Energy Dissipation Rate Research Articles

Comparison of hydrodynamics and micromixing quality in a two-stage microreactor with intensely swirled flows and in a T-mixer

The advantages of a two-stage microreactor with intensely swirled flows (MRISF-2) in comparison with a T-mixer are studied. Both numerical simulation and experimental study were used. The best way of solutions feeding was found experimentally, through the tangential inlet pipe and axial nozzle. It was revealed that the maximum values of the specific energy dissipation rate and correspondingly the best quality of micromixing are achieved with this method. The results of numerical simulation demonstrate the predominant energy dissipation in the neck of MRISF-2, which is a key knowledge for the proper use of such type of microreactors for co-precipitation reactions, because the micromixing quality plays crucial role in the synthesis of nanosized particles. The specific energy dissipation rate in the neck is from 10 to 20 times higher than just upstream or downstream the neck. The micromixing quality (index of segregation) in MRISF-2 was one order of magnitude better compared to the T-mixer; besides, the MRISF-2 allows to increase energy dissipation rate in a much wider range.

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.

A Novel Method to Characterize the Damping Capacity of EPDM/CIIR Blends Using Vibrating Rubber Balls.

An experimental device fixed with a laser displacement sensor was assembled to investigate the rebound behaviors and damping mechanism of rubber balls prepared with ethylene-propylene-diene monomer (EPDM)/chlorinated butyl rubber (CIIR) blends. The result showed that a prediction model was proposed to characterize the damping capacity by using the rebound height of the rubber balls. The lower rebound height corresponded to better damping capacity. A modified equation relating to the rebound height has been obtained from the theoretical derivation on the basis of the dynamic mechanical analysis, showing that the rebound height was affected by the deformation frequency, the external excitation, and the nature of rubber blends. Furthermore, the energy dissipation rate (EDR), defined by the ratio of the height loss to the rebound time, was proposed to further characterize the damping capacity. The EDR value was shown to be highest for the pure CIIR and lowest for the pure EPDM, exhibiting a decreasing trend with the increase in EPDM content in the rubber blends. It can be expected that the damping capacity of the EPDM/CIIR blends decreases with the decrease in external excitation, the conclusion of which plays a key role in the formulation design of viscoelastic damping rubber materials.

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.

CFD-DEM modeling of particle dissolution behavior in stirred tanks

A CFD-DEM particle dissolution model was established to study the particle dissolution process in a stirred tank. Firstly, the model's accuracy in simulating particle size and solute concentration was validated against experimental results, the errors were 6.13% and 12.5%, respectively. Secondly, the study delved into the mechanism of mass transfer dissolution from three dimensions: solute concentration distribution, particles spatial distribution, and energy dissipation rate of particles. It was found that the larger the concentration gradient, the better the dissolution of particles. As the dissolution progresses, the coupling force between the fluid and the particles weakens, and smaller particles are more easily suspended. Lastly, the dissolution behavior of particles at different rotation speeds was investigated. Stirring speed can significantly improve the dissolution rate of particles in the particle suspension and dispersion stage, but the difference of different rotational speeds on the dissolution rate becomes smaller in the particle circulation flow stage.

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).

Experimental study and turbulence dissipative scale modelling of the rapid micromixing of impinging thin sheets of liquids

Previous studies have shown that the impingement of thin liquid sheets produces high energy dissipation rates due to the release of kinetic energy in a very small mass of liquid (0.0001–0.01 g), even though flowrates are on the order of L/min. Rapid micromixing occurs because the dissipated energy leads to a substantial reduction in the initial segregation size scale of the liquids, which is the single-sheet thickness at impingement (~ 100 μm). In the present study, the micromixing was investigated by following the progress of an acid-base neutralization accompanied by a change in fluorescence intensity of a fluorophore. Micromixing was modeled using a framework that assumes diffusion and reaction of species occur within slabs of fixed thickness (2L). The slabs are fixed in size because the released kinetic energy is dissipated within one turnover time of the large energy-containing eddies produced in the turbulent impingement zone. A simulation, which included a module for calculating the fluorescence intensity, determined 2L for experimental energy dissipation rates (ϵ) ranging from 4×104 to 7.7×106 W/kg. 2L was found to lie in the range of turbulent dissipative scales less than the Taylor microscale but greater than the Kolmogorov microscale. 2L/v′ was found to be a function of ReΛ−1/4 and ν/ϵ1/2, where v′ is the velocity associated with the turbulent kinetic energy, ReΛ is the large-eddy Reynolds number and ν is the kinematic viscosity. Similar to η/Λ, 2L/Λ is a function of ReΛ−3/4, where ηis the Kolmogorov microscale and Λ is the size of the large energy-containing eddies.

Comparative Evaluation of Dissolution Performance in a USP 2 Setup and Alternative Stirrers and Vessel Designs: A Systematic Computational Investigation.

The dissolution testing method described in the United States Pharmacopeia (USP) Chapter ⟨711⟩ is widely used for assessing the release of active pharmaceutical ingredients from solid dosage forms. However, extensive use over the years has revealed certain issues, including high experimental intervariability observed in specific formulations and the settling of particles in the dead zone of the vessel. To address these concerns and gain a comprehensive understanding of the hydrodynamic conditions within the USP 2 apparatus, computational fluid dynamic simulations have been employed in this study. The base design employed in this study is the 900 mL USP 2 vessel along with a paddle stirrer at a 50 rpm rotational speed. Additionally, alternative stirrer designs, including the hydrofoil, pitched blade, and Rushton impeller, are investigated. A comparison is also made between a flat-bottom tank and the USP round-bottom vessel of the same volume and diameter. Furthermore, this work examines the impact of various parameters, such as clearance distance (distance between the bottom of the impeller and bottom of the vessel), number of impeller blades, impeller diameter, and impeller attachment angle. The volume-average shear rate (Stv), fluid velocity (Utv), and energy dissipation rates (ϵtv) represent the key properties evaluated in this study. Comparing the USP2 design and systems with the same stirrer but flat-bottom vessel reveals more homogeneous mixing compared to the USP2 design. Analyzing fluid flow streamlines in different designs demonstrates that hydrofoil stirrers generate more suspension or upward movement of fluid compared to paddle stirrers. Therefore, when impellers are of a similar size, hydrofoil designs generate higher fluid velocities in the coning area. Furthermore, the angle of blade attachment to the hub influences the fluid velocity in the coning area in a way that the 60° angle design generates more suspension than the 45° angle design. The findings indicate that the paddle stirrer design leads to a heterogeneous shear rate and velocity distributions within the vessel compared with the other designs, suggesting suboptimal performance. These insights provide valuable guidance for the development of improved in vitro dissolution testing devices, emphasizing the importance of optimized design considerations to minimize hydrodynamic variability, enhance dissolution characterization, and reduce variability in dissolution test results. Ultimately, such advancements hold potential for improving in vitro-in vivo correlations in drug development.

Application of nonlinear energy sink for vibration suppression of mine boring machines

The propulsion system of mine boring machines often experiences severe vibration during mining. To suppress the vibration of the main beam system of roadheader and prevent the excessive fatigue of propulsion system, a magnetic nonlinear energy sink (MNES) is designed to suppress vibration. In this paper, firstly, the structure and design principle of MNES are introduced, and the dynamic equations of the main beam-MNES system are established. On this basis, the genetic algorithm is applied to optimize the vibration suppression of MNES, and the optimal parameters are determined. In results, the accumulative energy dissipation rate of optimal MNES in transient vibration can reach 90.2% and the vibration reduction effect of the optimal MNES in steady-state vibration is about 82.2%.

A gelatin-based ionic conductor with a dense/loose alternating network enabled by surface active cellulose

Although conductive and stretchable ionic conductors are increasingly prepared for flexible sensing applications, such as health monitoring, tissue engineering, and electronic skin, achieving a balance between remarkable mechanical properties and high sensing sensitivity remains a significant challenge. In this work, a dense/loose alternating network was meticulously constructed through a pre-assembly process in sodium citrate solution and a subsequent re-assembly in FeCl3 solution. This approach ensured the robustness of the network structure and facilitated ion migration. Within the network, a gelatin network cross-linked via covalently and hydrogen bonds was significantly enhanced by a synergy of micro-enhancement and dynamic bidirectional crosslinking containing hydrogen bonds, imine bonds, and Fe coordinate bonds enabled by surface active cellulose. Benefiting from the dense network, the obtained composite hydrogels delivered a strong tensile strength (496.3 kPa), outstanding elastic modulus (917.6 kPa), and an excellent energy dissipation rate (55.6 %) at 80 % of strain. The loose polymer network can also endow Fe3+/Cl− ions with sensitive mobility, leading to an ultra-high sensing sensitivity (maximum GF: 20.06). These exceptional properties enable the ionic conductor to accurately detect a wide range of motions and pressures without being affected by environmental noise. With attributes such as reusability, biodegradability, strength, and sensitivity, this ionic conductor emerges as a reliable soft material with promising applications in the field of healthcare monitoring, wearable strain sensor sensors, and writing anti-counterfeiting materials.

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).

Study of hydrodynamic stress in cell culture bioreactors via lattice-Boltzmann CFD simulations supported by micro-probe shear stress method

Mammalian cell cultivation in pharmaceutical industry can last up to units of weeks and requires proper transport of nutrients and oxygen for cell growth and production. Given the long time period, cells experience flow fields from all bioreactor’s zones, where the energy dissipation rate (ε) varies substantially. Shear sensitive micro-probes with size comparable to cells and Kolmogorov eddies are used for the determination of the maximum hydrodynamic stress (τmax) in bioreactors. For the very first time, the micro-probe method is applied successfully not only to laboratory (3 L) and pilot scale (80 L and 200 L), but also to industrial production scale bioreactor (12,500 L) with Rushton turbine and pitched-blade (RT-PB) impeller configuration. Experimentally obtained data are used for the validation of comprehensive CFD scale-up study, using the Lattice-Boltzmann large eddy simulation (LB-LES) method. Besides τmax, this work also focuses on the study of mixing time and flow field attributes.

Study of energy dissipation mechanisms and hotspot formation patterns during impact process in octogen explosives with circular cavities

Considerable focus has been given to hotspot generation and ignition phenomena in impact-induced explosives. Hotspot formation in explosives is typically attributed to internal dissipation and heat transfer occurring within them. This study refines the momentum and energy equations to illustrate the entire process of particle collision, temperature-rise evolution, and hotspot formation in octogen explosive bed under impact. By octogen, we mean the substance known as cyclotetramethylene tetranitramine, which is also commonly referred to as HMX. Dense particles are considered to have pseudo-fluid properties. During the impact of the explosive, we captured the propagation of the stress wave and compared its similarities and differences with the shock wave. The collision force model incorporates a combination of Hertz–Mindlin elastic and Thornton elastoplastic contact theories. The temperature-governing equation includes sliding friction, rolling resistance, and plastic dissipations as energy sources, taking into account the heat transfer processes between particles. Temperature evolution is a spatiotemporally correlated phenomenon divided into three processes: high-temperature bands formation, cavity collapse, and particle bed dispersion, all of which lead to hotspot formation near the cavity and near the wall. Plastic dissipation is the primary source for particle temperature-rise and hotspot formation. Furthermore, the effect of cavity size, impact velocity, and particle size on temperature evolution and hotspot formation patterns is analyzed. It was found that higher impact velocities and smaller cavity sizes are associated with increased hotspot temperatures near the wall, but the hotspot temperature near the cavity does not consistently vary with impact velocity and cavity size. This is attributed to the relationship between energy dissipation rate and void collapse time.

Effect of Turbulence on the Collision Rate between Settling Ice Crystals and Droplets

Abstract In mixed-phase clouds, graupel forms by riming, a process whereby ice crystals and supercooled water droplets settling through a turbulent flow collide and aggregate. We consider here the early stage of the collision process of small ice crystals with water droplets and determine numerically the geometric collision kernel in turbulent flows (therefore neglecting all interactions between the particles and assuming a collision efficiency equal to unity), over a range of energy dissipation rate 1–250 cm2 s−3 relevant to cloud microphysics. We take into account the effect of small, but nonzero fluid inertia, which is essential since it favors a biased orientation of the crystals with their broad side down. Since water droplets and ice crystals have different masses and shapes, they generally settle with different velocities. Turbulence does not play any significant role on the collision kernel when the difference between the settling velocities of the two sets of particles is larger than a few millimeters per second. The situation is completely different when the settling speeds of droplets and crystals are comparable, in which case turbulence is the main cause of collisions. Our results are compatible with those of recent experiments according to which turbulence does not clearly increase the growth rate of tethered graupel in a flow transporting water droplets.

Transitory Tidal Heating and Its Impact on Cluster Isochrones

The kinetic energy in tidal flows, when converted into heat, can affect the internal structure of a star and shift its location on a color–magnitude diagram from that of standard models. In this paper we explore the impact of injecting heat into stars with masses near the main-sequence turnoff mass (1.26 M ⊙) of the open cluster M67. The heating rate is obtained from the tidal shear energy dissipation rate, which is calculated from first principles by simultaneously solving the equations that describe orbital motion and the response of a star’s layers to the gravitational, Coriolis, centrifugal, gas pressure, and viscous forces. The stellar structure models are computed with MESA. We focus on the effects of injecting heat in pulses lasting 0.01 Gyr, a time frame consistent with the synchronization timescale in binary systems. We find that the location of the tidally perturbed stars in the M67 color–magnitude diagram is shifted to significantly higher luminosities and effective temperatures than predicted by the standard model isochrone and includes locations corresponding to some of the blue straggler stars. Because tidal heating takes energy from the orbit, causing it to shrink, blue straggler stars could be merger or mass transfer progenitors, as well as products of these processes.

DUGKS-GPU: An efficient parallel GPU code for 3D turbulent flow simulations using Discrete Unified Gas Kinetic Scheme

This paper presents a parallel implementation of the Discrete Unified Gas Kinetic Scheme (DUGKS) on the GPU system using the CUDA Fortran and CUDA C++ programming languages. Firstly, we conducted an extensive revision of our original CPU-based code, resulting in a threefold decrease in memory usage. This new implementation is also paired with a novel approach to compute cell face flux using trilinear interpolation. It is shown analytically that the interpolation-based approach to flux calculation is more accurate compared to the one used in the original DUGKS. The initial simulation results using this new approach suggest that trilinear interpolation can reduce numerical errors on a coarse mesh. For example, in the case of the decaying Taylor-Green vortex flow at a 1283 mesh resolution, the relative numerical error in the energy dissipation rate at t⁎=2, using the spectral simulation result as the benchmark, is approximately 30% lower than that of the original implementation. The improved GPU DUGKS method is applied to laminar and turbulent flows in periodic and wall-bounded boundary configurations. A performance comparison of the GPU implementation is also presented and compared to the previous CPU implementation. A maximum speedup of 7.64x was achieved on a desktop-level GPU compared to a 32-core CPU. The strong scaling test, conducted on an eight-GPU node, demonstrated the efficient utilization of available multiple GPU resources by the code. Program summaryProgram Title: DUGKS-GPUCPC Library link to program files:https://doi.org/10.17632/yykv5s9g2n.1Developer's repository link:https://github.com/kairzhan/DUGKS-GPUCode Ocean capsule:https://codeocean.com/capsule/3b1e4f74-cdd3-4781-8923-8514d5923dfb/Licensing provisions: GNU General Public License 3Programming language: CUDA C++, CUDA FortranSupplementary material:Nature of problem: DUGKS-GPU is an advanced numerical code designed to accelerate the simulation of turbulent fluid flows through the application of the kinetic method known as the Discrete Unified Gas Kinetic Scheme (DUGKS). This computational tool comprises a CUDA Fortran version, tailored for a single GPU, as well as a CUDA C++ version developed for multi-GPU platforms.Solution method: The code employs a second-order finite-volume discretization of the discrete velocity Boltzmann equation with the BGK collision model. It can be used to simulate small to medium-scale problems on modern multi-GPU platforms with CUDA architecture.

Time-resolved solvation of alkali ions in superfluid helium nanodroplets.

The sinking of alkali cations in superfluid 4He nanodroplets is investigated theoretically using liquid 4He time-dependent density functional theory at zero temperature. The simulations illustrate the dynamics of the buildup of the first solvation shell around the ions. The number of helium atoms in this shell is found to linearly increase with time during the first stages of the dynamics. This points to a Poissonian capture process, as concluded in the work of Albrechtsen et al. on the primary steps of Na+ solvation in helium droplets [Albrechtsen et al., Nature 623, 319 (2023)]. The energy dissipation rate by helium atom ejection is found to be quite similar between all alkalis, the main difference being a larger energy dissipated per atom for the lighter alkalis at the beginning of the dynamics. In addition, the number of helium atoms in the first solvation shell is found to be lower at the end of the dynamics than at equilibrium for both Li+ and Na+, pointing to a kinetic rather than thermodynamical control of the snowball size for small and strongly attractive ions.

Nonlocal contributions to the turbulent cascade in magnetohydrodynamic plasmas.

We present evidence for nonlocal contributions to the turbulent energy cascade in magnetohydrodynamic (MHD) plasmas. Therefore, we revisit a well-known result derived directly from the MHD equations, i.e., the Politano and Pouquet law for the transfer of kinetic and magnetic energy in scale. We propose adding a term that accounts for nonlocal transfer and represents the influence of fluctuations from large scales due to the Alfvén effect. Supported by direct numerical simulations of homogeneous and isotropic MHD turbulence, we verify that in some plasma configurations, neglecting the additional nonlocal term might consistently overestimate energy dissipation rates and, thus, the contributions of turbulent energy dissipation potentially affecting solar wind heating, i.e., a central puzzle in space plasma physics that motivates the present work.

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.