Kinetic Energy Dissipation Rate Research Articles

Buoyancy Flux and Mixing Efficiency from Direct, Near-Bottom Turbulence Measurements in a Submarine Canyon

Abstract Turbulent kinetic energy and thermal variance dissipation rates ϵ and χ, buoyancy flux Jb, diffusivity κρ, and mixing coefficient , which is simply related to the mixing efficiency , are estimated from highly resolved microstructure measurements collected in a submarine canyon that has been previously shown to be experiencing near-bottom diapycnal upwelling. It is demonstrated that turbulence arises primarily from the convective instability of the internal tide. Twelve tidally resolving stations (12–48 h long) were conducted, wherein profiles were collected from between 5–15 m and 400 m above the bottom every 13–15 min using a custom turbulence vehicle. Turbulent buoyancy flux is estimated using the Osborn and Winters and D’Asaro methods, allowing direct estimation of the mixing coefficient as a function of time, temperature, and height above bottom. Turbulent dissipation and buoyancy flux generally increase toward the seafloor. The associated turbulent diapycnal diffusivity is 10−4–10−2 m2 s−1. Observed is ∼0.2 ± 0.05 near the top of our measurement range, as expected in the ocean interior, and increases to 0.3–0.7 approaching the bottom, consistent with turbulence generated by convective instability. Significance Statement We report detailed direct turbulence measurements very close to the seafloor in a submarine canyon that are well resolved enough in time to confidently understand the processes responsible for the turbulence. We compute the fraction of turbulent power that goes toward mixing, which is an important quantity to understand the role of turbulence in supporting the ocean’s large-scale circulation.

MicroRiYo : An observing system for deep repeated profiles of kinetic energy dissipation rates from shear-microstructure turbulence along a mooring line

Abstract A new observing system that provides deep repeated profiles of the oceanic kinetic energy dissipation rate and small-scale mixing is presented. The system is designed to provide 300 dissipation rate profiles using a vehicle that cycles along a mooring line from the sub-surface down to a maximum depth of 4000 m. The system was tested for two weeks between 630 and 1700 m during a cruise that took place on the Lucky Strike segment of the Mid-Atlantic Ridge. The vehicle collected 35 profiles at a mean downcast velocity of 0.63 m s−1. To quantify the quality of the measurements, profiles from the mooring are compared with nearby profiles from an autonomous microstructure free-falling instrument. The dissipation rate noise level varies between O(10−10) and O(10−9) W kg−1. This noise level is low enough to detect turbulent patches at depth. The largest dissipation rate measured at this site was O(10−7) W kg−1.

Microstructures along the Indian west-coast continental shelf: layering and vertical mixing

During the month of October, the West Indian Coastal Current (WICC) is in a stage of transition from equatorward to poleward flow. The sea surface salinity near the Indian Coast is lower in the south compared to the north. Whereas the sea surface temperature is higher in the north than in the south. A salinity maximum (SM, Salinity ≥ 35.7 psu) exists in the sub-surface between depth ranges of 50–80 m. In situ vertical microstructure profiles collected along the continental shelf off the West Coast of India (WCI) for the first time, are used in this study to characterize vertical mixing under these complex thermodynamic regimes. Estimated sectional mean (median) values of the dissipation rates of turbulent kinetic energy (ɛ) and thermal variance (χ) are in the range 10−9−10−8 (10−9−10−8) W kg−1 and 10−8−10−7 (10−9−10−8) °C2 s−1 respectively. Sectional mean (median) values of the diapycnal diffusivity (Kρ) and eddy thermal diffusivity (KT) are in the range 10−6−10−5 (10−6−10−5) m2 s−1 and 10−4−10−2 (10−6−10−4) m2 s−1, respectively. The barrier layer (BL) was observed at most of the measurement locations. The layering structures in the salinity profiles observed within BL indicate the phase of transition of halocline reformation. Experiments using a one-dimensional model suggest that this layering is caused by the mixing of surface freshwater (surface freshening caused by heavy rains) with mixed-layer water. Double diffusion with weak staircase structures in temperature and salinity is observed predominantly in the interior layer of the ocean in this region. The presence of SM at most stations, with its thickness decreasing from north to south, created conditions favorable for double-diffusive mixing. Signatures of salt fingering (SF) and diffusive convection (DC) were observed in 40% and 8% of the water column, respectively. Turbulent mixing in the column below the mixed layer (ML) is weak (KT≤10−6 m2 s−1) to moderate (KT∼10−4 m2 s−1), with some highly turbulent intermittent regions (KT∼10−2 m2 s−1) conducive to DC. The data presented here show the prevalence of two mixing regimes in the vertical: (1) vertical mixing of freshwater (due to rain) with the ambient mixed layer water, and (2) small-scale double-diffusive mixing due to contrasting temperature–salinity gradients predominantly in the ocean’s interior layer (below the isothermal layer).

Keplerian turbulence in Taylor–Couette flow of dilute polymeric solutions

Turbulent flow induced by elastorotational instability in viscoelastic Taylor–Couette flow (TCF) with Keplerian rotation is analogous to a turbulent accretion disk destabilized by magnetorotational instability. We examine this novel viscoelastic Keplerian turbulence via direct numerical simulations (DNS) for the shear Reynolds number ( $Re$ ) ranging from $10^2$ to $10^4$ . The observed characteristic flow structure consists of penetrating streamwise vortices with axial length scales much smaller than the gap width, distinct from the classic centrifugally induced Taylor vortices, which have axial lengths of the gap width. These intriguing vortices persist for the wide $Re$ range considered and give rise to intriguing scaling behaviour in key flow quantities. Specifically, the characteristic axial length of the penetrating vortices is shown to scale as $Re^{-0.22}$ ; the angular momentum transport scales as $Re^{0.42}$ ; the kinetic and elastic boundary-layer thicknesses based on angular velocity and hoop stress near the inner cylinder wall scale as $Re^{-0.48}$ and $Re^{-0.49}$ , respectively. This implies that the viscoelastic Keplerian turbulence belongs to the classical turbulent regime of TCF with the Prandtl–Blasius-type boundary layer. Furthermore, we present an analytical relation between the viscous and elastic dissipation rates of kinetic energy and the angular momentum transport and in turn demonstrate its validity using our DNS data. This study has paved the way for future research to explore astrophysics-related Keplerian turbulence and angular momentum transport via the scaling relations of the analogous TCF of dilute polymeric solutions.

Local precursors to anomalous dissipation in Navier-Stokes turbulence: Burgers vortex-type models and simulation analysis

Anomalous dissipation is a mechanism to dissipate kinetic energy which is established by a sufficiently spatially rough velocity field. It implies that the rescaled mean kinetic energy dissipation rate becomes constant with respect to Reynolds number Re, the dimensionless parameter that characterizes the strength of turbulence, given that Re≫1. The present study aims at bridging this statistical behavior of high-Reynolds-number turbulence to one specific structural building block of fluid turbulence—local vortex stretching configurations which take in the simplest case the form of Burgers's classical vortex stretching model from 1948. We discuss the anomalous dissipation in the framework of Duchon and Robert for this analytical solution of the Navier-Stokes equations, apply the same analysis subsequently to a generalized model of randomly oriented Burgers vortices by Kambe and Hatakeyama, and analyze finally direct numerical simulation data of three-dimensional homogeneous, isotropic box turbulence in this respect. We identify local high-vorticity events in fully developed Navier-Stokes turbulence that approximate the analytical models of strong vortex stretching well. They correspond to precursors of enhanced anomalous dissipation. Published by the American Physical Society 2024

Bubble fragmentation in turbulent flow and the potential implications of shear structures for bubbles formed by breaking waves

Large bubbles (1–5 mm radius) are important in a wide range of situations, including air-sea gas transfer, aerosol production as they burst at water surfaces, and the aeration of liquids in bioreactors and other industrial processes. When rising through turbulent flow, these bubbles are commonly distorted and may fragment to form daughter bubbles if their radius exceeds the Hinze scale (at which the restoring force due to surface tension is equal to the forces causing bubble distortion). Here, we present the results of laboratory experiments with fragmentation resulting from bubbles rising through a sheared and turbulent flow. The effects of water temperature, surface tension, local shear rate, and viscous dissipation rate of turbulent kinetic energy were assessed. Passive acoustical methods produce robust measurements of bubble fragmentation processes, allowing for rapid data collection to generate large data sets. In our experiments, even for bubbles very close to the Hinze scale, the dominant fragmentation mechanism is the capillary-driven fragmentation of elongated bubble filaments. The probability distribution of daughter bubble sizes from a single fragmentation event was independent of temperature, surface tension, and rate of viscous dissipation of turbulent kinetic energy. The overwhelming majority of fragmentation events resulted in one very large and one very small bubble, even for Hinze-scale parent bubbles and low Weber numbers (We < 5.3). Our results suggest that in a turbulent flow, there may be a link between the shear induced by large scale structures and the size of the smallest bubbles produced underneath a breaking wave.

Observations of Elevated Mixing and Periodic Structures Within Diurnal Warm Layers

AbstractSurface drifters (SWIFTs) equipped with down‐looking high‐resolution acoustic doppler current profilers (ADCPs) were used to estimate the turbulent kinetic energy (TKE) dissipation rate within highly stratified diurnal warm layers (DWLs) in the Southern California Bight. Over a 10‐day period, five instances of DWLs were observed with strong surface temperature anomalies up to 3°C and velocity anomalies up to 0.3 m . Profiles of in the upper 5 m suggest turbulence is strongly modulated by the DWL stratification. Burst‐averaged (8.5 min) is stronger than predicted by law‐of‐the‐wall boundary layer scaling within the DWLs and suppressed below. Predictions for within the DWLs are improved by a shear‐production scaling using observed shear and linearly decaying turbulent stress. However, is still under‐predicted. Examination of the un‐averaged acoustic backscatter data suggests elevated is related to the presence of turbulent structures in the DWLs which span the layer height and strongly modulate TKE. Evolution in the bulk Richardson number each day suggests the DWLs become unstable to layer‐scale overturning and entrainment each afternoon, thus the turbulent structures may result from shear‐driven instability. This interpretation is supported by a conditional average of the data during a burst characterized by strongly periodic structures. The structures resemble high‐frequency internal waves with strong asymmetry in the along‐flow direction (steepening) which suggests they are unstable. Coincident asymmetric patterns in upwelling/downwelling and corresponding regions of strong vertical convergence/divergence suggest that both vertical transport and local TKE generation are plausible sources of elevated in the DWLs.

Can intense storms affect sinking particle dynamics after the North Atlantic spring bloom?

AbstractThe sinking of large particles (i.e., marine snow) has long been recognized as a key pathway for efficient particulate organic carbon (POC) export to the ocean interior during the decline of spring diatom blooms. Recent work has suggested that particles smaller than marine snow can also substantially contribute to POC export. However, a detailed characterization of small and large sinking particles at the end of blooms is missing. Here, we separately collected suspended and small and large sinking particles using Marine Snow Catchers and assessed their biogeochemical composition after the North Atlantic spring bloom in May 2021. During the 3 weeks of sampling, when four intense storms (maximum wind speeds 37–50 kt) created high turbulent kinetic energy dissipation rates and deepened the mixed layer, we observed two distinct sedimentation events. At first, sinking particles were dominated by small (diameter < 0.1 mm), slowly sinking ( 18 m d−1), particles rich in silica that carried a moderate POC flux (< 6 mmol C m−2 d−1) to 500 m depth. Once the storms ceased, the volume of large (diameter > 0.1 mm), fast‐sinking (> 75 m d−1), carbon‐rich marine snow aggregates (not fecal pellets) increased exponentially and POC fluxes at 100 m depth were more than fourfold greater (30 ± 12 mmol C m−2 d−1) than those during the previous event. The aggregates consisted of a mixed post‐bloom plankton community. Our data suggest that the storms shaped the timing, type, and magnitude of POC flux at the end of this spring phytoplankton bloom.

Gas Transfer Across Air‐Water Interfaces in Inland Waters: From Micro‐Eddies to Super‐Statistics

AbstractIn inland water covering lakes, reservoirs, and ponds, the gas exchange of slightly soluble gases such as carbon dioxide, dimethyl sulfide, methane, or oxygen across a clean and nearly flat air‐water interface is routinely described using a water‐side mean gas transfer velocity , where overline indicates time or ensemble averaging. The micro‐eddy surface renewal model predicts , where is the molecular Schmidt number, is the water kinematic viscosity, and is the waterside mean turbulent kinetic energy dissipation rate at or near the interface. While has been reported across a number of data sets, others report large scatter or variability around this value range. It is shown here that this scatter can be partly explained by high temporal variability in instantaneous around , a mechanism that was not previously considered. As the coefficient of variation in increases, must be adjusted by a multiplier that was derived from a log‐normal model for the probability density function of . Reported variations in with a macro‐scale Reynolds number can also be partly attributed to intermittency effects in . Such intermittency is characterized by the long‐range (i.e., power‐law decay) spatial auto‐correlation function of . That varies with a macro‐scale Reynolds number does not necessarily violate the micro‐eddy model. Instead, it points to a coordination between the macro‐ and micro‐scales arising from the transfer of energy across scales in the energy cascade.

Exploration of micro-miniature venturi pump for continuous glucose monitoring through interstitial fluid (ISF) extraction

Interstitial Fluid (ISF) is a naturally occurring body fluid that surrounds cells and tissues and contains certain markers useful for continuously monitoring glucose levels in the blood without constantly extracting it. Miniaturizing can reduce its cost and timescale. In this study, for continuous glucose monitoring the numerical analysis of a Polymethyl methacrylate (PMMA) based Micro-miniature venturi pump was carried out to extract Interstitial Fluid (ISF). The numerical study was carried out using COMSOL Multiphysics software by employing the k-ε turbulence model to obtain output as a vacuum at the throat of the pump. The micro-miniature venturi pump was numerically analyzed for several key parameters, including the dimensions of the throat, the convergent angle, and the divergent angle. This study obtained a minimum pressure of 49.41 kPa numerically and 70 kPa experimentally when an input pressure of 252 kPa of compressed air was given to the system. Further influence of turbulence kinetic energy and turbulence dissipation rate on throat pressure output have been notified. Notably, the pressure output reaches its minimum value of 49.41 kPa when the turbulent kinetic energy and the turbulent dissipation rate reach maximum values of 5.0 × 109 m2/s3 and 7000 m2/s2 respectively. As per the previous research findings, for continuous glucose monitoring through ISF extraction, a pressure level of 95 kPa is deemed adequate hence the designed micro-miniature venturi pump is suitable for this application.

Diagnosing tracer transport in convective penetration of a stably stratified layer

We use large-eddy simulations to study the penetration of a buoyant plume carrying a passive tracer into a stably stratified layer with constant buoyancy frequency. Using a buoyancy-tracer volume distribution, we develop a method for objectively partitioning plume fluid in buoyancy-tracer space into three regions, each of which corresponds to a coherent region in physical space. Specifically, we identify a source region where undiluted plume fluid enters the stratified layer, a transport region where much of the transition from undiluted to mixed fluid occurs in the plume cap and an accumulation region corresponding to a radially spreading intrusion. This method enables quantification of different measures of turbulence and mixing within each of the three regions, including potential energy and turbulent kinetic energy dissipation rates, an activity parameter and the instantaneous mixing efficiency. We find that the most intense buoyancy gradients lie in a thin layer at the cap of the penetrating plume. This provides the primary stage of mixing between plume and environment and exhibits a mixing efficiency around 50 %. Newly generated mixtures of environmental and plume fluid join the intrusion and experience relatively weak turbulence and buoyancy gradients. As the intrusion spreads radially, environmental fluid surrounding the intrusion is mixed into the intrusion with moderate mixing efficiency. This dominates the volume of environmental fluid entrained into the region containing plume fluid. However, the ‘strongest’ entrainment, as measured by the specific entrainment rate, is largest in the plume cap, where the most buoyant environmental fluid is entrained.

Modeling and Parametric Study of Spent Refractory Material Dissolution in an Aluminum Reduction Cell

Utilizing spent refractory material (SRM), generated after the overhaul of aluminum electrolytic cells, as a raw material for producing Al-Si alloys presents an efficient approach towards achieving full resource utilization of SRM. However, a bottleneck restricting this technology has become the dissolution of SRM. Based on the heat and mass transfer mechanism, the shrinkage core model of SRM particle dissolution was established. The effects of alumina concentration, silica concentration, electrolyte superheat, particle temperature, and turbulent kinetic energy dissipation rate on the mass dissolution rate and dissolution time of SRM particles were investigated. Calculation results and experimental data were compared to confirm the accuracy of the established model. The results show that by maintaining low alumina and silica concentrations, increasing the electrolyte superheat and particle preheating temperature, and increasing the electrolyte turbulent kinetic energy dissipation rate, SRM particles can dissolve faster. The dissolution of agglomerated particles is greatly influenced by the turbulent kinetic energy dissipation rate and superheat. The present research provides promising guidance for practical application in predicting particle dissolution time, controlling process parameters, and accelerating the dissolution of SRM particles.

Scaling the Diurnal Mixing/Mixed Layer Depth in the Tropical Ocean: A Case Study in the South China Sea

AbstractThe diurnal cycling of the surface mixing/mixed layer (ML) depth, air‐sea heat flux, and vertical profiles of the temperature and turbulent kinetic energy dissipation rate in the tropical central South China Sea was observed in summer (June 2017) and winter (January 2018). In the daytime, solar heating warmed and stabilized the ML, and the thickness of the ML can be well characterized by the Zilitinkevich scale as noted in previous studies. By contrast, in the nighttime the ML was deepened by convective turbulence generated by surface cooling. Guided by these observations, we have derived a simple scaling for the nighttime deepening of the ML by simplifying the classic Kraus‐Turner type model. We show that the variation of the ML depth can be scaled by a function of the wind speed, air‐sea heat flux and the temporal variation of the sea surface temperature, all of which are observable variables at the sea surface. It is found that the scaling works well in reproducing observed variations of the ML depth from hydrographic data. As such, this study advances our understanding of the response of the upper ocean to atmospheric forcing and provides a simple way for predicting the ML depth with solely surface observations.

Particle image velocimetry in the impeller of a centrifugal pump: Relationship between turbulent flow and energy loss

Turbulent flows play a dominant role in the operation of centrifugal pumps, which find widespread use in industrial settings and various aspects of human life. The dissipation rate of turbulent kinetic energy emerges as a key parameter within these devices, with its local values exerting a significant influence on centrifugal pump performance. Recent advances in particle image velocimetry (PIV) techniques have expanded the ability to analyze complex turbulent flows across a broad spectrum of scales. In this context, this paper aims to deepen our understanding of the turbulent flow field and its correlation with energy loss in centrifugal pump impellers. To achieve this, experiments were conducted using PIV on a transparent pump operating under different conditions. Statistics of the turbulent flow were then obtained from phase-ensemble averages of velocities, vorticity, turbulence production, and local dissipation of turbulent kinetic energy. To overcome the limited spatial resolution constraint of PIV, the large-eddy PIV (LES-PIV) method was employed to estimate the local dissipation rate. In this method, it is assumed that the motion of larger scales is measured by the PIV technique, while the smaller scales (unresolved scales) are modeled by a sub-grid scale model, calculated from the strain rate tensors obtained from the measured fields. Energy losses in the impeller were studied using two methodologies: (i) a conventional method based on power measurements, and (ii) an alternative approach based on the budget of turbulent kinetic energy. Our results reveal that turbulent loss caused by turbulence production is the main source of energy loss in the pump impeller, and it is particularly pronounced in low-flow operating conditions characterized by large-scale structures. On the other hand, in situations where flow rates exceed the best efficiency point (BEP) condition, the predominant flow structures are marked by small-scale features, mainly attributed to local dissipation of turbulence. Our findings clarify the characteristics of energy losses in centrifugal pump impellers and their relationship with the turbulent flow field, and, in addition, providing a methodology for calculating the local turbulent dissipation rate and its limitations when derived from PIV measurements.

The coupling of winds, ocean turbulence, and High Salinity Shelf Water in the Terra Nova Bay Polynya

The Terra Nova Bay (TNB) Polynya in the Western Ross Sea of Antarctica is a major producer of High Salinity Shelf Water (HSSW), a precursor to Antarctica Bottom Water (AABW). Processes occurring in and around the polynya can therefore effect change in the lower limb of overturning circulation in this region. Here, we use data from a densely-instrumented upper-ocean mooring, deployed for 1 year in a region of active HSSW formation within TNB, to examine the coupling of surface brine rejection and vertical mixing to katabatic wind forcing. We find a high correlation between salinity and winds during the wintertime HSSW production season at the mooring site, with a lag-response of 20 h in near-surface (∼47 m) salinity to winds measured at the nearby Automatic Weather Station (AWS) Manuela. Salinity and temperature measurements show a fully destratified water column by June, with a lag-response of near-seabed (∼360 m) salinity to near-surface salinity of just 5 h. Measurements of turbulent kinetic energy (TKE) dissipation rate (ɛ) from moored pulse-coherent acoustic Doppler current profilers (ADCPs) show general agreement with classic boundary layer scaling (BLS), and calculations of a vertical mixing timescale using the Obukhov length scale average to ∼2.5 h during austral winter, consistent with the 5-h lag time observed in the salinity data. Comparisons to data from concurrent mooring deployments along the southern boundary of TNB, as well as to previously published assessments of model simulations and data from Climatic Long-term Interaction for the Mass-balance in Antarctica (CLIMA) moorings, allow us to explore spatial variability in the coupling of winds and salinity across TNB and to speculate on possible HSSW circulation pathways.

Understanding the effect of Prandtl number on momentum and scalar mixing rates in neutral and stably stratified flows using gradient field dynamics

Recently, direct numerical simulations (DNS) of stably stratified turbulence have shown that as the Prandtl number ( $Pr$ ) is increased from 1 to 7, the mean turbulent potential energy dissipation rate (TPE-DR) drops dramatically, while the mean turbulent kinetic energy dissipation rate (TKE-DR) increases significantly. Through an analysis of the equations governing the fluctuating velocity and density gradients we provide a mechanistic explanation for this surprising behaviour and test the predictions using DNS. We show that the mean density gradient gives rise to a mechanism that opposes the production of fluctuating density gradients, and this is connected to the emergence of ramp cliffs. The same term appears in the velocity gradient equation but with the opposite sign, and is the contribution from buoyancy. This term is ultimately the reason why the TPE-DR reduces while the TKE-DR increases with increasing $Pr$ . Our analysis also predicts that the effects of buoyancy on the smallest scales of the flow become stronger as $Pr$ is increased, and this is confirmed by our DNS data. A consequence of this is that the standard buoyancy Reynolds number does not correctly estimate the impact of buoyancy at the smallest scales when $Pr$ deviates from 1, and we derive a suitable alternative parameter. Finally, an analysis of the filtered gradient equations reveals that the mean density gradient term changes sign at sufficiently large scales, such that buoyancy acts as a source for velocity gradients at small scales, but as a sink at large scales.

Impingement of vortex dipole on heated boundaries and related thermal plume dynamics

The profound influence of an externally induced vortex dipole on thermal plume dynamics is numerically studied for varying Rayleigh numbers (Ra) employing the Bhatnagar–Gross–Krook collision model-based lattice Boltzmann method with a double distribution function approach. This study is extended to vortex dipole impingement with different types of heated bottom boundaries of two-dimensional domain, such as flat, “V-shaped,” and “inverted-V-shaped.” The vortex dipole impingement with the heated boundaries generates secondary vortices, which in turn produce vortex-driven thermal plumes, thereby advancing plume generation. The subsequent merging of the plumes enhances heat transport and leads to a continuous plume ascent. The presence of convex corners facilitates flow separation and also gives rise to the formation of secondary vortex dipoles, thereby significantly impacting the continuous generation of jet-like plumes when compared to concave configurations. The lack of an external vortex in pure buoyancy-driven flows produces less pronounced jet-like plumes and a relatively low Nusselt number. The boundary types and Ra significantly influence the vorticity production, resulting in higher enstrophy and palinstrophy for convex boundaries compared to flat and concave ones. A lower Prandtl number increases secondary vortices and corner rolls, leading to larger velocity gradients, higher thermal diffusivity, resulting in increased kinetic energy and thermal dissipation rates. The increased cell height enhances heat transfer at the top boundary due to improved heat convection from the slanted boundary and influence of early dipole impingement. Furthermore, kinetic energy dissipates in the dipole-driven flows and increases in the buoyancy-dominated flows.

Statistics of kinetic and thermal energy dissipation rates in vibrational turbulent Rayleigh–Bénard convection with rough surface

In this paper, the statistical properties of the kinetic εu and thermal εθ dissipation rates in two-dimensional (2D) turbulent Rayleigh–Bénard convection (RBC) are studied by using the thermal lattice Boltzmann method (LBM). A series of direct numerical simulations (DNS) are implemented in a square cell with the unit aspect ratio for the Rayleigh number Ra = 108 and Prandtl number Pr = 4.38. The roughness height h* and vary the vibration frequency ω* from 0 to 1000 are fixed in the vibrational RBC with rough plates to explore their effect on the kinetic and thermal dissipation rates. The global features indicate that the εu and εθ are more intense in the regions with high gradients of velocity and temperature, which is in good agreement with the previous work. The scalings of Nu∼ω *0.55±0.1 and Re∼0.59±0.2 are proposed between the ensemble averaged Nusselt number Nu and Reynolds number Re. The probability density functions (PDFs) of both logarithmic kinetic dissipation rate lg εu and thermal dissipation rate lg εθ are not conformed to the log-normal distributions. Through the analysis of the time-averaged εu and εθ vertical profiles, it is further demonstrated that the local dissipation rates from the boundary layer region are still the major contribution in the vibrational RBC with rough plates.

Mechanism of rapid settling algal flocs formation in a novel fluidized bed flocculator

Coagulation-sedimentation has been widely used for the emergency removal of harmful algal blooms (HABs). The technical challenge of how to construct special structured flocs in a targeted manner to achieve ideal settling performance remains unsolved, especially for algae with gas vesicles, such as Microcystis. In this study, a novel fluidized bed flocculator (FBF) was proposed to construct nearly spherical and compact algal flocs with its multi-stage velocity gradient flow field characteristics, thus enhancing the continuous sedimentation performance of Microcystis flos-aquae flocs, compared with a conventional mechanical stirring flocculator (MSF). The results revealed that the harvesting efficiency in the FBF reached 93 % after 30 s of settling at a dose of 30 mg L−1 FeCl3 and 1 mg L−1 PAM, whereas the efficiency in the MSF was only 47 %. Although the flocs generated in the FBF and MSF were similar in size, the former exhibited a settling velocity of 22.4 m h−1, which was 2.7 times higher than that of the latter. This difference can be attributed to the significantly higher fractal dimension of the flocs in the FBF (1.80) compared to the MSF (1.62). The settling velocity of the flocs was determined by both the floc size and fractal dimension, and flocs with large, compact and spherical shape structure yielded faster settling performance than small, loose, and multi-branched floc. The velocity, turbulent kinetic energy, and turbulent kinetic energy dissipation rate in the FBF decreased uniformly and gradually along the direction of floc formation, resulting in the formation of compact and spherical flocs and consequently rapid settling performance. This study may provide a novel solution for the rapid sedimentation of microalgae and enhance our understanding of the flow field characteristics required for an effective flocculator.

Statistics of kinetic and thermal energy dissipation rates in two-dimensional thermal vibrational convection

We investigate the statistical properties of kinetic ϵu and thermal ϵθ energy dissipation rates in two-dimensional (2D) thermal vibrational convection (TVC). Direct numerical simulations were conducted in a unit aspect ratio box across a dimensionless angular frequency range of 103≤ω≤107 for amplitudes 0.001≤a≤0.1, with a fixed Prandtl number of 4.38. Our findings indicate ϵu is primarily associated with the characteristics of the vibration force, while ϵθ is more related to the large-scale columnar structures. Both energy dissipation rates exhibit a power-law relationship with the oscillational Reynolds number Reos. ϵu exhibits a scaling relation as ⟨ϵu⟩V,t∼a−1Reos0.93±0.01, while ϵθ exhibits two distinct scaling behaviors, i.e., ⟨ϵθ⟩V,t∼a−1Reos1.97±0.04 for Reos<Reos,cr and ⟨ϵθ⟩V,t∼a−1Reos1.31±0.02 for Reos>Reos,cr, where the fitted critical oscillational Reynolds number is approximately Reos,cr≈80. The different scaling of ⟨ϵθ⟩V,t is determined by the competition between the thermal boundary layer and the oscillating boundary layer. Moreover, the probability density functions (PDFs) of both dissipation rates deviate significantly from the lognormal distribution and exhibit a bimodal shape. By partitioning the contributions from the boundary layer and bulk regions, it is shown that the bulk contributes to the small and moderate dissipation rates, whereas the high dissipation rates are predominantly contributed by the boundary layer. As Reos increases, the heavy tail of the PDFs becomes more pronounced, revealing an enhanced level of small-scale intermittency. This small-scale intermittency is mainly caused by the influence of BL due to vibration. Our study provides insight into the small-scale characteristics of 2D TVC, highlighting the non-trivial scaling laws and intermittent behavior of energy dissipation rates with respect to vibration intensity.