Turbulent Kinetic Energy Dissipation Research Articles

Experimental study of velocity and turbulence fields in a square mixer-settler tank: Comparison of shake the box PTV and 2D2C PIV

The characterization of flows in agitated vessels is essential for a good understanding of physical and chemical processes and to validate computational fluid dynamics code. The hydrodynamics of cylindrical vessels have been well studied at various scales, mostly in the turbulent regime, typically using particle image velocimetry (PIV). Studies of square tanks or at moderate Reynolds numbers are much rarer however, and 3D Shake-The-Box (STB) Lagrangian particle tracking has never been used in this context. The objective of the present work was to compare two-dimensional, two-component PIV (2D2C-PIV) and STB particle tracking in characterizing the hydrodynamics of a stirred 20 cm sided (8 L) square tank at Reynolds numbers ranging from 1700 to 4300. The velocity fields, velocity profiles, turbulent kinetic energy fields and turbulent kinetic energy dissipation rates obtained using the two approaches were compared. The velocity fields measured with the two methods were found to be in good agreement, except for a few discrepancies in the velocity profiles of the turbine discharge at 250 rpm. The dimensionless velocity profiles were similar above 100 rpm and indicated that the flow was turbulent at the Reynolds numbers considered. The turbulent kinetic energy fields obtained with the two approaches were globally similar, although with STB, the energy tended to be underestimated, especially in the jet discharge area. The STB method was also found to have lower spatial resolution and precision in measuring turbulent kinetic energy dissipation rates, a consequence of a too large interrogation window. Recommendations are proposed to improve the precision of STB measurements.

Turbulence spectra in natural and forced convection

Fourier spectra have been traditionally used to get insight into the flow structures of turbulence. In wall-bounded flows these are not reported usually in Kolmogorov units. In this paper the spectra are evaluated in these units to compare with the case of isotropic turbulence, to investigate at which distance from the wall flow isotropy is achieved. We have found that improvement of universality of the spectra in the near-wall region is achieved by evaluating the dissipative length scale from the total turbulence kinetic energy dissipation, rather than through the rate of isotropic dissipation as customary. The database of Lee and Moser [1] for flow in plane channel and of Pirozzoli et al. [2] for flow in a circular pipe have been considered. We have found similarities between pipe and channel flow up to a non-dimensional distance 0.2. Farther from the wall the spectra tend to become universal and similar to isotropic turbulence in channels, whereas the geometry of the circular pipe prevents universality. Large part of the paper is also focused on turbulent natural convection in rectangular enclosures. In that flow, comparison between velocity and temperature spectra allows to answer about possible differences in the slope of the inertial ranges. In this respect, the importance of the spectral bottleneck in the cascade of kinetic and thermal energy is stressed. The large amplitude of the bottleneck in the temperature spectra might be the cause for the k−4/3 spectral range observed at wall distances greater than the thermal boundary layer thickness, defined in terms of the maximum turbulent thermal energy production. Also in this flow evaluating the Kolmogorov length scale through the total dissipation yields better collapse of the spectral range with exponential decay on that of isotropic turbulence in the near-wall region. Flow visualisations and joint PDFs are used for deeper understanding of the complex physics of turbulent convection.

A turbulence data reduction scheme for autonomous and expendable profiling floats

Abstract. Autonomous and expendable profiling-float arrays such as those deployed in the Argo Program require the transmission of reliable data from remote sites. However, existing satellite data transfer rates preclude complete transmission of rapidly sampled turbulence measurements. It is therefore necessary to reduce turbulence data on board. Here we propose a scheme for onboard data reduction and test it with existing turbulence data obtained with a modified SOLO-II profiling float. First, voltage spectra are derived from shear probe and fast-thermistor signals. Then, we focus on a fixed-frequency band that we know to be unaffected by vibrations and that approximately corresponds to a wavenumber band of 5–25 cpm. Over the fixed-frequency band, we make simple power law fits that – after calibration and correction in post-processing – yield values for the turbulent kinetic energy dissipation rate ϵ and thermal-variance dissipation rate χ. With roughly 1 m vertical segments, this scheme reduces the necessary data transfer volume 300-fold to approximately 2.5 kB for every 100 m of a profile (when profiling at 0.2 m s−1). As a test, we apply our scheme to a dataset comprising 650 profiles and compare its output to that from our standard turbulence-processing algorithm. For ϵ, values from the two approaches agree within a factor of 2 87 % of the time; for χ, they agree 78 % of the time. These levels of agreement are greater than or comparable to that between the ϵ and χ values derived from two shear probes and two fast thermistors, respectively, on the same profiler.

Adjustments to the law of the wall above an Amazon forest explained by a spectral link

Modification to the law of the wall represented by a dimensionless correction function ϕRSL(z/h) is derived using atmospheric turbulence measurements collected at two sites in the Amazon in near-neutral stratification, where z is the distance from the forest floor and h is the mean canopy height. The sites are the Amazon Tall Tower Observatory for z/h∈[1,2.3] and the Green Ocean Amazon (GoAmazon) site for z/h∈[1,1.4]. A link between the vertical velocity spectrum Eww(k) (k is the longitudinal wavenumber) and ϕRSL is then established using a co-spectral budget (CSB) model interpreted by the moving-equilibrium hypothesis. The key finding is that ϕRSL is determined by the ratio of two turbulent viscosities and is given as νt,BL/νt,RSL, where νt,RSL=(1/A)∫0∞τ(k)Eww(k)dk, νt,BL=kv(z−d)u*, τ(k) is a scale-dependent decorrelation time scale between velocity components, A=CR/(1−CI)=4.5 is predicted from the Rotta constant CR=1.8, and the isotropization of production constant CI=3/5 given by rapid distortion theory, kv is the von Kármán constant, u* is the friction velocity at the canopy top, and d is the zero-plane displacement. Because the transfer of energy across scales is conserved in Eww(k) and is determined by the turbulent kinetic energy dissipation rate (ε), the CSB model also predicts that ϕRSL scales with LBL/Ld, where LBL is the length scale of attached eddies to z=d, and Ld=u*3/ε is a macro-scale dissipation length.

Turbulent kinetic energy dissipation rate and associated fluxes in the western tropical Atlantic estimated from ocean glider observations

Abstract. Ocean gliders enable us to collect the high-resolution microstructure observations necessary to calculate the dissipation rate of turbulent kinetic energy, ε, on timescales of weeks to months: far longer than is normally possible using traditional ship-based platforms. Slocum gliders have previously been used to this end; here, we report the first detailed estimates of ε calculated using the Batchelor spectrum method on observations collected by a FP07 fast thermistor mounted on a Seaglider. We use these same fast thermistor observations to calculate ε following the Thorpe scale method and find very good agreement between the two methods. The Thorpe scale method yields larger values of ε, but the average difference, which is less than an order of magnitude, is smaller than reported elsewhere. The spatio-temporal distribution of ε is comparable for both methods. Maximum values of ε (10−7 W kg−1) are observed in the surface mixed layer; values of approximately 10−9 W kg−1 are observed between approximately 200 and 500 m depth. These two layers are separated by a 100 m thick layer of low ε (10−10 W kg−1), which is co-located with a high-salinity layer of Subtropical Underwater and a peak in the strength of stratification. We calculate the turbulent heat and salt fluxes associated with the observed turbulence. Between 200 and 500 m, ε induces downward fluxes of both properties that, if typical of the annual average, would have a very small influence on the heat and salt content of the overlying salinity-maximum layer. We compare these turbulent fluxes with two estimates of double-diffusive fluxes that occur in regions susceptible to salt fingers, such as the western tropical Atlantic. We find that the double-diffusive fluxes of both heat and salt are larger than the corresponding turbulent fluxes.

Not All Clear Air Turbulence Is Kolmogorov—The Fine‐Scale Nature of Atmospheric Turbulence

AbstractWe study a strong clear air turbulence (CAT) event experienced by the German High‐Altitude Long‐Range research aircraft (HALO) during the Southern Hemisphere Transport, Dynamics, and Chemistry campaign. HALO encountered CAT leeward of the southern Andes Mountains, where tropospheric airflow favored vertically propagating mountain waves that were refracted southeastward into the core of tropopause jet. Turbulence is quantified using spectral quantities and structure functions computed from in situ 100 Hz flight level data. The detected CAT region exhibits strong patchiness, characterized by separated bursts in turbulent kinetic energy and energy dissipation rate. The high resolution in situ observations reveal different turbulent scaling within each patch, in both spectra and structure functions, and following Monin and Yaglom's conversion law. One patch follows power laws with exponents −1.71 ± 0.06, −1.771 ± 0.006, and −1.56 ± 0.05 for the velocity components w, v, and u, respectively, while another patch has exponents −2.17 ± 0.12, −2.50 ± 0.08, and −1.92 ± 0.09. These patches are mediated by a third patch with less clear scaling. While the patches can deviate from Kolmogorov scaling due to the anisotropy of the airflow, they still display evidence of CAT with enhanced energy dissipation rates.

Study on hydrodynamics characteristics in a gas-liquid stirred tank with a self-similarity impeller based on CFD-PBM coupled model

BackgroundIn general, radial impeller has been the most widely employed for the gas-liquid mixing process in the stirred tank. However, gas cavities are easy to form behind the impeller blades, which results in the waste of power consumption, the limited gas handling capacity of impeller and the poor dispersion of gas. Based on self-similarity property of nonlinear theory, a type of self-similarity impeller was employed to strengthen gas-liquid dispersion process in this work. MethodsThe hydrodynamics of gas-liquid dispersion process in a stirred tank with Rushton turbine and self-similarity impeller were comparatively investigated by computational fluid dynamics (CFD) simulation combined with a population balance model (PBM). The gas holdup distribution, gas cavities, relative power demand (RPD), bubble size distribution and turbulent intensity analysis in the gas-liquid dispersion process were predicted. Significant findingsResults showed that self-similarity impeller could destroy the gas cavity structure, reduce the negative pressure zone and gas accumulation, enhance the relative power demand (RPD) and improve the uniformity of gas holdup distribution compared with Rushton turbine, and the gas-liquid mixing efficiency can be further improved with the increase of the self-similar iteration number of self-similarity impeller. The proper increase of impeller speed was beneficial to overcome gas flooding and improve the gas-liquid two phase dispersion uniformity. The increase of gas flow rate obviously increased the gas holdup in liquid phase. Meanwhile, self-similarity impeller could increase the uniformity of bubble size compared with Rushton turbine, and increasingly so with the increase of self-similar iteration number of self-similarity impeller. The uniformity of bubble size was improved with the increase of impeller speed and was decreased with the increase of gas flow rate. In addition, self-similarity impeller could significantly enhance the turbulent intensity and turbulent kinetic energy dissipation rate by the jet flows through the concave-convex edges, which was beneficial to the gas dispersion process.

Anisotropic property of turbulent flow control through multiple stenosed microtubes

Rapid development in micro-scale systems and devices for drug delivery and biotechnical analysis has been scurrying. Microtube or microchannel roughness is another challenging factor in microfabrication technology. Moreover, the irregular roughness occurs due to the multiple depositions of cholesterol and other substances in the endothelium of the arterial wall. To investigate those issues, the effect of the irregular roughness of the wall on the anisotropy of the turbulent blood flow through an atherosclerotic artery has been analyzed. The flow through a stenosed microtube has been numerically simulated to understand the blood flow phenomenon through arterial stenosis and different turbulent states. The Reynolds stress components are estimated and plotted an invariant map and Eigen map to examine the turbulent states. The comparison results have been studied to show the nature of turbulent flow in low Reynolds numbers due to irregular roughness. The turbulent kinetic energy and turbulent viscous dissipation rate are also examined. Due to wall shear stress, the flow deserves the turbulence flow characteristic downstream of the abnormally narrowed regions of the microtube. The nature of the wall shear rate and the high viscosity of blood impact the disturbance in the flow velocity in microtubes.

Mixing in the upper western equatorial Pacific driven by westerly wind event

Diapycnal mixing in the upper western equatorial Pacific (WEP) plays an important role in the tropical air–sea interactions and in the formation of the global climate system. Yet, the WEP is uniquely rich in water masses originating from the two hemispheres and in multiscale processes of different dynamical nature, thus creating a complex regime of mixing remains to be fully characterized by elaborate observations. Here, on the basis of microstructure measurements in the WEP, we report the observations on a strong deep cycle turbulence extending well into the upper thermocline by westerly wind event, with the turbulent kinetic energy dissipation rate ε~O(10−8–10−7) W kg−1 and diapycnal diffusivity Kρ∼O(10−4) m2 s−1. Below the deep cycle turbulence layer, turbulence and mixing are generally weak with ε~O(10−10–10−9) W kg−1 and Kρ∼O(10−7–10−6) m2 s−1, a prototype of the weak mixing nature of the low-latitude western Pacific. The observed turbulence below the deep cycle turbulence layer can be satisfactorily scaled by either the MacKinnon–Gregg model or the Richardson number–based model with tuned model parameters.

On the dynamics of buoyant jets in a linearly stratified ambient

We report mean flow and turbulence characteristics of a buoyant jet evolving in a linearly stratified ambient with stratification strength N=0.4 s−1. The velocity and density fields are captured experimentally using simultaneous particle image velocimetry and planar laser-induced fluorescence technique. We report our findings by strategically choosing four axial locations such that it covers different flow regimes; namely, momentum-dominated region, buoyancy-dominated region, neutral buoyant layer, and plume cap region. The results at these axial locations are presented as a function of the radial co-ordinate to provide a whole field picture of the flow dynamics. From the mean axial velocity and density fields, it is seen that the velocity and the scalar (density) widths are of the same magnitude in the momentum-dominated region but show significant difference in the buoyancy-dominated region and beyond. It is also seen that the axial velocity for the buoyant jet is consistently higher than pure jet at different axial locations due to buoyancy-aided momentum. With the help of turbulent kinetic energy (TKE) budget analysis, it is seen that the shear production (P) and TKE dissipation (ϵ) for a buoyant jet are higher compared to the case of pure jet at different axial locations, cementing the role of buoyancy and stratification on the flow dynamics. Further, it is observed that the buoyancy flux (B) aids and destroys TKE intermittently in the radial direction, and it is at least O(102) smaller than P, ϵ, and the mean flow buoyancy flux (F). Finally, the relative strength of the turbulent transport of momentum to that of scalar in the radial direction is quantified using the turbulent Prandtl number, Prt. It is seen that Prt ≈1 upto the neutral buoyant layer and ≈ 0.6 in the plume cap region. The current set of results obtained from experiments are first of its kind and elucidates various aspects of the flow which hitherto remained unknown and will also prove to be useful in testing numerical simulations for buoyancy-driven flows.

Contribution of meteorological factors based on explainable artificial intelligence in predicting wind farm power production using machine learning algorithms

Wind fields are intermittent and nonlinear to meteorological factors and external environmental conditions. Statistical models have been proposed based on various approaches to precisely predict wind speed and energy production. However, determining the most suitable approach is challenging, regardless of the conditions. Currently, only wind speed, wind direction, temperature, atmospheric pressure, and humidity have been used as input features of models in most wind-power forecasting studies. However, few studies have described each feature's contribution to prediction performance when using meteorological factors, such as atmospheric stability and turbulence components, as input features. This study predicted the 10 min average power and daily energy production of a wind farm using four machine learning (ML) algorithms and 13 meteorological factors. The ultimate goal was to present the individual prediction contribution of meteorological factors using the Shapley additive explanations algorithm, which is an explainable artificial intelligence technique, based on the prediction results. Wind speed showed a dominant influence in the determination of energy production, followed by turbulent kinetic energy, turbulence intensity, and turbulence dissipation rate. Thus, insights into the detailed contribution of turbulence components to predict the performance facilitate the advancement of ML-based approaches, which can yield significant benefits in increasing the predictability of actual wind energy, thereby ensuring efficiency and stability in wind farm operations.

Removing Biases in Oceanic Turbulent Kinetic Energy Dissipation Rate Estimated from Microstructure Shear Data

Abstract To calculate a turbulent kinetic energy dissipation rate from the microstructure vertical shear of the horizontal velocity via a spectral analysis, shear spectra need first to be cleaned from vibrations of the moving vehicle. Unambiguously, this study shows that the spectral cleaning must be applied all over the frequency range and not only at frequencies larger than 10 Hz, as a recent study suggested. For a Vertical Microstructure Profiler (VMP-6000), not correcting for vehicle vibrations below 10 Hz leads to overestimated dissipation rates from 50% to 700% for usual downcast velocities and for weak dissipation rates (ε < 1 × 10−9 W kg−1). Vibrations concern all vehicles, but the exact vibrational frequency signature depends on the vehicle shape and its downcast velocity. In any case, a spectral cleaning over the whole frequency range is strongly advised. This study also reports on a systematic low bias of inferred dissipation rates induced by the spectral cleaning when too few degrees of freedom are available for the cleaning, which is usually the default of the standard processing. Whatever the dissipation rate level, not correcting for the bias leads to underestimated dissipation rates by a factor 1.4–2.7 (with usual parameters), the exact amplitude of the bias depending on the number of degrees of freedom and on the number of independent accelerometer axes used for the cleaning. It is strongly advised that such a bias be taken into account to recompute dissipation rates of past datasets and for future observations.

Widespread Intensified Pycnocline Turbulence in the Summer Stratified Yellow Sea

AbstractPycnocline mixing lies at the heart of seasonally stratified shelf sea systems, regulating vertical exchange of momentum, mass, heat, and biogeochemical constituents. Based on microstructure measurements in the summer of 2013 and 2017, here we report on the widespread occurrence of intensified pycnocline turbulence in the summer stratified Yellow Sea (YS). Large turbulent kinetic energy dissipation rates ∼ (10−7 W kg−1) and microscale thermal dissipation rates ∼ (10−6 K2 s−1) are found in the pycnocline below the depth of the strongest stratification at many sampling stations. Shipboard velocity measurements suggest that wind‐induced near‐inertial internal waves induced strong velocity shear; however, the calculated velocity shear peaked exactly at (instead of below) the strongest stratification layer and is generally not strong enough to trigger shear instabilities according to the Richardson number criterion. Example results at two repeated sampling stations clearly showed the presence of a low‐salinity water layer (with a thickness of 5–15 m), at the upper boundary of which salt fingering is expected to occur according to the Turner angle. The observed elevated and tended to occur in the salt‐finger‐favorable layers. Although the distribution of and reveals the relation with Turner angle, we further note the possible complexity in the driving mechanisms with the thermohaline‐shear instability potentially playing a role. Given the widespread nature of the intensified pycnocline turbulence, it is expected that this turbulence has important implications for nutrients cycling and thus the maintenance of primary productivity in the summer stratified YS.

Scaling of Moored Surface Ocean Turbulence Measurements in the Southeast Pacific Ocean

AbstractEstimates of turbulence kinetic energy (TKE) dissipation rate (ε) are key in understanding how heat, gas, and other climate‐relevant properties are transferred across the air‐sea interface and mixed within the ocean. A relatively new method involving moored pulse‐coherent acoustic Doppler current profilers (ADCPs) allows for estimates of ε with concurrent surface flux and wave measurements across an extensive length of time and range of conditions. Here, we present 9 months of moored estimates of ε at a fixed depth of 8.4 m at the Stratus mooring site (20°S, 85°W). We find that turbulence regimes are quantified similarly using the Obukhov length scale and the newer Langmuir stability length scale , suggesting that ocean‐side friction velocity implicitly captures the influence of Langmuir turbulence at this site. This is illustrated by a strong correlation between surface Stokes drift and that is likely facilitated by the steady Southeast trade winds regime. In certain regimes, , where is the von Kármán constant and is instrument depth, and surface buoyancy flux capture our estimates of well, collapsing data points near unity. We find that a newer Langmuir turbulence scaling, based on and , scales ε well at times but is overall less consistent than . Monin‐Obukhov similarity theory (MOST) relationships from prior studies in a variety of aquatic and atmospheric settings largely agree with our data in conditions where convection and wind‐driven current shear are both significant sources of TKE, but diverge in other regimes.

Laser beam scintillations of LIDAR operating in weak oceanic turbulence

The formulation of light detection and ranging (LIDAR) systems is derived and examined for the scintillation index, evaluated on-axis, of laser beams in horizontal links in the ocean with weak turbulence by utilizing the Rytov method. These scintillation indices, obtained for the Gaussian beam which is collimated, the limits of plane and spherical waves, are depicted versus the source size, target size, and parameter of the normalized reflector size. It is found that the source size, target size, and normalized reflector size parameter, lessening the scintillation index evaluated on-axis, are approximately 0.44 cm, 56 × 10 − 4 c m , and 2.2, respectively. Additionally, by using these values that minimize the scintillation index, the variation of the scintillations is shown against the propagation distance, radius of reflector, temperature and salinity fluctuation effects, mean squared temperature, and turbulent kinetic energy dissipation rate per unit mass of fluid at various selected source size and radius of reflector values.

Propagation properties of rotationally-symmetric power-exponent-phase vortex beam through oceanic turbulence

In this paper we explored the propagation characteristics of rotationally-symmetric power-exponent-phase vortex beam (RSPEPVB) through the oceanic turbulence. Based on the extended Huygens-Fresnel diffraction integral and the oceanic turbulence theory the theoretical model of RSPEPVBs propagating in oceanic turbulence was established. Then the propagation properties of RSPEPVBs were explored by numerical simulation and the influences of the propagation distance z the rate of dissipation of turbulence kinetic energy per unit mass of fluid ε the temperature-salinity contribution ratio ω and the dissipation rate of the mean-squared temperature χT were discussed. The results illustrated that the intensity of RSPEPVBs propagating through oceanic turbulence weakened and the size of RSPEPVBs diffused with the increasing distance and strong oceanic turbulence of larger values of parameters χT and ω and the smaller value of the parameter ε. Meanwhile the coherence of RSPEPVBs would decrease in stronger oceanic turbulence. Further an experimental setup was demonstrated to confirm that the RSPEPVBs will diffuse in strong oceanic turbulence which was strengthened with the rise of salinity and the increase of propagation distance. Contrarily with the increase of temperature the loss of RSPEPVBs mitigated and the intensity increased gradually. The obtained results may provide a potential application for optical underwater communication and imaging.

Bolus degeneration on uniform slopes

Shoaling internal solitary waves (ISWs) occur on nearly every coastline worldwide but are difficult to track between moorings as they shoal, fission into boluses and ultimately degenerate. In the present study, experiments in a 18 m long internal wave flume, measured the rate of dissipation of turbulent kinetic energy, as boluses shoaled, in order to parameterize the associated dissipation lengthscale. Dissipation was proportional to incident wave amplitude and wave Reynolds number, from 102 (lab) to 106 (coastal ocean). However, energetics calculations (wave energy/dissipation rate) failed to predict the dissipation lengthscale, which was empirically parameterized as a function of the wave Reynolds number (R2 = 0.84 to 0.96), the wave Froude number (R2 = 0.83) and the internal Iribarren number (R2 = 0.94). These parameterizations may be readily applied to oceanic mooring data, as they only require knowledge of the bulk incident wave properties and the bottom boundary slope. We found that shoaling ISWs propagate significantly further than boluses (∼10 times further in the lab and ∼100 times further in coastal ocean) and, therefore, it is important to distinguish these waveforms when computing dissipation lengthscales from observations.

Simultaneous In Situ Characterization of Turbulent Flocculation and Reactor Mixing Using Image Analysis and Particle Image Velocimetry in Unison

Floc characteristics, including their size distribution, mean size, and fractal dimension, are impacted by mixing intensity and duration, coagulant dosing method, dose, type, and pH. Herein, we directly employ flocs inherently generated during treatment to determine instantaneous velocity fields, which were further utilized to estimate local velocity gradients and turbulent kinetic energy dissipation (TKED) rates. This novel non-intrusive methodology, which combines particle image velocimetry (PIV) and an imagery-based sizing scheme, was examined through the characteristics of reactor mixing and flocculation from in situ measurements for conventional FeCl3 chemical coagulation and iron electrocoagulation (EC). Our first-of-its-kind procedure avoids the need to externally add artificial seeding particles for PIV analysis, automatically reducing the number of experiments, and simultaneously improves both accuracy and precision by linking fluid dynamics and particle characteristics with only a single experiment. The TKED rates estimated using flocs were largely similar with conventional artificial seeding at the early stage of flocculation when flocs were smaller. However, the new method is expected to estimate turbulence more accurately in the flocs’ microenvironment during the later stages of tapered flocculation when particle sizes are similar to dissipation eddy dimensions, especially at high particle concentrations (i.e., highly turbid waters). Measured size distributions, mean sizes, and fractal dimensions confirm the robustness of the present imagery-based sizing scheme and showed that EC produced numerous and more compact flocs than conventional coagulation.

Numerical Study of Turbulent Mixed Convection in a Square Lid Driven Cavity with an Inside Hot Bloc

In this study, we are interested in the two-dimensional numerical simulation of the turbulent mixed convection in the case of a square with two side lid-driven cavity containing a hot obstacle. The transfer equations coupled with those of the K - ε closure model and the boundary conditions were presented and discretized using the finite volume method. The coupling between the velocity and pressure fields is achieved by the SIMPLE algorithm. The technique of line-by-line scanning with the Thomas algorithm (TDMA) is used for the iterative resolution of discretized equations. The control parameters of the present study are the temperature gradient between the hot walls and the cold walls, and the speed imposed on the mobile walls. Streamlines generally show flow characterized by the presence of two counter-rotating cells. The areas adjacent to the isothermal walls and to the moving walls are the site of the development of thermal and dynamic boundary layers, where significant temperature and velocity gradients have been observed, subsequently influencing the profiles of turbulent quantities such as turbulent viscosity, the production and dissipation of turbulent kinetic energy and the intensity of turbulence.

Internal solitary waves enhancing turbulent mixing in the bottom boundary layer of continental slope

The importance of internal solitary waves (ISWs) to the energy and material transport in the upper ocean has been confirmed, but how ISWs affect turbulent mixing in the bottom boundary layer is lack of direct field observation. To reveal the characteristics of ISWs and the turbulent mixing they cause in the bottom boundary layer, a 36-h fine-scale observation of ISWs and their influence on turbulent mixing was conducted at the South China Sea slope (water depth: 659 m). During the observation, a group of ISWs passed by with horizontal and vertical velocities of 0.2 and 0.04 m/s at 0.1 m above bottom (mab) respectively, resulting in strong velocity shear exceeding 0.5 m/s per meter. When the ISWs passed through the slope, although they did not deform and break near the seabed, they increased the bottom shear stress, turbulent kinetic energy production rate and turbulent kinetic energy dissipation rate ( ε ) at 0.6 mab several times. The ISWs induced ε reached O (10 −6 ) W/kg, which was one order of magnitude higher than the previously observed ε in the upper ocean of the South China Sea slope. At the same observation site, the internal tides induced ε in the bottom boundary layer was O (10 −5 ) W/kg, which indicated that the internal tides played a more important role than the ISWs in enhancing bottom turbulent mixing. • Direct observation reveals strong internal solitary waves near seabed of slope. • Solitary waves cause strong velocity (0.2 m/s) near seabed at depth of 659 m. • Internal solitary waves increase bottom layer turbulent mixing several times.