Turbulent Kinetic Energy Dissipation Research Articles

Similarity of the turbulent kinetic energy dissipation rate distribution in the upper mixed layer of the tropical Indian Ocean

Turbulence within the upper ocean mixed layer plays a key role in various physical, biological, and chemical processes. Between September and November 2011, a dataset of 570 vertical profiles of the turbulent kinetic energy (TKE) dissipation rate, as well as conventional hydrological and meteorological data, were collected in the upper layer of the tropical Indian Ocean. These data were used to statistically analyze the vertical distribution of the TKE dissipation rate in the mixed layer. The arithmetic-mean method made the statistical TKE dissipation rate profile more scattered than the median and geometric-mean methods. The statistical TKE dissipation rate were respectively scaled by the surface buoyancy flux and the TKE dissipation rate at the mixed-layer base. It was found that the TKE dissipation rate scaled by that at the mixed-layer base exhibited better similarity characteristics than that scaled by the surface buoyancy flux, whether the stability parameter D/|LMO| was greater or less than 10, indicating that the TKE dissipation rate at the mixed-layer base is a better characteristic scaling parameter for reflecting the intrinsic structure of the TKE dissipation rate in the mixed layer, where D and LMO are respectively the mixed-layer thickness and the Monin-Obukhov length scale. The parameterization of the TKE dissipation rate at the mixed-layer base on the shear-driven dissipation rate and the surface buoyancy flux was further explored. It was found that the TKE dissipation rate at the mixed-layer base could be well fitted by a linear combination of three terms: the wind-shear-driven dissipation rate, the surface buoyancy flux, and a simple nonlinear coupling term of these two .

Resonant growth of inertial oscillations from lee waves in the deep ocean

The interactions between inertial oscillations (IO) and lee waves (LW) close to the bottom of the ocean and the role of IO in energy dissipation are addressed for a range of physical parameters typical of Southern Ocean conditions. Idealized numerical simulations in a vertical plane and resonant interaction theory are combined for this purpose. The lee waves are emitted by a uniform geostrophic flow over a sinusoidal topography for a constant buoyancy frequency at mid-latitude. We show that IO can grow by triadic resonant interactions with the LW. Two triads are dominant, which involve waves with frequency , f and , where is the intrinsic frequency of the LW and f the Coriolis frequency (assumed positive). These triads differ by the sign and value of the IO vertical wavenumber. Results from the numerical simulations show that the triad associated with the upward phase propagation of the IO is selected, consistent with oceanic observations, that a good agreement is obtained with the IO growth rate predicted theoretically and that the IO develop in a bottom layer of height less than 1000 m. A quasi-steady flow regime is eventually reached, with the IO amplitude being of the same order as the geostrophic flow speed. During this regime, depending upon the flow parameters, the IO kinetic energy is equal to 30–70% of the LW energy flux during one inertial period. This large range of values is not reflected in the turbulent kinetic energy (TKE) dissipation rate, which is comprised between 10 and 30% of the LW energy flux, whatever the IO amplitude, even if vanishingly small. Therefore, for the set of parameters we consider, the TKE dissipation rate cannot be inferred from the IO amplitude. Yet, the nonlinear interactions between the lee waves and the IO are critical in setting the energy spectrum, and similarly for the internal tide and the IO at low latitudes according to the literature. This implies that IO should be taken into account in the parameterisation of mixing in the ocean.

Моделирование траектории струи огнетушащего средства из пожарного лафетного ствола при возмущающих воздействиях

One of the important stages in the development of fire safety systems and determining the area of efficient fire extinguishing of robotic fire extinguishing installations using remotely controlled fire monitors is a calculation of the trajectory of the fire extinguishing agent jet. In the absence of disturbing influences, the jet trajectory is well described by mathematical models built based on the empirical data. However, in the presence of wind action in open space and automatic control mode, significant disturbing factors are introduced into the calculation of the jet trajectory, which make it difficult to construct the required trajectory of the fire extinguishing agent. To solve this problem, the algorithms were developed to simulate the movement of a jet under disturbing influences using the methods of computational fluid dynamics and verification based on the results of field tests. Algorithms of the computational fluid dynamics based on numerical methods for solving the equations of gas-hydrodynamics of flows (equations of conservation of energy, momentum, continuity, state, etc.) allow to model the corresponding processes with high accuracy. Based on the simulation results, the jet trajectory was obtained, and its comparison with the results of field experiments indicates that the use of computational fluid dynamics methods in particular the k–ε model (mass density and turbulence kinetic energy dissipation rate) allows to describe the jet trajectory from the fire monitor with a sufficiently high accuracy under disturbing influences. The obtained calculation methods can be used in the development of algorithms for automatic control of fire robots operating under wind load conditions, including for solving the problem of determining its identification by the deviation of the jet from the calculated trajectory.

Impact of Cloud-Base Turbulence on CCN Activation: CCN Distribution

Abstract Following our previous investigation of the turbulence impact on cloud-base single-size CCN activation, this study considers a similar problem assuming CCN size distribution obtained from field measurements. The total CNN concentration is taken as either 200 cm−3 to represent clean conditions, or as 2000 cm−3 to represent polluted conditions. CCN is assumed to be sodium chloride. The CCN activation in the rising nonturbulent adiabatic parcel is contrasted with the activation within a rising adiabatic parcel filled with inertial-range homogeneous isotropic turbulence. The turbulent parcel of 643 m3 and the turbulent kinetic energy dissipation rate of 10−3 m−2 s−3 are used in most of the simulations. Results for a range of mean parcel ascent rates, between 0.125 and 8 m s−1, are discussed. Overall, the adiabatic turbulent parcel simulations show results consistent with the adiabatic nonturbulent parcel, with higher activated CCN concentrations for stronger parcel ascent rates. The key difference is a blurriness of the separation between dry CCN size bins featuring activated and nonactivated (haze) CCN, especially for weak mean ascent rates. The blurriness comes from CCN getting activated and subsequently deactivated in the fluctuating supersaturation field, instead of all becoming cloud droplets above the cloud base. This leads to significantly larger spectral widths in turbulent parcel simulations compared to the nonturbulent parcel when activation is completed. Modeling results are discussed in the context of the impact of turbulent fluctuations on CCN activation documented in laboratory experiments using the Pi chamber.

Direct numerical simulations of a turbulent channel flow developing over convergent–divergent riblets

Direct numerical simulations of a turbulent channel flow developing over convergent–divergent (C–D) riblets at a Reynolds number of Reb=2800 are presented. It is found that, with a fixed normalized riblet height of h+=5, as the ratio of the riblet spacing and the height, s/h, increases from 2 to 10, the strength of the large-scale secondary flow motion Γ generated by the C–D riblets peaks around s/h=4 when the C–D riblets behavior lies between d- and k-type roughness. Compared to the baseline case with smooth walls, the turbulent activities and energy level increase significantly and peak at s/h=4 when Γ is the highest. It is shown that while the intense local turbulent kinetic energy (TKE) production occurring in the diverging region is caused by the high local velocity gradient due to the downwelling of the secondary flow, the strong local TKE production occurring in the converging region is caused by the high turbulent shear stress associated with upwelling. Furthermore, the TKE transport characteristics are significantly altered by the secondary flow motion, especially over the converging and diverging regions. The secondary flow is not caused by the local imbalance between turbulent kinetic energy production and dissipation but by the yawed riblets. It is then more appropriate to classify this flow as a Prandtl’s secondary flow of the first kind, also known as the geometry-driven secondary flow. Finally, in comparison with the baseline case, the drag increases for all the riblet cases examined, and a direct correlation between the amount of drag and intensity of the secondary flow exists, both peaking at s/h=4.

Turbulent kinetic energy evolution in turbulent boundary layers during head-on interaction of premixed flames with inert walls for different thermal boundary conditions

The statistical behaviour of turbulent kinetic energy, and its transport in turbulent boundary layers during premixed flame-wall interaction for isothermal and adiabatic chemically inert walls have been analysed using a Direct Numerical Simulation (DNS) database. The terms due to the mean velocity gradient (commonly known as the production term) and viscous dissipation remain leading order contributors to the turbulent kinetic energy transport when the flame is away from the wall, similar to that in the corresponding non-reacting turbulent boundary layer, but in addition to these terms, the pressure dilatation and pressure transport contributions play leading order roles when the flame interacts with the wall. It has been found that the gradient hypothesis-based Reynolds stress closures in the context of the k−ε model may yield an inaccurate prediction of the mean velocity gradient term due to the counter-gradient behaviour of Reynolds stresses in the premixed flame cases considered in this analysis. The thermal boundary condition at the wall does not have a major influence apart from a higher wall friction velocity for adiabatic boundary condition than in the case of isothermal boundary condition. The assumption of local equilibrium of production and dissipation of turbulent kinetic energy has been found to be rendered invalid when the flame is either near to the wall or interacting with the wall. This invalidates the conventional log-law for mean streamwise velocity variation, and the wall functions derived based on production-dissipation balance equipped by the usual gradient hypothesis in the context of the standard k−ε model for premixed flame-wall interaction in turbulent boundary layers. Therefore, improved wall functions are necessary for Reynolds averaged Navier-Stokes simulations of premixed flame-wall interaction in turbulent boundary layers.

Understanding of turbulence modulation and particle response in a particle-laden jet from direct numerical simulations

Abstract Point-particle direct numerical simulations have been employed to quantify the turbulence modulation and particle responses in a turbulent particle-laden jet in the two-way coupled regime with an inlet Reynolds number based on bulk velocity and jet diameter $({D_j})$ of ~10 000. The investigation focuses on three cases with inlet bulk Stokes numbers of 0.3, 1.4 and 11.2. Special care is taken to account for the particle–gas slip velocity and non-uniform particle concentrations at the nozzle outlet, enabling a reasonable prediction of particle velocity and concentration fields. Turbulence modulation is quantified by the variation of the gas-phase turbulent kinetic energy (TKE). The presence of the particle phase is found to damp the gas-phase TKE in the near-field region within $5{D_j}$ from the inlet but subsequently increases the TKE in the intermediate region of (5–20)Dj. An analysis of the gas-phase TKE transport equation reveals that the direct impact of the particle phase is to dissipate TKE via the particle-induced source term. However, the finite inertia of the particle phase affects the gas-phase velocity gradients, which indirectly affects the TKE production and dissipation, leading to the observed TKE attenuation and enhancement. Particle response to the gas-phase flow is quantified. Particles are found to exhibit notably stronger response to the gas-phase axial velocity than to the radial velocity. A new dimensionless figure is presented that collapses both the axial and radial components of the particle response as a function of the local Stokes number based on their respective integral length scales.

The effect of tilt on turbulent thermal convection for a heated soap bubble

We use direct numerical simulation (DNS) to explore the effect of tilt on two-dimensional turbulent thermal convection on a half-soap bubble that is heated at its equator. In the DNS, the bubble is tilted by an angle δ∈[0°,90°], the Rayleigh number is varied between Ra∈[3×106,3×109], and the Prandlt number is fixed at Pr = 7. The DNS reveals two qualitatively different flow regimes: the dynamic plume regime (DPR) and the stable plume regime (SPR). In the DPR, small dynamic plumes constantly emerge from random locations on the equator and dissipate on the bubble. In the SPR, the flow is dominated by a single large and stable plume rising from the lower edge of the bubble. The scaling behavior of the Nusselt number Nu and Reynolds number Re is different in these two regimes, with Nu∝Ra0.3 for the DPR and Nu∝Ra0.24 for the SPR. Concerning Re, the scaling in the DPR lies between Re∝Ra0.48 and Re∝Ra0.53 depending on Ra and δ, while in the SPR, the scaling lies between Re∝Ra0.44 and Re∝Ra0.45 depending on δ. The turbulent thermal and kinetic energy dissipation rates (εT′ and εu′, respectively) are also very different in the DPR and SPR. The probability density functions (PDF) of the normalized log εT′ and log εu′ are close to a Gaussian PDF for small fluctuations but deviate considerably from a Gaussian at large fluctuations in the DPR. In the SPR, the PDFs of normalized log εT′ and log εu′ deviate considerably from a Gaussian PDF even for small values. The globally averaged thermal energy dissipation rate due to the mean temperature field was shown to exhibit the scaling ⟨ε⟨T⟩⟩B∝Ra−0.23 in the DPR and ⟨ε⟨T⟩⟩B∝Ra−0.28 in the SPR. The globally averaged kinetic energy dissipation rate due to the mean velocity field is shown to exhibit the scaling ⟨ε⟨u⟩⟩B∝Ra−0.47 in the DPR (the exponent reduces from 0.47 to 0.43 as δ is increased up to 30°). In the SPR, the behavior changes considerably to ⟨ε⟨u⟩⟩B∝Ra−0.27. For the turbulent dissipation rates, the results indicate the scaling ⟨εT′⟩B∝Ra−0.18 and ⟨εu′⟩B∝Ra−0.29 in the DPR. However, the dependencies of ⟨εT′⟩B and ⟨εu′⟩B on Ra cannot be described by power-laws in the SPR.

Effect of swirling addition on the liquid mixing performance in a T-jets mixer

Swirling addition to the stream is beneficial for the fluid mixing. This work aims to study the mixing process intensification in a conventional T-jets mixer by the swirling addition. After experimental verification by the planar laser-induced fluorescence technique, large eddy simulation with the dynamic kinetic energy sub-grid stress model is used to predict how the swirling strength (in terms of swirling number, S w ) and swirling directions affect the mixing performance, e.g . the tracer concentration distribution, mixing time, and turbulent characteristics in the T-jets mixers. Predictions show that the swirling strength is the key factor affecting the mixing efficiency of the process. The overall mixing time, τ 90 , can be significantly reduced by increasing S w . Vortex analysis shows that more turbulent eddies appear in the collision zone and the turbulent kinetic energy dissipation rate increases obviously with the swirling addition. When S w is kept constant, the mixing process can be accelerated and intensified by adding swirling to only one stream, to both streams with the opposite swirling directions, or to both streams with the same swirling directions. Amplification of the mixing process by enlarging the mixer size or increasing the flow rates is also optimized. Thus, this work provides a new strategy to improve the mixing performance of the traditional T-jets mixers by the swirling addition.

Impacts of Instrumented Bottom Frame on Flow and Turbulence Measurements

Abstract A series of laboratory experiments are carried out to demonstrate the impacts of instrumented bottom frame legs on flow and turbulence. The magnitudes of vertical velocity, turbulent kinetic energy, dissipation, and shear stress induced by the frame legs depend on several factors, including the diameter and number of the frame legs, distances between the legs and the observational location, and the magnitude of the incoming flow and its direction with respect to the layout of the frame. In situ observations were carried out near the mouth of the Yellow River using two acoustic Doppler velocimeters mounted on a bottom frame. The estimated vertical velocity and turbulent kinetic energy dissipation rate show a significant asymmetry with flood and ebb tidal flows. This asymmetry can be partly explained by the influences of the bottom frame legs. Finally, the design and deployment principles of bottom frames are discussed for the purpose of reducing the impacts of the frame legs. Significance Statement Instrumented bottom frames are widely used for observations in the oceanic bottom boundary layer and above. However, the impacts of frame legs on the observed flow and turbulence have rarely been investigated. A series of laboratory experiments demonstrate that frame legs can induce vertical flow and enhanced turbulence, and the magnitudes of these influences vary with the size and layout of the frame legs and the magnitude and direction of the background flow. The results of the laboratory experiments can partially explain an “asymmetry” behavior of the vertical flow and turbulent kinetic energy with the flood and ebb tidal flows, derived from in situ observations near the mouth of the Yellow River.

An experimental Stommel Retention Zone facility with an application to oil droplet dispersion

AbstractStommel Retention Zones (SRZs) associated with wind‐driven Langmuir circulation (LC) facilitate the subsurface retention of particles and thus affect processes such as oil spill dispersion, sediment suspension, oil–particle aggregation, and plankton distribution. Since the effect of SRZs on these processes is difficult to study in the field, we present a novel laboratory facility designed to recreate the counterrotating vortex pair flow pattern associated with small‐scale SRZs of various strengths in two dimensions (2D). We then inject an oil jet into this facility to study buoyant oil droplet retention in these SRZs. 2D particle image velocimetry and hybrid Reynolds‐averaged Navier–Stokes/large eddy simulation are used to characterize the flow. Large‐scale oil droplet trajectories in the SRZs are visualized, and oil droplet statistics in the downwelling region and vortex core are measured using high‐magnification brightfield imaging and a droplet detection algorithm. Values of maximum velocity (7.7–32.2 mm s−1), turbulent kinetic energy (10−6 to 10−4 m2 s−2), and turbulent kinetic energy dissipation rate (10−7 to 10−5 m2 s−3) in the downwelling region of the facility fall within the range of values observed in the field. Flow field strength strongly influences oil droplet trajectories, the shape and size of the SRZ, and oil droplet statistics over time, with stronger flows retaining larger oil droplets in the downwelling region over longer periods of time. Indeed, droplets of almost 400 μm diameter are observed in the downwelling region after almost 10 min for the strongest flow. The facility may be used to study the behavior of microplastics, sediments, and zooplankton in LC in the future.

Effects of barotropic tides and ocean stratification on the generation and propagation of internal solitary waves in the deep south Andaman Sea

The Andaman Sea is one of the sea areas with the most internal solitary waves (ISWs) observed in the world and an ideal experimental site for studying the generation and propagation characteristics of ISWs. In this paper the generation and propagation characteristics of the ISWs in the deep south Andaman Sea are investigated based on the results of Massachusetts Institute of Technology General Circulation Model (MITgcm) numerical models. The reliability of the model is verified. The sea surface current gradient of 3D model is consistent with Terra MODIS and Sentinel-1A SAR remote sensing images. The turbulent kinetic energy dissipation rate of 2D model is also consistent with in-situ mooring measurements in other sea areas. The variation of temperature, energy and current field caused by barotropic tides and oceanic stratification are analyzed and compared. The results show that ISWs cannot be generated directly by the individual diurnal tides in our 2D model, and ISWs are mainly generated by the semidiurnal tides in the deep south Andaman Sea. Ocean stratification affects the waveform, the velocity and the generation position of ISWs. ISWs are easier to form in the hot season because of a larger Ursell number and stronger nonlinearity.

Numerical Prediction of Turbulent Drag Reduction with Different Solid Fractions and Distribution Shapes over Superhydrophobic Surfaces

The exploration of superhydrophobic drag reduction has been and continues to be of significant interest to various industries. In the present work, direct numerical simulation (DNS) is utilized to investigate the effect of the parameters on the drag-reducing performance of superhydrophobic surfaces (SHS). Simulations with a friction Reynolds number of 180 were carried out at solid fraction values of ϕs=116,111, and 14, and three distribution shapes: aligned, staggered, and random. The top wall is the smooth one, and the bottom wall is a superhydrophobic surface (SHS). Drag reduction and Reynolds stress profiles are compared for all cases. The turbulent kinetic energy budget, including production, dissipation, and diffusion, is presented with respect to the solid fraction and type of distribution to investigate the drag reduction mechanism. The sizes of the longitudinal vortices and formation of hairpin vortices are investigated through the observation of coherent structures. The simulation of a post model is a useful method to study the drag reduction for different solid fraction values and distribution geometries. Our study demonstrates that the drag reduction could acquire 42% with the solid fraction value ϕs=116 and an aligned distribution shape for post superhydrophobic surface geometry. Our study also showed the relationship of the Reynolds stress component (R11, R22, and R33) to the drag reduction with the differences in the solid fraction values and distribution geometry. In which, the R11 component has the most change between an aligned distribution and a random one. The peak value of R11 tends to shift away from the SHS wall. In addition, the analysis of the TKE budget over the superhydrophobic surface was performed, which can be adopted as a useful resource in turbulence modeling based on RANS methodology.

An evaluation of vertical mixing parameterization of ocean boundary layer turbulence for cohesive sediments

Accurate parameterization for both diffusivity and turbulent kinetic energy (TKE) dissipation rate is important for the simulation of reactive tracers such as cohesive sediments. We implemented a second-order closure parameterization for mixing in ocean surface boundary layer in the Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) model. The parameterization is more suitable than the existing parameterizations in the COAWST model for the modeling of cohesive sediments: It includes the wave-driven Langmuir turbulent effect, a more complete pressure strain covariance parameterization in the eddy viscosity and diffusivity, and also TKE dissipation rate. Solutions using a one-dimensional configuration are compared to solutions using a three-dimensional model that simulates the ocean surface boundary layer turbulence and size distributions of flocs of different sizes. The result shows that the simulation using the newly implemented parameterization reproduces fairly well the profiles of vertical eddy viscosity, TKE dissipation rate, total mass concentration of suspended sediment, and mass averaged settling velocity in wave-driven Langmuir turbulence. The water depth dependence of floc size distribution is also reproduced in the one-dimensional model. In addition, the result based on the standard k − ω model mostly underestimates (up to ∼90%) the averaged settling velocity of suspended sediments in the water column. The result also suggests that misrepresentation of Langmuir turbulence effect in vertical mixing parameterization could cause substantial biases in the forecast/hindcast transport model for cohesive sediment.

Some new insights for inferring diapycnal (irreversible) diffusivity in stably stratified turbulence

New insight for inferring diapycnal diffusivity in stably stratified turbulent flows is obtained based on physical scaling arguments and tested using high-resolution direct numerical simulation data. It is shown that the irreversible diapycnal diffusivity can be decomposed into a diapycnal length scale that represents an inner scale of turbulence and a diapycnal velocity scale. Furthermore, it is shown that the diapycnal length scale and velocity scale can be related to the measurable Ellison length scale (LE) that represents outer scale of turbulence and vertical turbulent velocity scale (w′) through a turbulent Froude number scaling analysis. The turbulent Froude number is defined as Fr=ε/Nk, where ε is the rate of dissipation of turbulent kinetic energy, N is the buoyancy frequency, and k is the turbulent kinetic energy. The scaling analysis suggests that the diapycnal diffusivity Kρ∼w′LE in the weakly stratified regime (Fr >1) and Kρ∼(w′LE)×Fr for the strongly stratified regime (Fr <1).

The Statistics of Oceanic Turbulence Measurements. Part I: Shear Variance and Dissipation Rates

Abstract An empirically derived statistic is used to estimate the confidence interval of a dissipation estimate that uses a finite amount of shear data. Four collocated shear probes, mounted on a bottom anchored float, are used to measure the rate of dissipation of turbulence kinetic energy ϵ at a height of 15 m above the bottom in a 55 m deep tidal channel. One pair of probes measures ∂w/∂x while the other measures ∂υ/∂x, where w and υ are the vertical and lateral velocity. The shear-probe signals are converted into a regularly resampled space series to permit the rate of dissipation to be estimated directly from the variance of the shear using (and similarly for the υ component), for averaging lengths, L ranging from 1 to 104 Kolmogorov lengths. While the rate of dissipation fluctuates by more than a factor of 100, the fluctuations of the differences of between pairs of probes are stationary, zero mean, and distributed normally for averaging lengths of L = ∼30 to 104 Kolmogorov lengths. The variance of the differences, , scales as L−7/9, independent of stratification for buoyancy Reynolds numbers larger than ∼600, and for dissipation rates from ∼10−10 to ∼10−5 W kg−1. The variance decreases more slowly than L−1 because the averaging is done in linear space while the variance is evaluated in logarithmic space. This statistic provides the confidence interval of an ϵ estimate such as the 95% interval . This result also applies to the traditional ϵ estimates that are made by way of spectral integration, after L is adjusted for the truncation of the shear spectrum. Significance Statement The results reported here can be used to estimate the statistical uncertainty of a dissipation estimate that is derived from a finite length of turbulence shear data.

Bubble-Turbulence Dynamics and Dissipation Beneath Laboratory Breaking Waves

Abstract Bubbles directly link sea surface structure to the dissipation rate of turbulence in the ocean surface layer through wave breaking, and they are an important vehicle for air–sea transfer of heat and gases and important for understanding both hurricanes and global climate. Adequate parameterization of bubble dynamics, especially in high winds, requires simultaneous measurements of surface waves and breaking-induced turbulence; collection of such data would be hazardous in the field, and they are largely absent from laboratory studies to date. We therefore present data from a series of laboratory wind-wave tank experiments designed to observe bubble size distributions in natural seawater beneath hurricane conditions and connect them to surface wave statistics and subsurface turbulence. A shadowgraph imager was used to observe bubbles in three different water temperature conditions. We used these controlled conditions to examine the role of stability, surface tension, and water temperature on bubble distributions. Turbulent kinetic energy dissipation rates were determined from subsurface ADCP data using a robust inertial-subrange identification algorithm and related to wind input via wave-dependent scaling. Bubble distributions shift from narrow to broadbanded and toward smaller radius with increased wind input and wave steepness. TKE dissipation rate and shear were shown to increase with wave steepness; this behavior is associated with a larger number of small bubbles in the distributions, suggesting shear is dominant in forcing bubbles in hurricane wind-wave conditions. These results have important implications for bubble-facilitated air–sea exchanges, near-surface ocean mixing, and the distribution of turbulence beneath the air–sea interface in hurricanes. Significance Statement Bubbles are a vehicle for the flux of heat, momentum, and gases between the atmosphere and ocean. These fluxes contribute to the energy budgets of hurricanes, climate, and upper-ocean biology. Few to no simultaneous measurements of surface waves, bubbles, and turbulence have been made in hurricane conditions. To improve numerical model representation of bubbles, we performed laboratory experiments to parameterize bubble size distributions using physical variables including wind and waves. Bubble distributions were found to become broadbanded and shift toward smaller radius with increased wind stress and wave steepness. Turbulence dissipation rate and shear were shown to increase with wave steepness. Our results give the first physically based bubble distribution parameterization from naturally breaking waves in hurricane-force conditions.

Effects of abundance, water temperature and light on the turbulence and mixing generated by fish schools of different sizes in quiescent water in a laboratory

The turbulence and mixing generated by schools of three fish species, namely koi, pangasius, and goldfish, were quantified in a series of controlled laboratory experiments. The effects of fish abundance, light, and water temperature on the turbulence parameters of the flow produced by the three fish species in a quiescent background were investigated by measuring the velocity field using acoustic Doppler velocimetry. It was observed that the turbulent flow was approximately homogeneous and isotropic and had low-mean velocities. The results show that increasing fish abundance and body size, dimming the ambient light, and increasing the water temperature increase the root-mean-square velocity, the integral time scale, and the rate of dissipation of turbulent kinetic energy. Consequently, fish abundance and body size, as well as environmental parameters, can influence fish-generated turbulence. To further quantify turbulent mixing, the dissipation rate, the mixing efficiency, and the vertical eddy diffusivity were extrapolated for the three fish species at their natural abundances. The dissipation rate of O(10-7-10-6) W/kg, the mixing efficiency of O(10-2-10-1), and the vertical eddy diffusivity of O(10-4) m2/s were estimated. These values are within the range of those of the physical sources. This demonstrates that the contribution of aquatic animals to the turbulent mixing of water environments may be significant, at least locally" to the end of the sentence so that it reads: "mixing of water environments may be significant, at least locally. Furthermore, the dissipation rate and eddy diffusivity are found to increase with the Reynolds numbers of aquatic species.

Numerical analysis of key structural parameters of ejector for PEMFC system under low power conditions

In this study, a three-dimensional numerical model of an ejector is established, which is based on a 40 W power proton exchange membrane fuel cell (PEMFC) system. Computational Fluid Dynamics (CFD) technique is used to analyze the ejector in low power condition. The effects of two key structural parameters (distance from the mixing chamber to the nozzle and the mixing chamber diameter) on the ejector performance at different currents are investigated. It is found that ejector entrainment ratio changes slightly with the distance from mixing chamber to nozzle. The ejector entrainment ratio increases first and then decreases with the mixing chamber diameter. Moreover, with the increase of mixing chamber diameter, the turbulent kinetic energy and turbulent dissipation rate decrease obviously.

Turbulence parameters measured by the Beijing mesosphere–stratosphere–troposphere radar in the troposphere and lower stratosphere with three models: comparison and analyses

Abstract. Based on the quality-controlled observational spectral width data of the Beijing mesosphere–stratosphere–troposphere (MST) radar in the altitudinal range of 3–19.8 km from 2012 to 2014, this paper analyses the relationship between the proportion of negative turbulent kinetic energy (N-TKE) and the horizontal wind speed and the vertical shear of horizontal wind domain and gives the distributional characteristics of atmospheric turbulence parameters obtained by using different calculation models. Three calculation models of the spectral width method were used in this study – namely the H model (Hocking, 1985), N-2D model (Nastrom, 1997) and D–H model (Dehghan and Hocking, 2011). The results showed that the proportion of N-TKE in the H model, N-2D model and D–H model increases with the horizontal wind speed u and/or the vertical shear of horizontal wind speed ∂u∂z, and the maximum values are 60 %, 45 % and 35 %, respectively. When the∂u∂z is greater than 0.006 s−1, the N-TKE of the H model increases sharply with ∂u∂z; the increase rate is about 20%0.002s-1. For these three models, the results are similar except that the vertical shear of the horizontal wind speed is greater than 0.006 s−1. When ∂u∂z>0.006 s−1, the proportion of N-TKE in the N-2D and H models increases with ∂u∂z, while the proportion in the D–H model is less than 10 % and has slight variation. However, it is still necessary to consider the applicability of the N-2D model and D–H model in some weather processes with strong winds. The distributional characteristics with height of the turbulent kinetic energy dissipation rate ε and the vertical eddy diffusion coefficient Kz derived by the three models are consistent with previous studies. Still, there are differences in the values of turbulence parameters. Also, the range resolution of the radar has little effect on the differences in the range of turbulence parameters' values. The median values of ε in the H model, N-2D model and D–H model is 10−3.2–10−2.7, 10−3.0–10−2.6 and 10−3.3–10−2.8 m2 s−3, respectively. The median values of Kz in these three models are 100.3–100.7, 100.4–100.7 and 100.1–100.5 m2 s−1.