Kinetic Energy Dissipation Rate Research Articles

Performance analysis of an underwater wireless optical communication link with Lommel beam

In order to mitigate the stochastic interference of underwater channels and improve the quality of underwater communication systems, it is essential to study the performance of the underwater wireless optical communication (UWOC) links utilizing vortex beams with unique attributes. In this paper, the analytical formulae for the bit error rate (BER) and the average capacity of the UWOC link with diffraction-free Lommel beam are derived under the Rytov theory. Simulation results demonstrate that the system with a long wavelength, a high system signal-to-noise ratio(SNR), a small asymmetric parameter and receiving aperture diameter achieves a high average capacity and a low BER. Furthermore, in the underwater channel with a larger kinetic energy dissipation rate per unit mass of fluid and inner scale, a smaller mean-squared temperature dissipation rate, temperature salinity contribution ratio and transmission distance, the performance of the communication link can be improved. Meanwhile, it is found that the performance of the link with carrier Lommel beam are less sensitive to the topological charge, the scaling factor of the beam and the turbulent outer scale. These findings provide theoretical support for the design and implementation of an UWOC link utilizing the Lommel beam.

Transmission characteristics of partially coherent pin-like optical vortex beams in oceanic turbulence

Based on the Rytov approximation theory, the analytical formulae for the mode detection probability and channel capacity of the partially coherent pin-like optical (PCPO) vortex beams propagating in oceanic turbulence are obtained. The effects of light source parameters and oceanic turbulence parameters on the transmission characteristics of the PCPO vortex beams are analyzed in detail by numerical simulations. According to numerical results, a larger spatial coherence length of the partially coherent source endows the beams with a superior channel capacity performance while accompanied by a decrease in transmission robustness. Meanwhile, PCPO vortex beam with greater phase modulation power parameter and longer wavelength is conducive to enhancing the transmission quality through oceanic turbulence. In addition, the channel capacity of the system can be effectively augmented with the increase of the dissipation rate of kinetic energy per unit mass of fluid, the anisotropy factor, the inner scale radius and the decrease of the mean square temperature dissipation rate, the temperature-salinity contribution ratio. The results also indicate that PCPO vortex beam is a better candidate than Gaussian vortex beam for long-distance transmission. This paper provides a theoretical reference for studying an underwater communication link using PCPO vortex beams as the transmission carrier.

ATOMIX benchmark datasets for dissipation rate measurements using shear probes

Turbulent mixing in the ocean, lakes and reservoirs facilitates the transport of momentum, heat, nutrients, and other passive tracers. Turbulent fluxes are proportional to the rate of turbulent kinetic energy dissipation per unit mass, ε. A common method for ε measurements is using microstructure profilers with shear probes. Such measurements are now widespread, and a non-expert practitioner will benefit from best practice guidelines and benchmark datasets. As a part of the Scientific Committee on Oceanographic Research (SCOR) working group on “Analysing ocean turbulence observations to quantify mixing” (ATOMIX), we compiled a collection of five benchmark data of ε from measurements of turbulence shear using shear probes. The datasets are processed using the ATOMIX recommendations for best practices documented separately. Here, we describe and validate the datasets. The benchmark collection is from different types of instruments and covers a wide range of environmental conditions. These datasets serve to guide the users to test their ε estimation methods and quality-assurance metrics, and to standardize their data for archiving.

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

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).

Evolution of small-scale turbulence at large Richardson numbers

Abstract. The theory of stratified turbulent flow developed earlier by the authors is applied to data from different areas of the ocean. It is shown that turbulence can be amplified and supported even at large gradient Richardson numbers. The cause of that is the exchange between kinetic and potential energies of turbulence. Using the profiles of Brunt–Väisälä frequency and vertical current shear given in Forryan et al. (2013), the profiles of the kinetic energy dissipation rate are calculated. The results are in reasonable agreement with the experimental data.

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.

Optimum scaling relation for dynamic shear enhanced membrane filtration pilots in nutrient and mineral recovery from wastewater

Recovery of nutrients and minerals from wastewater by membrane filtration holds promise for sustainable water processing. While dealing with such processes that often result in substantial filtrate throughput decline due to membrane fouling, Dynamic Shear Enhanced Membrane Filtration Pilots (DSEMFPs) have proven to be an ideal contender. These devices generate feed flow-independent shear that triggers solute back-transport away from the membrane. Subsequent flux enhancement is a congruous merit. Power-law correlation between the flux and average shear rate has been so extensively used in several studies so that it became the ubiquitous scaling relation for DSEMFPs. However, in this article, we have demonstrated a novel and more expansive scaling between flux and a set of prototypical turbulent measures (i.e., turbulent kinetic energy, kinetic energy dissipation rate, and Kolmogorov scale), relative to shear rate, ranging over five different DSEMFPs. Flux data were collected from previous studies, whereas hydrodynamic variables were evaluated computationally. All turbulent measures exhibited better correlation compared to shear rate with the Kolmogorov scale being the best regressor (R2 > 0.96). The study demonstrates that turbulence has an equivalent, if not superior, role in upscaling flux in DSEMFPs against the conventional idea of shear generation being primary.

Rainfall as a driver for near-surface turbulence and air-water gas exchange in freshwater aquatic systems.

Gas fluxes from aquatic ecosystems are a significant component of the carbon cycle. Gas exchange across the air-water interface is regulated by near-surface turbulence and can be controlled by different atmospheric forcing conditions, with wind speed and surface buoyancy flux being the most recognized drivers in empirical studies and modeling approaches. The effect of rainfall on near-surface turbulence has rarely been studied and a consistent relationship between rain rate and near-surface turbulence has not yet been established. In this study, we addressed some limitations still present in the quantitative understanding of the effect of rain rate on near-surface turbulence and on the resulting gas transfer velocity in freshwater. We performed controlled laboratory experiments over a wide range of rain rates (7 to 90 mm h-1) and estimated gas transfer velocities from high-resolution measurements of O2 concentration, while rain-induced turbulence was characterized based on particle image velocimetry. We found that the rain-induced dissipation rates of turbulent kinetic energy declined with depth following a consistent power-law relationship. Both energy dissipation rates and gas transfer velocity increased systematically with the rain rate. The results confirm a causal relationship between rainfall, turbulence, and gas exchange. We propose a power-law relationship between near-surface turbulent dissipation rates and rain rate. In combination with surface renewal theory, we derived a direct relationship between gas transfer velocity and rain rate, which can be used to assess the importance of short-term drivers, such as rain events, on gas dynamics and biogeochemical cycling in aquatic ecosystems.

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.

Turbulent Diffusivity Profiles on the Shelf and Slope at the Southern Edge of the Canada Basin

AbstractVertical profiles of temperature microstructure at 95 stations were obtained over the Beaufort shelf and shelfbreak in the southern Canada Basin during a November 2018 research cruise. Two methods for estimating the dissipation rates of temperature variance and turbulent kinetic energy were compared using this data set. Both methods require fitting a theoretical spectrum to observed temperature gradient spectra, but differ in their assumptions. The two methods agree for calculations of the dissipation rate of temperature variance, but not for that of turbulent kinetic energy. After applying a rigorous data rejection framework, estimates of turbulent diffusivity and heat flux are made across different depth ranges. The turbulent diffusivity of temperature is typically enhanced by about one order of magnitude in profiles on the shelf compared to near the shelfbreak, and similarly near the shelfbreak compared to profiles with bottom depth >1,000 m. Depth bin means are shown to vary depending on the averaging method (geometric means tend to be smaller than arithmetic means and maximum likelihood estimates). The statistical distributions of heat flux within the surface, cold halocline, and Atlantic water layer change with depth. Heat fluxes are typically <1 Wm−2, but are greater than 50 Wm−2 in ∼8% of the overall data. These largest fluxes are located almost exclusively within the surface layer, where temperature gradients can be large.

Shortcomings of the dissipation rate for understanding the turbulent environment of plankton—And a potential solution

AbstractFundamental marine ecosystem dynamics such as mating, predation, and infection require individual plankton to move relative to one another. Ambient turbulence is often invoked as a mechanism to facilitate such interactions. The local intensity of turbulence is quantified as the dissipation rate of turbulent kinetic energy. While the dissipation rate is central to understanding large‐scale fluxes of heat, salt, and nutrients in the ocean, we show that it can be a poor descriptor of the turbulent environment experienced by individual plankton. A dissipation rate is a single integrated quantity representing all the complex motions in a turbulent region; the instantaneous turbulent environment of plankton may bear little resemblance to that predicted by the dissipation rate or quantities derived from it. Most importantly, the statistics (probabilities) of the relative motions of plankton in turbulence cannot be recovered from the dissipation rate or its spectrum: the probabilities of the plankton experiencing any given turbulent relative velocity are lost in the calculation. This presents a fundamental barrier to our understanding of the effects of ambient turbulence on planktonic ecosystem dynamics in the ocean. Rather than relying on dissipation rates, we show that quantifying the probability distributions of the microscale turbulent motions can provide much richer insights into the turbulent environment of individual plankton. Expanding such statistical analyses, and improving our understanding of the Lagrangian properties of ocean turbulence as experienced by plankton in the ocean will lead to significant increases in our ability to understand and quantify the effects of turbulence on plankton.

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.

Effect of hemispherical roughness spacing on double-averaged turbulence characteristics for different flow submergence

The double-averaged (DA) turbulence characteristics over rough bed comprising of hemispherical elements with different spacing ( p/ r = 2, 4, 6, and 8; p = pitch distance; r = height of hemisphere) is quantified for three flow-submergences ( h/ r = 7.14, 5.35, 3.57; mean flow-depth ( h) = 20 cm, 15 cm, and 10 cm). The production and dissipation rates of turbulent kinetic energy are maximum at and below the crest level. Within interfacial sublayer, the degree of anisotropy is observed to be maximum for p/ r = 4 and the tendency for the return to isotropy is strongest for p/ r = 8 in the outer layer. The turbulence generated in the bottom region is still present in the outer region for low flow-submergences. The turbulence strength is maintained in the roughness order (descending) as p/ r = 4 > 2 > 6 > 8 > plane bed; wherein the change in flow-submergence does not change this order.

Low-Prandtl-number effects on global and local statistics in two-dimensional Rayleigh–Bénard convection

We present global and local statistical properties of turbulent Rayleigh–Bénard (RB) convection at low Prandtl numbers in this work. A series of high resolution two-dimensional (2D) direct numerical simulations are carried out in a square box for the Prandtl number ranges 0.005≤Pr≤0.07 and 0.01≤Pr≤0.15 at Rayleigh numbers Ra=107 and Ra=108, respectively. The global heat and momentum transport expressed as Nusselt number Nu and Reynolds number Re are found to scale as Nu∼Pr0.14 and Re∼Pr−0.82 for Ra=107, and Nu∼Pr0.11Re∼Pr−0.93 for Ra=108. The local velocity fluctuation at the cell center shows larger amplitudes at lowered Pr, indicating a stronger turbulence in the bulk. The magnitudes of kinetic and thermal energy dissipation rates in the bulk also increase with the decreasing of Pr, due to the intensified velocity gradient and larger thermal diffusivity, respectively. In the cell central region, probability density functions (PDFs) of velocity show a bimodal distribution, and it approaches the Gaussian distribution at higher Pr, while the PDFs of temperature display a stretched exponential shape with intermittent behavior. The kinetic energy spectra further reveal that the velocity cascade follows the Bolgiano–Obukhov scaling in the bulk of the convective flow.