Turbulent Kinetic Energy Production Rate Research Articles

Hydrodynamics of turbidity currents evolving over a plane bed

In this paper, we investigate the hydrodynamics of turbidity currents evolving over a plane bed. The analytical framework encompasses the depth-averaged conservation equations for fluid mass, sediment mass, momentum, and turbulent kinetic energy (TKE). The analysis incorporates self-similar distributions of streamwise velocity, sediment concentration, and TKE. Using the self-similar distributions of streamwise velocity and sediment concentration, the distributions of turbulent diffusivity, Reynolds shear stress, and TKE production rate are determined. The analytical model of turbidity currents enables the prediction of streamwise evolutions of flow depth, depth-averaged velocity, depth-averaged sediment concentration, and depth-averaged TKE. The self-acceleration and subsidence of turbidity currents are found to depend on the initial conditions. Additionally, the model results demonstrate the sensitivity of turbidity current hydrodynamics to grain size and longitudinal bed slope. Importantly, increased grain size and longitudinal bed slope contribute to enhanced self-acceleration, leading to a decrease in the subsidence rate of turbidity currents. The model predictions satisfactorily capture the available experimental data.

Turbulence in a wall-wake flow downstream of two horizontal cylinders

Experimental investigations of flow past two (one above other) horizontal cylinders have been presented in this paper. The experimental data captured over a rough-bed with double cylinders having three different diameters, were used for the analysis. Firstly, general characteristics such as streamwise velocity, Reynolds shear stress and turbulence intensity profiles have been elucidated at different downstream locations from cylinder position; then some advanced analysis such as length scales, turbulent kinetic energy (TKE) fluxes and budget have been investigated to exhibit their variations. Length scale profiles exhibit higher values in near bed; indicating comparatively larger eddies’ downstream of both cylinders. TKE budget profiles indicate highly negative pressure energy diffusion rate together with a sufficient TKE production rate, stabilized by the amplified TKE diffusion and dissipation rates. To determine one of the most prime behaviors of turbulence characteristics, namely TKE dissipation rate more accurately, the concept of structure function has been employed. Primarily velocity gradient method elucidates TKE dissipation rate, then it has been verified by Kolmogorov’s two-thirds law using second order structure function and Kolmogorov’s − 5/3 law using the method of power spectra.

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.

Nonlinearly interacting entrainment due to shear and convection in the surface ocean

Large-eddy simulations were performed to investigate the entrainment buoyancy flux at the mixed layer base due to nonlinearly interacting shear-driven turbulence (ST) and convective turbulence (CT). The fluxes due to pure ST and pure CT were first evaluated, and their scalings were derived. The entrainment flux due to coexisting ST and CT was then evaluated and compared to the scaling-based fluxes due to the pure turbulences. It was found that nonlinear effects reduce the entrainment flux by 30 % when the turbulent kinetic energy production rates of ST and CT are comparable. The mixing parameterization schemes used in ocean general circulation models (OGCMs) fail to accurately reproduce the mixing due to the pure turbulences and/or the nonlinear effects, and thus the mixed layer depth (MLD). Because analysis using global datasets suggests that nonlinear effects are large at the mid-latitudes, these results indicate that the nonlinear effects might be responsible for the deep MLD biases in OGCMs and that mixing parameterization schemes need to be improved to correctly represent ocean surface mixing due to shear and convection, as well as waves, in OGCMs.

Macroscopic turbulent kinetic energy budget in flow through a wall-bounded compact bank of cylinders

The flow in devices, such as heat exchangers, can be idealized as turbulent flow past an array of regularly spaced obstacles. Engineering calculations in such devices are easily handled if the flow can be represented by its volume-average quantities. This paper reports an investigation into the volume-averaged flowfield in a regular array of cylinders of finite height in crossflow at two Reynolds numbers (ReD). The investigation is based on scale-resolving computations and is thus the first to analyze the true form of the macroscopic turbulent kinetic energy (TKE) conservation law in the presence of macroscopic shear. Volume-averaging is performed parallel to the end walls in order to obtain profiles of macroscopic flow quantities. In inner coordinates, the macroscopic velocity profiles are similar to the canonical turbulent channel flow profiles, but with different values of the von Kármán constant and log-law y-intercept. The volume-averaged TKE is defined so as to include contributions from both the macroscopic and microscopic components of the flow. While the macroscopic TKE profile is very different to that of channel flow, the macroscopic TKE budget terms are remarkably similar. One notable exception is that the production rate stays large throughout the domain rather than attenuating rapidly after a near-wall peak. An extension to a widely used macroscopic turbulence model is proposed, which enables it to match the volume-averaged TKE production rate predicted by the large eddy simulations.

Effects of Axial Casing Grooves on the Structure of Turbulence in the Tip Region of an Axial Turbomachine Rotor

Abstract Challenges in turbulence modeling in the tip region of turbomachines include anisotropy, inhomogeneity, and non-equilibrium conditions, resulting in poor correlations between Reynolds stresses and the corresponding mean strain-rate components. The geometric complexity introduced by casing grooves exacerbates this problem. Taking advantage of a large database collected in the refractive index-matched liquid facility at Johns Hopkins University (JHU), this paper examines the effect of axial casing grooves on the distributions of turbulent kinetic energy (TKE), Reynolds stresses, anisotropy tensor, and TKE production rate in the tip region of an axial turbomachine. The comparisons are performed at flowrates corresponding to prestall and best efficiency points of the untreated machine. Common features include high TKE near the tip leakage vortex center and in the shear layer connecting it to the blade suction side tip corner. The turbulence is highly anisotropic and inhomogeneous, with the anisotropy tensor shifting from one-dimensional (1D) to 2D and 3D structures over small distances. With the grooves, the flow structure, hence the distribution of Reynolds stresses, becomes more complex. Additional sites with elevated turbulence include the corner vortex that develops at the entrance to the grooves, and in the flow jetting out of the grooves into the passage. Consistent with trends of the production rates of normal Reynolds stress components, the grooves increase the axial but reduce the radial velocity fluctuations as the inflow and outflow from the groove interact with the passage flow. These findings might assist the development of Reynolds stress models suitable for tip flows.

Direct numerical simulation of a turbulent boundary layer over a bump with strong pressure gradients

Abstract

Assessing the turbulent kinetic energy budget in an energetic tidal flow from measurements of coupled ADCPs.

Two coupled four-beam acoustic Doppler current profilers were used to provide simultaneous and independent measurements of the turbulent kinetic energy (TKE) dissipation rate ε and the TKE production rate [Formula: see text] over a 36 h long period at a highly energetic tidal energy site in the Alderney Race. The eight-beam arrangement enabled the evaluation of the six components of the Reynolds stress tensor which allows for an improved estimation of the TKE production rate. Depth-time series of ε, [Formula: see text] and the Reynolds stresses are provided. The comparison between ε and [Formula: see text] was performed by calculating individual ratios of ε corresponding to [Formula: see text]. The depth-averaged ratio [Formula: see text] averaged over whole flood and ebb tide were found to be 2.2 and 2.8 respectively, indicating that TKE dissipation exceeds TKE production. It is shown that the term of diffusive transport of TKE is significant. As a result, non-local transport is important to the TKE budget and the common assumption of a local balance, i.e. a balance between production and dissipation, is not valid at the measurement site. This article is part of the theme issue 'New insights on tidal dynamics and tidal energy harvesting in the Alderney Race'.

Flow characteristics around a deformable stenosis under pulsatile flow condition

A specific portion of a vulnerable stenosis is deformed periodically under a pulsatile blood flow condition. Detailed analysis of such deformable stenosis is important because stenotic deformation can increase the likelihood of rupture, which may lead to sudden cardiac death or stroke. Various diagnostic indices have been developed for a nondeformable stenosis by using flow characteristics and resultant pressure drop across the stenosis. However, the effects of the stenotic deformation on the flow characteristics remain poorly understood. In this study, the flows around a deformable stenosis model and two different rigid stenosis models were investigated under a pulsatile flow condition. Particle image velocimetry was employed to measure flow structures around the three stenosis models. The deformable stenosis model was deformed to achieve high geometrical slope and height when the flow rate was increased. The deformation of the stenotic shape enhanced jet deflection toward the opposite vessel wall of the stenosis. The jet deflection in the deformable model increased the rate of jet velocity and turbulent kinetic energy (TKE) production as compared with those in the rigid models. The effect of stenotic deformation on the pulsating waveform related with the pressure drop was analyzed using the TKE production rate. The deformable stenosis model exhibited a phase delay of the peak point in the waveform. These results revealed the potential use of pressure drop waveform as a diagnostic index for deformable stenosis.

Double-averaging analysis of turbulent kinetic energy fluxes and budget based on large-eddy simulation

The turbulent flow over a channel bed roughened by three layers of closely packed spheres with a Reynolds number of Re = 15000 is investigated using the large eddy simulation (LES) and the double-averaging (DA) method. The DA velocity is compared with the results of the corresponding laboratory experiments to validate the LES results. The existence of the types of vortex structures is demonstrated by the Q - criterion above the permeable bed. The turbulent kinetic energy (TKE) fluxes and budget are quantified and discussed. The results show that the TKE fluxes are directed downward and downstream near the virtual bed level. In the TKE budget, the form-induced diffusion rate is significant in the vicinity of the crest bed level, and the TKE production rate and the dissipation rate attain their peaks at the crest bed level and decrease sharply below it.

Experimental determination of tunnel ventilation axial ducted fan performance

To investigate traffic tunnel ventilation flows, a scaled model of a traffic tunnel with longitudinal ventilation system based on ducted fans is used. Flows in tunnels are influenced by tunnel geometry, fan characteristics, ventilation operation scenario, vehicle traffic, atmospheric factors, etc. To analyze flow fields of tunnels in detail, knowledge of tunnel jet-fan properties and turbulent flow characteristics at the fan exit are required, and can be used as input data for CFD boundary conditions of tunnel flow computation. For this purpose experimental measurements were done using the hot wire anemometry technique. The obtained results, trough ensemble-averaged and time averaged profiles of all velocity components, turbulence intensity, turbulent kinetic energy, integral flow length scales, available Reynolds stresses, Turbulent kinetic energy production rates and the fan thrust performance, are presented. These data allow us to analyze in more detail the influence of fan flow on energy and pollutant removal efficiencies of the tunnel ventilation and to evaluate accuracy of CFD studies on fan improvements.

Turbulence and mixing in a freshwater-influenced tidal bay: Observations and numerical modeling

In situ observations and numerical simulations of turbulence are essential to understanding vertical mixing processes and their dynamical controls on both physical and biogeochemical processes in coastal embayments. Using in situ data collected by bottom-mounted acoustic Doppler current profilers (ADCPs) and a free-falling microstructure profiler, as well as numerical simulations with a second-moment turbulence closure model, we studied turbulence and mixing in the Xiamen Bay, a freshwater-influenced tidal bay located at the west coast of the Taiwan Strait. Dynamically, the bay is driven predominantly by the M2 tide, and it is under a significant influence of the freshwater discharged from the Jiulong River. It is found that turbulence quantities such as the production and dissipation rates of the turbulent kinetic energy (TKE) were all subject to significant tidal variations, with a pronounced ebb-flood asymmetry. Turbulence was stronger during flood than ebb. During the flooding period, the whole water column was nearly well mixed with the depth-averaged TKE production rate and vertical eddy viscosity being up to 5×10−6 W kg−1 and 2×10−2 m2 s−1, respectively. In contrast, during the ebb strong turbulence was confined only to a 5–8 m thick bottom boundary layer, where turbulence intensity generally decreases with distance from the seafloor. Diagnosis of the potential energy anomaly showed that the ebb-flood asymmetry in turbulent dissipation and mixing was due mainly to tidal straining process as a result of the interaction between vertically shared tidal currents and horizontal density gradients. The role of vertical mixing in generating the asymmetry was secondary. A direct comparison of the modeled and observed turbulence quantities confirmed the applicability of the second-moment turbulence closure scheme in modeling turbulent processes in this weakly stratified tidally energetic environment, but also pointed out the necessity of further refinements of the model.

Effect of variable winds on current structure and Reynolds stresses in a tidal flow: analysis of experimental data in the eastern English Channel

Abstract. Wind and wave effects on tidal current structure and turbulence throughout the water column are examined using an upward-looking acoustic Doppler current profiler (ADCP). The instrument has been deployed on the seafloor of 18-m mean depth, off the north-eastern French coast in the eastern English Channel, over 12 tidal cycles, and covered the period of the transition from mean spring to neap tide, and forcing regimes varied from calm to moderate storm conditions. During storms, we observed gusty winds with magnitudes reaching 15 m s−1 and wave heights reaching up to 1.3 m. Analysis of velocity spectra revealed a noticeable contribution of wind-induced waves to spectral structure of velocity fluctuations within the subsurface layer. Near the surface, stormy winds and waves produced a significant intensification of velocity fluctuations, particularly when the sustained wind blew against the ebb tide flow. As during wavy periods, the variance-derived Reynolds stress estimates might include a wave-induced contamination, we applied the Variance Fit method to obtain unbiased stresses and other turbulent quantities. Over calm periods, the turbulent quantities usually decreased with height above the seabed. The stresses were found to vary regularly with the predominantly semidiurnal tidal flow. The along-shore stress being generally greater during the flood flow (~2.7 Pa) than during the ebb flow (~−0.6 Pa). The turbulent kinetic energy production rate, P, and eddy viscosity, Az, followed a nearly regular cycle with close to a quarter-diurnal period. As for the stresses, near the seabed, we found the maximum values of estimated quantities of P and Az to be 0.1 Wm−3 and 0.5 m2 s−1, respectively, during the flood flow. Over the storm periods, we found the highest unbiased stress values (~−2.6 Pa) during ebb when tidal currents were opposite to the southwesterly winds while, during the flood, the surface stresses slightly exceeded those estimated for a calm period. A comparison of obtained results gives a good agreement with those of other researchers working on direct measurements of turbulence in tidal flows.

Observations of turbulence under weakly and highly stratified conditions in the Ariake Sea

Observations of turbulence, stratification, and mean current were made using a microstructure profiler and an acoustic Doppler current profiler (ADCP) during four cruises at a central location in the Ariake Sea, under weakly and strongly stratified conditions. Continuous measurements of the dissipation rate of turbulent kinetic energy (TKE), e, were made. These revealed that frictional bed turbulence with quarterdiurnal variation in the bottom boundary layer (BBL) was one of the most energetic sources of vertical mixing in the sea. Thickness of the BBL was strongly confined by the stable stratification. We investigate a relationship between the BBL height h and the Ozmidov scale. We present a systematic argument that describes the vertical structure and characteristic scales of velocity and turbulence inside the frictional BBL, where the stratification persisted. Considerable deviation of observed vertical shear from the law of the wall indicated a modification of turbulent scales by the stratification. Shear stress calculated from the velocity data using vertical integration of the equation of motion was found to decrease approximately linearly with height. The TKE production rate P, estimated using the shear stress, was highly correlated with the dissipation rate. The buoyancy contribution to TKE balance in the BBL was quantified in terms of the flux Richardson number R f as R f = 0.12.

The Internal Structure of the Tip Leakage Vortex Within the Rotor of an Axial Waterjet Pump

The complex flow field in the tip region of a turbomachine rotor, including the tip leakage flow and tip leakage vortex (TLV), has been studied for decades. Yet many associated phenomena are still not understood. This paper provides detailed data on the instantaneous and phase-averaged inner structures of the tip flow and evolution of the TLV. Observations are based on series of high resolution planar particle image velocimetry measurements performed in a transparent waterjet pump fitted into an optical refractive index-matched test facility. Velocity distributions and turbulence statistics are obtained in several meridional planes inside the rotor. We observe that the instantaneous TLV structure is composed of unsteady vortex filaments that propagate into the tip region of the blade passage. These filaments are first embedded into a vortex sheet, which is generated at the suction side of the blade tip, and then they wrap around each other and roll up into the TLV. We also find that the leakage vortex induces flow separation at the casing endwall and entrains the casing boundary layer with its counter-rotating vorticity. As it propagates in the rotor passage, the TLV migrates toward the pressure side of the neighboring blade. Unsteadiness associated with vortical structures is also investigated. We notice that, at early stages of the TLV evolution, turbulence is elevated in the vortex sheet, in the flow entrained from the endwall, and near the vortex core. Interestingly, the turbulence observed around the core is not consistent with the local distribution of turbulent kinetic energy production rate. This mismatch indicates that, given a TLV section, production likely occurs at preceding stages of the vortex evolution. Then, the turbulence is convected to the core of the TLV, and we suggest that this transport has substantial component along the vortex. We observe that the meandering of vortex filaments dominates the flow in the passage and we decompose the unsteadiness surrounding the TLV core to contributions from interlaced vortices and broadband turbulence. The two contributions are of the same order of magnitude. During late stages of its evolution, TLV breakdown occurs, causing rapid broadening of the phase-averaged core, with little change in overall circulation. Associated turbulence occupies almost half the width of the tip region of blade passage and turbulence production there is also broadly distributed. Proximity of the TLV to the pressure side of the neighboring blade also affects entrainment of flow into the incoming tip region.

In situ measurements of turbulence in fish shoals

Turbulence was measured in situ within shoals of juvenile perch Perca fluviatilis with a self‐contained autonomous microstructure profiler near an artificial reef in Lake Constance, Germany. Depth‐averaged dissipation rates of turbulent kinetic energy (TKE) correlated with the density of shoaling fish, providing evidence for fish‐induced turbulence in a large and stratified lake. The observed range and the depth‐averaged values of TKE dissipation rates associated with fish‐generated turbulence were comparable with magnitudes of turbulence typically caused by internal waves or wind forcing. Enhanced turbulence within fish shoals could only be observed during periods of low background turbulence and high fish abundance. The observed rates of dissipation of TKE are about two orders of magnitude smaller than production rates of TKE estimated from empirical models on the basis of observed fish size and swimming speed.

On the asymptotic behaviour of large-scale turbulence in homogeneous shear flow

The asymptotic behaviour of large-scale velocity statistics in an homogeneous turbulent shear flow is investigated using direct numerical simulations (DNS) of the incompressible Navier–Stokes equations on a 5123 grid, and with viscous rapid distortion theory (RDT). We use a novel pseudo-spectral algorithm that allows us to set the initial value of the shear parameter in the range 3–30 without the shortcomings of previous numerical approaches. We find there is an explicit dependence of the early-time behaviour on the initial value of the shear parameter. Moreover, the long-time asymptotes of large-scale quantities such as the ratio of the turbulent kinetic energy production rate over dissipation rate, the Reynolds stress anisotropic tensor and the shear parameter itself depend sensitively on the initial value of the shear parameter over the range of Reynolds number we could achieve (26 ≤ Rλ ≤ 63) with the stringent resolution requirements that were satisfied. To gain further insight into the matter, we analyse the full viscous RDT. While inviscid RDT has received a great deal of attention, viscous RDT has not been fully analysed. Our motivation for considering viscous RDT is so that the energy dissipation rate enters the problem, enabling the shear parameter to be defined. We show asymptotic expansions for the short-time behaviour and numerically evaluate the integrals to determine the long-time prediction of viscous RDT. The results are in quantitative agreement with DNS for short times; however, at long times viscous RDT predicts the turbulent energy decays to zero. Through an analysis of the pressure–strain terms, we show that the nonlinear ‘slow’ terms are essential for rearranging turbulent energy from the streamwise direction to the mean shear direction, and this sustains the indefinite growth of the kinetic energy at long times. In effect, the nonlinear pressure–strain correlation maintains the three-dimensionality of the turbulence, countering the tendency of the mean shear to project the turbulence onto the two-dimensional plane of the mean-flow streamlines. We postulate that the predictions of viscous RDT at long times could be improved by introducing a model for the ‘slow’ pressure–strain term, along the lines of the Rotta model.

Observations of wind-driven deepening of the surface mixing layer in the Tsushima strait

A detailed description of wind-driven deepening of the mixing layer in the Tsushima strait is given by combining current data from the acoustic Doppler current profiler (ADCP) attached to a satellite-tracked surface drifter, with microstructure data from the Turbulence Ocean Microstructure Acquisition Profiler (TurboMAP) deployed from a ship following the surface drifter. By collecting data in a Lagrangian manner we attempted to minimize the effect of horizontal advection. The dissipation rate of turbulent kinetic energy (TKE), ɛ, was measured directly using the TurboMAP, whereas the production rate of TKE, P, was estimated from horizontal velocities obtained using the ADCP based on the one-dimensional linear equation of motion. The TKE budget in the mixing layer is examined by applying the integrated TKE equation to the observed data. The sum of the temporal change of potential energy, shear production, dissipation, TKE flux, and the surface buoyancy flux terms changes dramatically with time, indicating the importance of the temporal change of TKE in the deepening process on a time scale shorter than one day, which is neglected in widely used bulk mixedlayer models.

Reynolds stress and TKE production in an estuary with a tidal bore

We report new measurements of the turbulent properties of the flow in a tidally energetic estuarine channel of almost uniform cross-section. A high-frequency (1.2 MHz), bottom-mounted Acoustic Doppler Current Profiler (ADCP) has been used to observe the velocity field at a sampling rate of 10 Hz in parallel with measurements of the surface elevation by tide gauges. Our data have been analysed using the Variance Method to determine turbulent kinetic energy (TKE), shear stress and TKE production over the tidal cycle with a time resolution of 60 s. During the highly energetic but brief flood period, when the surface axial velocity reaches ∼2 m s −1, we observed large values of stress (>2 Pa) and shear production (∼5 W m −3). TKE is also input through the release of energy in the bore itself which results in a brief but intense injection of energy at the bore front with large transient TKE levels (∼100 J m −3). Subsequent input by shear production maintains TKE levels which are generally lower (∼20 J m −3) than the strong peak associated with the bore for the rest of the flood. On the ebb, the flow is relatively tranquil with maximum speeds ∼0.5 m s −1 and peak TKE production rates of ∼0.1 W m −3. The flow and elevation data have also been used to estimate the energy fluxes into and out of the estuary. Short (∼1 h), intense energy inputs (∼8 MW at springs) on the flood flow are largely balanced by longer, less intense seaward energy flow on the ebb. The net energy input is found to be ∼0.1 MW at springs which is consistent with estimates of upstream dissipation. Peak dissipation in the bore itself may exceed the mean energy input but it is active only for a small fraction of the tidal cycle and its average contribution does not exceed ∼12% of total dissipation.

Observations of a quasi shear‐free lacustrine convective boundary layer: Stratification and its implications on turbulence

Convection due to surface cooling has been investigated in the surface boundary layer of a small lake under near‐ideal conditions undisturbed by wind, large‐scale currents, and differential cooling. Successive temperature microstructure profiles revealed a stable stratification in the lower bulk of the convective boundary layer despite strong cooling over the entire layer. Lateral heat fluxes as well as heat exchange with the thermocline could be excluded as driving mechanism of the observed stratification. Acoustic Doppler current profiler (ADCP) measurements indicated an asymmetric pattern of vertical velocities: strong downward plumes were observed upon a background of slow upflow. We suggest that this asymmetry allows cold water from the super‐adiabatic surface layer to intrude at the base of the convective layer, thus causing the observed stratification. This in particular involves downward plumes that feature a relatively low entrainment rate in the center bulk of the convective layer. Corresponding large‐eddy simulation studies, as well as thermistor string and ADCP data, were found consistent with this scenario. The dissipation rate of turbulent kinetic energy (TKE) was estimated on the basis of the temperature microstructure profiles and from the ADCP data. Mean dissipation rates of only about 20% of the surface buoyancy flux were typically identified. This finding is attributed to respectively low buoyant production rates of TKE, attenuated by strong convective plumes penetrating through the stable stratification in the lower bulk of the convective layer into the thermocline.