the mechanical dissipation rate which is by definition the difference between the plastic work rate and the inelastic stored energy rate. Yet, in constitutive modeling, the evaluation of the inelastic stored energy strongly depends on the adopted approach, viz. irreversible thermodynamics vs microstructure-motivated approach, and, whatever the approach, does not yet lead to realistic results in terms of self-heating. The aim of the present study is to attempt to conciliate both above mentioned approaches by building constitutive models that relate strain hardening, inelastic stored energy and self-heating in a consistent way. The models in question are developed in agreement with experimental results obtained on five high-strength steels.

Improved dissipation rate estimation method based on time-varying glide parameter analysis of underwater gliders

Improved dissipation rate estimation method based on time-varying glide parameter analysis of underwater gliders

Tidally Forced Turbulent Dissipation on a Three-Dimensional Fan in Luzon Strait

Abstract Moored observations and a realistic, tidally forced 3D model are presented of flow and internal-tide-driven turbulence over a supercritical 3D fan in southeastern Luzon Strait. Two stacked moored profilers, an acoustic Doppler current profiler, and a thermistor string measured horizontal velocity, density, and salinity over nearly the entire water column every 1.5 h for 50 days. Observed dissipation rate computed from Thorpe scales decays away from the bottom and shows a strong spring–neap cycle; observed depth-integrated dissipation rate scales as where UBT is the barotropic velocity. Vertical velocities are strong enough to be comparable at times to the vertical profiling speed of the moored profilers, requiring careful treatment to quantify bias in dissipation rate estimates. Observations and the model are in reasonable agreement for velocity, internal wave displacement and depth-integrated dissipation rate, allowing the model to be used to understand the 3D flow. Turbulence is maximum following the transition from up-fan to down-fan flow, consistent with breaking lee waves advected past the mooring as seen previously at the Hawaiian Ridge, but asymmetric flow arises because of the 3D topography. Observed turbulence varies by a factor of 2 over the four observed spring tides as low-frequency near-bottom flow changes, but the exact means for inclusion of such low-frequency effects is not clear. Our results suggest that for the extremely energetic turbulence associated with breaking lee waves, dissipation rates may be quantitatively predicted to within a factor of 2 or so using numerical models and simple scalings. Significance Statement This paper describes deep ocean turbulence caused by strong tidal and low-frequency meandering flows over and around a three-dimensional bump, using moored observations and a computer simulation. Such information is important for accurately including these effects in climate simulations. The observations and model agree well enough to be able to use both to synthesize a coherent picture. The observed and modeled turbulence scale as the cube of the tidal speed as expected from theory, but low-frequency flows complicate the picture. We also demonstrate the underestimation of the turbulence that can result when vertical profiling rates are comparable to the internal wave velocities.

Numerical estimation of critical local energy dissipation rate for particle detachment from a bubble-particle aggregate captured within a confined vortex

In flotation, interactions of bubble-particle aggregates with turbulent flow structures in the liquid medium result in particle detachment. This study aims to simulate this phenomenon involving a bubble-particle aggregate (bubble diameter ∼ 3 mm and particle diameter ∼ 314 µm) interacting with a turbulent flow structure manifested as a confined vortex in a square cavity connected to a square cross-section channel. An interface resolved three dimensional (3D) computational fluid dynamics (CFD) model was developed to quantify the bubble-vortex interaction dynamics over a range of channel Reynolds numbers. The CFD model produced a good agreement with the experimentally measured vorticity magnitude, local energy dissipation rate, and bubble motion. It was shown that a bubble-particle aggregate could be captured within the vortex by suitably varying the channel Reynolds number, eventually leading to particle detachment. A separate force balance analysis was performed to determine a criterion for particle detachment utilising the CFD model predicted vorticity and local energy dissipation rate. It was shown that a critical local energy dissipation rate ∼ 1.59 m2/s3 was required for particle detachment to occur, which was also verified experimentally.

Pressure–Strain Interaction as the Energy Dissipation Estimate in Collisionless Plasma

The dissipative mechanism in weakly collisional plasma is a topic that pervades decades of studies without a consensus solution. We compare several energy dissipation estimates based on energy transfer processes in plasma turbulence and provide justification for the pressure–strain interaction as a direct estimate of the energy dissipation rate. The global and scale-by-scale energy balances are examined in 2.5D and 3D kinetic simulations. We show that the global internal energy increase and the temperature enhancement of each species are directly tracked by the pressure–strain interaction. The incompressive part of the pressure–strain interaction dominates over its compressive part in all simulations considered. The scale-by-scale energy balance is quantified by scale filtered Vlasov–Maxwell equations, a kinetic plasma approach, and the lag dependent von Kármán–Howarth equation, an approach based on fluid models. We find that the energy balance is exactly satisfied across all scales, but the lack of a well-defined inertial range influences the distribution of the energy budget among different terms in the inertial range. Therefore, the widespread use of the Yaglom relation in estimating the dissipation rate is questionable in some cases, especially when the scale separation in the system is not clearly defined. In contrast, the pressure–strain interaction balances exactly the dissipation rate at kinetic scales regardless of the scale separation.

Technical note: Turbulence measurements from a light autonomous underwater vehicle

Abstract. A self-contained turbulence instrument from Rockland Scientific was installed on a light autonomous underwater vehicle (AUV) from OceanScan Marine Systems and Technology Lda. We report on the data quality and discuss limitations of dissipation estimated from two shear probes during a deployment in the Barents Sea in February 2021. The AUV mission lasted for 5 h, operating at a typical horizontal speed of 1.1 m s−1. The AUV was programmed to find and cross the maximum along-path thermal gradient at 10, 20 and 30 m depths along 4 km transects. Although the AUV vibrations contaminate the shear probe records, the noise is mitigated by removing vibration-induced components from shear spectra using the accelerometer signal measured in multiple directions. Dissipation rate estimates in the observed transects varied in the range 1×10-8 and 6×10-6 W kg−1, with the values from the two orthogonal probes typically in agreement to within a factor of 2. Dissipation estimates from the AUV show good agreement with nearby vertical microstructure profiles obtained from the ship during the transects, indicating that the turbulence measurements from the AUV are reliable for this relatively turbulent environment. However, the lowest reliable dissipation rates are limited to 5×10-8 W kg−1, making this setup unfit for use in quiescent environments.

Impact of acoustic Doppler current profiler (ADCP) motion on structure function estimates of turbulent kinetic energy dissipation rate

Abstract. Turbulent mixing is a key process in the transport of heat, salt, and nutrients in the marine environment, with fluxes commonly derived directly from estimates of the turbulent kinetic energy dissipation rate, ε. Time series of ε estimates are therefore useful in helping to identify and quantify key biogeochemical processes. The velocity structure function method can be used to determine time series of ε estimates using along-beam velocity measurements from suitably configured acoustic Doppler current profilers (ADCPs). Shear in the background current can bias such estimates; therefore, standard practice is to deduct the mean or linear trend from the along-beam velocity over the period of an observation burst. This procedure is effective if the orientation of the ADCP to the current remains constant over the burst period. However, if the orientation of the ADCP varies, a proportion of the velocity difference between bins is retained in the structure function and the resulting ε estimates will be biased. Long-term observations from a mooring with three inline ADCPs show the heading oscillating with an angular range that depends on the flow speed: from large, slow oscillations at low flow speeds to smaller, higher-frequency oscillations at higher flow speeds. The mean tilt was also determined by the flow speed, whilst the tilt oscillation range was primarily determined by surface wave height. Synthesised along-beam velocity data for an ADCP subject to sinusoidal oscillation in a sheared flow indicate that the retained proportion of the potential bias is primarily determined by the angular range of the oscillation, with the impact varying between beams depending on the mean heading relative to the flow. Since the heading is typically unconstrained in a tethered mooring, heading oscillation is likely to be the most significant influence on the retained bias for a given level of shear. Use of an instrument housing designed to reduce oscillation would mitigate the impact, whilst if the shear is linear over the observation depth range, the bias can be corrected using a modified structure function method designed to correct for bias due to surface waves.

A Comparison Study of EDR Estimates from the NLR and NCAR Algorithms

A comparison was made of two eddy dissipation rate (EDR) estimates based on flight data recorded by commercial flights. The EDR estimates from real-time data using the National Center for Atmospheric Research (NCAR) Algorithm were compared with the EDR estimates derived using the Netherlands Aerospace Centre (NLR) Algorithm using quick assess recorder (QAR) data. The estimates were found to be in good agreement in general, although subtle differences were found. The agreement between the two algorithms was better when the flight was above 10,000 ft. The EDR estimates from the two algorithms were also compared with the vertical acceleration experienced by the aircraft. Both EDR estimates showed good correlation with the vertical acceleration and would effectively capture the turbulence subjectively experienced by pilots.

A comparison of different methods for estimating turbulent dissipation rate in under-resolved flow fields from synthetic PIV images

The turbulent energy dissipation rate is an important parameter that determines the transfer rates of mass, heat and momentum in chemical engineering industry. Especially in a multiphase reactor, the local instantaneous turbulent dissipation rate affects the breakage and coalescence of bubbles or droplets. To directly determine the local turbulent dissipation rate, fluctuating velocity gradients have to be measured down to the Kolmogorov length scale. This paper compares the advantages and disadvantages of three different methods, namely, correlation method, optical flow method and hybrid method, in the evaluation of velocity fields, which are subsequently used to calculate the turbulent dissipation rate. An instantaneous flow field of homogeneous isotropic turbulence from DNS results is used as a benchmark. The velocity field and turbulent dissipation rate field obtained by these three methods are compared to the DNS results. It is shown that the hybrid method performs better in both velocity field evaluation and local turbulent dissipation rate estimation compared to the other two methods. This is because the hybrid method combines the advantages of the correlation method in achieving a stable averaged velocity field and the optical flow method in achieving pixel-level resolution measurement of the flow field.

Extracting turbulence parameters of smoke via video analysis

Turbulence can be observed in almost all the smoke videos, so turbulence parameters can be extracted as features of smoke in the video smoke detection system. A video-based turbulence parameter measuring method is proposed in this paper. Turbulence can be regarded as a series of irregular flow states with instantaneous velocity fluctuations. First, the instantaneous turbulent velocity field is obtained from the real-time video using an optical flow method, and based on the velocity field information, the turbulence kinetic energy (TKE) and dissipation rate are calculated using large eddy simulation and sub-grid scale (SGS) models. Three different methods, Smagorinsky model, gradient model, and dimensional analysis, are used to obtain the dissipation rate. The results obtained using different methods are compared. The dissipation rate estimated using the SGS models shows high consistency and that estimated by the dimensional analysis has a similar distribution, which shows that the choice of the SGS model is not important for the dissipation rate estimation. Then the TKE is calculated, and the processed images show that each plume structure has its own life cycle and the rising velocity of each plume structure is steady. This method is efficient for the plume turbulence measurement, and it provides benefits to the experimental study of fire plumes. Furthermore, the measured parameters can be analyzed for video-based fire detection. It is a useful method in both scientific research and industrial development.

How close are shell models to the 3D Navier–Stokes equations?

Shell models have found wide application in the study of hydrodynamic turbulence because they are easily solved numerically even at very large Reynolds numbers. Although bereft of spatial variation, they accurately reproduce the main statistical properties of fully-developed homogeneous and isotropic turbulence. Moreover, they enjoy regularity properties which still remain open for the three-dimensional (3D) Navier–Stokes equations (NSEs). The goal of this study is to make a rigorous comparison between shell models and the NSEs. It turns out that only the estimate of the mean energy dissipation rate is the same in both systems. The estimates of the velocity and its higher-order derivatives display a weaker Reynolds number dependence for shell models than for the 3D NSEs. Indeed, the velocity-derivative estimates for shell models are found to be equivalent to those corresponding to a velocity gradient averaged version of the 3D Navier–Stokes equations (VGA-NSEs), while the velocity estimates are even milder. Numerical simulations over a wide range of Reynolds numbers confirm the estimates for shell models.

The Optimization of Aircraft Acceleration Response and EDR Estimation Based on Linear Turbulence Field Approximation

The estimation of aircraft vertical acceleration response to atmospheric turbulence is fundamental to acceleration-based eddy dissipation rate (EDR) estimation. The linear turbulence field approximation with the wind gradients effects is utilized to describe the turbulence effects on civil aviation aircraft. To consider the wind gradients effects, the aircraft was modeled by a cruciform assembly in this study. A vertical acceleration estimation based on the unsteady vortex lattice method (UVLM) was proposed, in which the air-compression effects in high-subsonic flight were compensated by the Karman–Tsien rule. Results indicate that compared with the wing-tail assembly, the cruciform assembly with the wind gradients effects has better accuracy in computing acceleration response. The vertical acceleration response only induced by turbulence can be obtained for acceleration-based EDR estimation. Furthermore, with the optimized acceleration response, the estimated EDR value has got better accuracy and stability.

Estimating the Parameters of Wind Turbulence from Spectra of Radial Velocity Measured by a Pulsed Doppler Lidar

The strategy providing an estimation of both the mean velocity and the temporal and spatial spectra of radial velocity from data of the same pulse coherent Doppler lidar is proposed. Theoretical relations taking into account the averaging over the probing volume while estimating the spectra of fluctuations of the radial velocity measured by lidar are presented. The method of estimation of the turbulent energy dissipation rate and the variance of the vertical component of wind velocity vector from the spectra of radial velocity is carried out. The results of the comparative experiments are discussed and used in further studies of wind turbulence in the atmospheric boundary layer during the formation of low-level jets and propagation of internal gravity waves.

Crushed recycled glass as a substrate for constructed wetland wastewater treatment: a case study of its potential to facilitate pharmaceutical removal

The use of recycled glass as a substrate for constructed wetlands was assessed through two studies. The first study examined the dissipation of atenolol, carbamazepine, and sulfamethoxazole in mesocosm-modeled wetlands using glass or limestone gravel as substrates, with or without cattails (Typha spp.). Following pseudo-first-order kinetics, atenolol dissipated the fastest from the water surface of the mesocosms (t1/2~1 day), followed by sulfamethoxazole (t1/2~14 days), and carbamazepine (t1/2~48 days), with no significant differences across treatments. Increased half-lives were observed at greater depth, likely due to light screening. A Monte Carlo sensitivity analysis diagnosed sunlight absorption rates and second-order hydroxyl-mediated indirect photolysis rates to be the main sources of uncertainty in our dissipation rate estimates, compared to our observed rates. The second study examined in situ pharmaceutical removal in tertiary pilot-scale subsurface filters made of crushed recycled glass or sand in a wastewater treatment facility in Manitoba, Canada. Glass and sand showed no significant differences for pharmaceutical removals; atenolol and metoprolol were removed below limits of detection, while carbamazepine and sulfamethoxazole persisted over a retention time of 24 h. Overall, recycled glass performed similarly to traditional substrates for wetland-based wastewater treatment.

Best Practices for Comparing Ocean Turbulence Measurements across Spatiotemporal Scales

AbstractThe turbulent energy dissipation rate in the ocean can be measured by using rapidly sampling microstructure shear probes, or by applying a finescale parameterization to coarser-resolution density and/or shear profiles. The two techniques require measurements that are on different spatiotemporal scales and generate dissipation rate estimates that also differ in spatiotemporal scale. Since the distribution of the measured energy dissipation rate is closer to lognormal than normal and fluctuates with the strength of the turbulence, averaging the two approaches on equivalent spatiotemporal scales is critical for accurately comparing the two methods. Here, microstructure data from the 1997 Brazil Basin Tracer Release Experiment (BBTRE) is used to demonstrate that comparing averages of the dissipation rate on different spatiotemporal scales can generate spurious discrepancies of up to a factor of order 10 in regions of strong turbulence and smaller biases of up to a factor of 2 in the presence of weaker turbulence.

Estimate of turbulent energy dissipation rate using free-fall and CTD-attached fast-response thermistors in weak ocean turbulence

The measurement of turbulence is necessary to quantify the vertical, diapycnal transport of heat, water and substances influencing climate, nutrient supply and marine ecosystems. As specialist instrumentation and ship-time are required to conduct microstructure measurements to quantify turbulence intensity, there is a need for more inexpensive and easy measurement methods. This study demonstrated that the turbulent energy dissipation rate, ε, estimated from fast-response thermistors Fastip Probe model 07 (FP07) with the depth-average of a > 10 m depth interval well agreed with those from current shear probes to a range of 10–11 W/kg (m2s−3) in the two casts of the most accurate and stable free-fall vertical microstructure profiler, VMP6000 in the Oyashio water. This range cannot be measured with velocity shear probes equipped in smaller profilers in which the lower limit of ε > O (10–10) W/kg. These results extend turbulence measurements using the FP07 to 10–11 W/kg. They may be especially useful for turbulence observations in deep oceans where ε is generally weak (< 10–10 W/kg). As FP07 are much less sensitive to instrument vibrations than current shear and may be attached to various observational platforms such as temperature-conductivity-depth (CTD) profilers and floats. The CTD-attached FP07 observations near the VMP6000 profiles demonstrated their capabilities in the ε range of 10–11–10–8 W/kg by data screening using a Wsd>0.1(W-0.3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${W}_{\\mathrm{sd}}>0.1(W-0.3)$$\\end{document} criterion (1 s mean lowering rate W\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W$$\\end{document} m/s and its standard deviation Wsd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${W}_{\\mathrm{sd}}$$\\end{document}) under rough conditions where the cast-mean Wsd>\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${W}_{\\mathrm{sd}}>$$\\end{document} 0.07 m/s and the standard deviation of Wsd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${W}_{\\mathrm{sd}}$$\\end{document} in each cast σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma$$\\end{document} >0.05 m/s.

Aviation Turbulence Forecasting at Upper Levels with Machine Learning Techniques Based on Regression Trees

AbstractWe explore the use of machine learning (ML) techniques, namely, regression trees (RT), for the purpose of aviation turbulence forecasting at upper levels [20–45 kft (~6–14 km) in altitude]. In particular, we develop a series of RT-based algorithms that include random forests (RF) and gradient-boosted regression trees (GBRT) methods. Numerical weather prediction model prognostic variables and derived turbulence diagnostics based on 6-h forecasts from the 3-km High-Resolution Rapid Refresh model are used as features to train these data-driven models. Training and evaluation are based on turbulence estimates of eddy dissipation rate (EDR) obtained from automated in situ aircraft reports. Our baseline RF model, consisting of 100 trees with 30 layers of maximum depth, significantly reduces forecast errors for EDR &lt; 0.1 m2/3 s−1 (which corresponds roughly to null and light turbulence) when compared with a simple regression model, increasing the probability of detection and in turn reducing the number of false alarms. Model complexity reduction via GBRT and feature-relevance analyses is performed, indicating that considerable execution speedups can be achieved while maintaining the model’s predictive skill. Overall, the ML models exhibit enhanced performance in discriminating the EDR forecast among the light, moderate, and severe turbulence categories. In addition, these artificial intelligence techniques significantly simplify the generation of new NWP and grid-spacing specific turbulence forecast products.

A-Priori Validation of Scalar Dissipation Rate Models for Turbulent Non-Premixed Flames

The modelling of scalar dissipation rate in conditional methods for large-eddy simulations is investigated based on a priori direct numerical simulation analysis using a dataset representing an igniting non-premixed planar jet flame. The main objective is to provide a comprehensive assessment of models typically used for large-eddy simulations of non-premixed turbulent flames with the Conditional Moment Closure combustion model. The linear relaxation model gives a good estimate of the Favre-filtered scalar dissipation rate throughout the ignition with a value of the related constant close to the one deduced from theoretical arguments. Such value of the constant is one order of magnitude higher than typical values used in Reynolds-averaged approaches. The amplitude mapping closure model provides a satisfactory estimate of the conditionally filtered scalar dissipation rate even in flows characterised by shear driven turbulence and strong density variation.