Diffusion Of Turbulent Kinetic Energy Research Articles

Spacing Ratio Effects on the Evolution of the Flow Structure of Two Tandem Circular Cylinders in Proximity to a Wall

The flow around two tandem circular cylinders in proximity to a wall is investigated using particle image velocimetry (PIV) for Re = 2 × 103. The spacing ratios L/D are 1, 2, and 5, and the gap ratios G/D are 0.3, 0.6, and 1. The proper orthogonal decomposition (POD) method and λci vortex identification method are used to investigate the evolution of flow structure, and the influences of L/D and G/D on flow physics are shown. At L/D = 2 and G/D = 0.3, a “pairing” process occurs between the wall shear layer and the upstream cylinder’s lower shear layer, resulting in a small separation bubble behind the upstream cylinder. At L/D = 1, the Strouhal number (St) increases with decreasing G/D. At three gap ratios, the St gradually decreases as L/D increases. At G/D = 0.3, there is nearly a 49.98% decrease from St = 0.3295 at L/D = 1 to St = 0.1648 at L/D = 5, which is larger than the reductions in cases of G/D = 0.6 and G/D = 1. The effects of L/D on the evolution of flow structure at G/D = 0.6 are revealed in detail. At L/D = 1, the vortex shedding resembles that of the single cylinder. As L/D increases to 2, a squarish flow structure is formed between two cylinders, and a small secondary vortex is formed due to induction of the lower shear layer of the upstream cylinder. At L/D = 5, there is a vortex merging process between the upper wake vortices of the upstream and downstream cylinders, and the lower wake vortex of the upstream cylinder directly impinges the downstream cylinder. In addition, the shear layers and wake vortices of the upstream cylinder interact with the wake of the downstream cylinder as L/D increases, resulting in reductions in velocity fluctuations, and the production and turbulent diffusion of turbulent kinetic energy are decreased behind the downstream cylinder.

Turbulent kinetic energy redistribution in a gravity current interacting with an emergent cylinder

Gravity currents are flows driven by density gradients between two or more contacting fluids and play a key role in nature and industrial environments via global ocean circulations, climate variability and the distribution of airborne pollutants. In the present work, we study, experimentally, the changes induced by an emergent vertical PVC cylinder on the mean and turbulent flow fields of an unsteady bottom-generated lock release gravity current. Tests were carried out, with and without the cylinder, in refractive index matching conditions and instantaneous velocities were acquired with a Particle Image Velocimetry system. The mean velocity field, Reynolds stresses and terms of turbulent kinetic energy (TKE) budget for the currents head were presented and discussed. The results show that the adverse pressure gradient generated by the cylinder induces a uniform deceleration of the current head. Hence, there are no appreciable differences on the spatial distribution of the mean velocities in the current head, compared to the undisturbed current. On the other hand, the changes on the turbulent flow field are remarkable. The total diffusion of TKE decays in the inner part of the head while becoming stronger at the interface between the two fluids, as the current approaches the cylinder. This is associated to an increase of the diffusion term due to pressure fluctuations, that acts against diffusion due to velocity fluctuations and contributes to disrupt the transport of TKE from the interface between the fluids and the inner part of the current. As a result, in the presence of an obstacle, Reynolds stresses are suppressed in the inner part of the current head and enhanced at the interface.

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.

Numerical study on the effects of cylindrical roughness on heat transfer performance and entropy generation of supercritical carbon dioxide in vertical tubes

In view of heat transfer deterioration(HTD), rough tubes may help improve heat transfer performance and reduce irreversibility simultaneously. The effects of the tube with cylindrical roughness (CRT) on heat transfer and entropy generation of S-CO2 are studied numerically. The considered variables are the protrusion's axial spacing(l/L), height(e/d), width(w/d) and circumferential angle(α/2π), in the range of l/L = 1/50∼1, e/d = 0∼0.0656, w/d = 0∼0.153 and α/2π=1/12∼1. The results show CRT helps improve heat transfer, the heat transfer coefficient increases about 20% as e/d, w/d increases or l/L, α/2π decreases. Regarding irreversibility, on the one hand, CRT helps entropy generation drop in the HTD area. With e/d, w/d increasing or l/L, α/2π decreasing, entropy generation in the HTD area decreases. On the other hand, CRT causes entropy generation to rise in the non-HTD area. In the non-HTD area, with l/L increasing, entropy generation increases, with e/d, w/d increasing or α/2π decreasing, entropy generation initially increases and then essentially remains constant. The overall entropy generation through the whole tube is the combination of these two areas. In some ranges, the heat transfer coefficient and overall entropy generation of CRT are both better than those of smooth tubes. Because the disturbance effect of protrusions promotes the generation and diffusion of turbulent kinetic energy, thereby alleviating heat transfer deterioration. This study may provide references for S-CO2 heat transfer enhancement and the design of related components.

The characteristics and mechanisms of self-excited oscillation pulsating flow on heat transfer deterioration of supercritical CO2 heated in vertical upward tube

Heat transfer deterioration (HTD) of supercritical CO2 heated in a tube influences the efficiency and safe operation of the system due to the occurrence of local high temperature. To suppress and delay the HTD, the characteristics and mechanisms of self-excited oscillation pulsating flow on HTD of supercritical CO2 are studied by experiment and simulation at pressure 8 MPa, mass fluxes from 350 to 800 kg/m2·s, heat fluxes from 30 to 200 kW/m2. The Helmholtz oscillator is introduced into the inlet of the vertical tube for generating a pulsating flow of supercritical CO2. The heat transfer performance is compared with that of without Helmholtz oscillator at the inlet of the tube. The results show that the self-excited oscillation pulsating flow improve the heat transfer performance significantly. The heat transfer parameters present oscillations with small amplitude along flow direction before pseudo-critical point (Tpc). The average heat transfer coefficient can be up to 3.4 times and the enhancement takes place mainly at the HTD region which is located at the entrance section of the heated tube. The effect of suppressing HTD is more significant at higher heat flux, and the peak of wall temperature can be reduced by 100 K at a heat flux of 200 kW/m2. Compared to the steady flow, the mechanism analysis of the self-excited oscillation pulsating flow based on radial distributions of velocity, turbulent kinetic energy (TKE), and density reveals that the velocity distribution of “M−shape” appears later and gentler. The production and diffusion of TKE are improved at log layer (30 < y+ < 0.2r). In addition, the period and the amplitude do not show monotonous trends on heat transfer performance. The effects of pulsating parameters on HTD are optimized that the heat transfer performance with the period of 0.016 s and the amplitude of 100 kg/m2·s is the best in calculated cases.

Hydrodynamics of flow over a gradually varied bed roughness

Turbulence characteristics in a fully developed flow over a gradually varied bed roughness are investigated. The results of the Reynolds stress profiles indicate that they increase with an increase in bed roughness height. Their peaks occur within the wall-shear layer close to the bed. Besides, the bed shear stress rises in accordance with the roughness height. The roughness-induced layer grows as the roughness height increases with the streamwise distance. The velocity profiles fitted with the logarithmic law reveal that the zero-velocity level is elevated as the roughness height increases, but the zero-plane displacement is not influenced by the roughness. The turbulent kinetic energy (TKE) flux results indicate that an inrush of faster moving fluid parcels composing the sweep event is the dominant mechanism in the near-bed flow zone. The magnitude of the sweep event escalates, as the roughness height increases. On the other hand, a process of slowly moving fluid parcels forming the ejection event prevails in the outer flow layer. The TKE flux results agree with those obtained from the bursting analysis. Concerning the TKE budget, the peaks of the TKE production, dissipation, and pressure energy diffusion rates being positive appear near the bed and grow as the roughness height increases, whereas the peak of the TKE diffusion rate being negative behaves in the similar way as the other terms of the TKE budget behave.

Turbulent flow characteristics over an abrupt step change in bed roughness

Turbulent flow characteristics over an abrupt step change in bed roughness from smooth to rough are studied measuring the flow field by a Particle Image Velocimetry (PIV) system. The smooth and rough beds are referred to as the upstream and downstream beds, respectively. The velocity color maps and profiles show that an abrupt step change in bed roughness causes flow retardation in the downstream bed owing to the combined effects of roughness-induced and separated flows. The results of the Reynolds stresses reveal that the profiles in the downstream bed exhibit discriminable bulges, whose size increases with an increase in the streamwise distance. The stress color maps illustrate the creation of a roughness-induced layer that grows over the downstream bed as the streamwise distance increases. The bed shear stress evidences an overshooting behavior immediate downstream of the abrupt step change in bed roughness to reach its peak magnitude. The third-order correlations indicate that the effects of the abrupt step change in bed roughness produce an inrush of rapidly moving fluid streaks in the near-bed flow and arrival of slowly moving fluid streaks in the away-bed flow. Regarding the turbulent kinetic energy (TKE) budget, the enhanced magnitudes of the TKE budget terms within the roughness-induced layer are prevalent. The TKE dissipation rate lags the production rate, and the negative TKE diffusion rate implies an addition in the TKE production. Bursting analysis endorses that the sweeps govern the near-bed flow on the downstream bed and the ejections prevail far from the bed.

Wavelet analysis of shearless turbulent mixing layer

The intermittency and scaling exponents of structure functions are experimentally studied in a shearless turbulent mixing layer. Motivated by previous studies on the anomalous scaling in homogeneous/inhomogeneous turbulent flows, this study aims to investigate the effect of strong intermittency caused by turbulent kinetic energy diffusion without energy production by mean shear. We applied an orthonormal wavelet transformation to time series data of streamwise velocity fluctuations measured by hot-wire anemometry. Intermittent fluctuations are extracted by a conditional method with the local intermittency measure, and the scaling exponents of strong and weak intermittent fluctuations are calculated based on the extended self-similarity. The results show that the intermittency is stronger in the mixing layer region than in the quasi-homogeneous isotropic turbulent regions, especially at small scales. The deviation of higher-order scaling exponents from Kolmogorov's self-similarity hypothesis is significant in the mixing layer region, and the large deviation is caused by strong, intermittent fluctuations even without mean shear. The total intermittent energy ratio is also different in the mixing layer region, suggesting that the total intermittent energy ratio is not universal but depends on turbulent flows. The scaling exponents of weak fluctuations with a wavelet coefficient flatness corresponding to the Gaussian distribution value of 3 follow the Kolmogorov theory up to fifth order. However, the sixth order scaling exponent is still affected by these weak fluctuations.

Hydrodynamics of flow over two-dimensional dunes

The turbulence characteristics in flow over and within the interface of two-dimensional dunes are investigated experimentally. Besides the spatial flow and turbulence quantities, their double-averaged profiles are also analyzed. The flow over dunes is recognized to be a wake-interference flow, where the decelerated flow at the immediate downstream of the crest causes the kolk-boil effect. The flow reattachment can be explained from the perspective of the Coandă effect. The inner boundary layer edge follows the locus of the inflection points of velocity profiles having a velocity defect. The Reynolds shear stress profiles attain their respective peaks along this locus. In addition, the dispersive shear stress initiates from the edge of the form-induced sublayer being negative, indicating a spatially decelerated flow. The third-order correlations reveal that an inrush of rapidly moving fluid streaks coupled with a downward-downstream Reynolds stress diffusion prevails within the interfacial sublayer, while an arrival of slowly moving fluid streaks coupled with an upward-upstream stress diffusion governs the flow zone above the crest. The turbulent kinetic energy (TKE) flux results corroborate the similar findings. Concerning the TKE budget, the dispersive kinetic energy diffusion is found to be substantial within the roughness sublayer. The budget terms exhibit their respective peaks near the crest. The production rate is greater than the dissipation rate. However, the TKE diffusion and pressure energy diffusion rates are negative in the interfacial sublayer. The bursting analysis endorses that the sweeps and ejections govern within the interfacial sublayer and the flow zone above the crest, respectively.

Turbulence in Wall-Wake Flow Downstream of an Isolated Dunal Bedform

This study examines the turbulence in wall-wake flow downstream of an isolated dunal bedform. The streamwise flow velocity and Reynolds shear stress profiles at the upstream and various streamwise distances downstream of the dune were obtained. The results reveal that in the wall-wake flow, the third-order moments change their signs below the dune crest, whereas their signs remain unaltered above the crest. The near-wake flow is featured by sweep events, whereas the far-wake flow is controlled by the ejection events. Downstream of the dune, the turbulent kinetic energy production and dissipation rates, in the near-bed flow zone, are positive. However, they reduce as the vertical distance increases up to the lower-half of the dune height and beyond that, they increase with an increase in vertical distance, attaining their peaks at the crest. The turbulent kinetic energy diffusion and pressure energy diffusion rates, in the near-bed flow zone, are negative, whereas they attain their positive peaks at the crest. The anisotropy invariant maps indicate that the data plots in the wall-wake flow form a looping trend. Below the crest, the turbulence has an affinity to a two-dimensional isotropy, whereas above the crest, the anisotropy tends to reduce to a quasi-three-dimensional isotropy.

Measurement of Transitional Surface Roughness Effects on Flat-Plate Boundary Layer Transition

An experimental study has been conducted to investigate the effects of transitionally rough surface on the flat-plate boundary layer transition. Transitional boundary layers with three different flat plates (ks+ = 0.07 ∼ 0.19, 2.71 ∼ 7.05, and 13.65 ∼ 41.09) have been measured with a single-sensor hot-wire probe. All of the measurements have been conducted under zero pressure gradient (ZPG) at the fixed Reynolds number (ReL) and freestream turbulence intensity (Tu) of 3.05 × 106 and 0.2%. Transitionally, rough surface does not affect the sigmoidal distribution of turbulence intermittency model; but induces earlier transition onset and shortens the transition length. For all surfaces, streamwise turbulence intensity profiles with similar values of turbulence intermittency are similar for the transition length less than 60%. Therefore, mean velocity profiles with the similar values of turbulence intermittency are similar regardless of surface conditions. However, downstream of 60% of the transition length, mean velocity defect increases as the surface roughness increases. Enhanced diffusion of turbulent kinetic energy from the near wall (y/δ &lt; 0.1) to the outer part (y/δ ≈ 0.4) of the boundary layer due to the surface roughness is responsible for the increased momentum deficit.

On the phase lag of turbulent dissipation in rotating tidal flows

Field observations of rotating tidal flows in a shallow tidally swept sea reveal that a notable phase lag of both shear production and turbulent dissipation increases with height above the seafloor. These vertical delays of turbulent quantities are approximately equivalent in magnitude to that of squared mean shear. The shear production approximately equals turbulent dissipation over the phase-lag column, and thus a main mechanism of phase lag of dissipation is mean shear, rather than vertical diffusion of turbulent kinetic energy. By relating the phase lag of dissipation to that of the mean shear, a simple formulation with constant eddy viscosity is developed to describe the phase lag in rotating tidal flows. An analytical solution indicates that the phase lag increases linearly with height subjected to a combined effect of tidal frequency, Coriolis parameter and eddy viscosity. The vertical diffusion of momentum associated with eddy viscosity produces the phase lag of squared mean shear, and resultant delay of turbulent quantities. Its magnitude is inhibited by Earth's rotation. Furthermore, a theoretical formulation of the phase lag with a parabolic eddy viscosity profile can be constructed. A first-order approximation of this formulation is still a linear function of height, and its magnitude is approximately 0.8 times that with constant viscosity. Finally, the theoretical solutions of phase lag with realistic viscosity can be satisfactorily justified by realistic phase lags of dissipation.

Turbulence characteristics in wall-wake flows downstream of wall-mounted and near-wall horizontal cylinders

Turbulent characteristics in wall-wake flows downstream of wall-mounted and near-wall cylinders are investigated. The distributions of the defect of streamwise velocity, Reynolds shear stress and turbulence intensities exhibit a certain degree of self-preserving characteristic when they are scaled by their respective peak defect values. For the velocity defect distributions, the vertical distances are scaled by the half-width of peak defect velocity. However, for the distributions of the defects of the Reynolds shear stress and the turbulence intensities, the vertical distances are scaled by the half-width of Reynolds shear stress defect. The peak defects of all the quantities reduce with longitudinal distance signifying the recovery of the upstream distributions of the individual quantities. The third-order correlations reveal that for the wall-mounted cylinder, a streamwise acceleration associated with a downward flux of streamwise Reynolds normal stress (SRNS) in the inner-layer of wall-wake composes sweeps and a streamwise deceleration associated with an upward flux of SRNS in the outer-layer forms ejections. On the other hand, for the near-wall cylinder, a streamwise deceleration associated with a downward flux of SRNS in the inner-layer of wall-wake flow and the gap flow produces the inward interaction events, while the outer-layer characteristic is similar to that of wall-mounted cylinder. The turbulent kinetic energy (TKE) budget in the wake flow demonstrates strong negative pressure energy diffusion in addition to a strong TKE dissipation and diffusion and that in the gap flow exhibits a minor positive peak of pressure energy diffusion and a minor negative peak of TKE diffusion.

Hydrodynamics of submerged turbulent plane offset jets

The results of an experimental study on the turbulent flow characteristics in submerged plane offset jets are presented. The vertical profiles of time-averaged velocity components and Reynolds stresses at different horizontal locations are depicted to illustrate their variations across the pre-attachment, impingement, and wall jet regions. The characteristic lengths and the jet profile of submerged offset jets in the pre-attachment region are determined from the velocity profiles. The regional profiles of velocity and Reynolds stresses are analyzed in the context of the self-similarity, the decay of their representative scales, and the development of the length scales. The self-similarity characteristics in the pre-attachment and wall jet regions are preserved better than those in the impingement region. The turbulent kinetic energy (TKE) fluxes suggest that within the jet layer in the pre-attachment region, an upward advection of low-speed fluid streaks induces a strong retardation to the jet; while in the wall jet region, an inrush of low-speed fluid streaks induces a weak retardation. Analysis of the TKE budget reveals that within the jet layer, the TKE diffusion rate and the pressure energy diffusion rate oppose each other, and the peaks of the dissipation rate lag from those of the corresponding production rate.

An axisymmetric model for draft tube flow at partial load

A new Reynolds-averaged Navier-Stokes (RANS) turbulence model is developed in order to correctly predict the mean flow field in a draft tube operating under partial load using 2-D axisymmetric simulations. It is shown that although 2-D axisymme- tric simulations cannot model the 3-D unsteady features of the vortex rope, they can give the average location of the vortex rope in the draft tube. Nevertheless, RANS simulations underpredict the turbulent kinetic energy (TKE) production and diffusion near the center of the draft tube where the vortex rope forms, resulting in incorrect calculation of TKE profiles and, hence, poor prediction of the axial velocity. Based on this observation, a new k-ɛ turbulence RANS model taking into account the extra production and diffusion of TKE due to coherent structures associated with the vortex rope formation is developed. The new model can successfully predict the mean flow velocity with significant improvements in comparison with the realizable k-ɛ model. This is attributed to better prediction of TKE production and diffusion by the new model in the draft tube under partial load. Specifically, the new model calculates 31% more production and 46% more diffusion right at the shear layer when compared to the k-ɛ model.

A one-dimensional modeling study of the diurnal cycle in the equatorial Atlantic at the PIRATA buoys during the EGEE-3 campaign

A one-dimensional model is used to analyze, at the local scale, the response of the equatorial Atlantic Ocean under different meteorological conditions. The study was performed at the location of three moored buoys of the Pilot Research Moored Array in the Tropical Atlantic located at 10° W, 0° N; 10° W, 6° S; and 10° W, 10° S. During the EGEE-3 (Etude de la circulation oceanique et de sa variabilite dans le Golfe de Guinee) campaign of May–June 2006, each buoy was visited for maintenance during 2 days. On board the ship, high-resolution atmospheric parameters were collected, as were profiles of temperature, salinity, and current. These data are used here to initialize, force, and validate a one-dimensional model in order to study the diurnal oceanic mixed-layer variability. It is shown that the diurnal variability of the sea surface temperatures is mainly driven by the solar heat flux. The diurnal response of the near-surface temperatures to daytime heating and nighttime cooling has an amplitude of a few tenths of degree. The computed diurnal heat budget experiences a net warming tendency of 31 and 27 W m−2 at 0° N and 10° S, respectively, and a cooling tendency of 122 W m−2 at 6° S. Both observed and simulated mixed-layer depths experience a jump between the nighttime convection phase and the well-stabilized diurnal water column. Its amplitude changes dramatically depending on the meteorological conditions occurring at the stations and reaches its maximum amplitude (~50 m) at 10° S. At 6° and 10° S, the presence of barrier layers is observed, a feature that is clearer at 10° S. Simulated turbulent kinetic energy (TKE) dissipation rates, compared to independent microstructure measurements, show that the model tracks their diurnal evolution reasonably well. It is also shown that the shear and buoyancy productions and the vertical diffusion of TKE all contribute to the supply of TKE, but the buoyancy production is the main source of TKE during the period of the simulation.

Studies of shock/turbulent shear layer interaction using Large-Eddy Simulation

Shock/shear/turbulence interactions are simulated using Large-Eddy Simulation (LES) with a new localized subgrid closure approach. Both normal and oblique shocks interactions with turbulence are considered. The LES methodology adopted here combines a hybrid numerical scheme that switches automatically and locally between a shock-capturing scheme and a low-dissipation high-order central scheme. The fundamental role of the diffusion of turbulent kinetic energy by pressure fluctuations in the problem of normal shock/isotropic turbulence interaction is stressed in the DNS study, and accounted for in the closure model. The study of the interaction between two oblique shocks and a turbulent shear layer shows that the turbulence evolution is mostly affected by two competing phenomena. An amplification of the turbulent levels occurs downstream of the interaction, and the mixing layer growth rate is significantly increased. However, the integrated production of turbulent energy across the mixing layer is reduced, and the increase in mixing is found to be localized in space, the turbulent statistics quickly relaxing to their undisturbed levels. Furthermore, the increase in vorticity from the compression of the mixing layer remains small, unaffected by the presence of turbulent and coherent structures.

Turbulence Within a Turbomachine Rotor Wake Subject to Nonuniform Contraction

The flow and turbulence in a rotor near wake located within a nonuniform field, generated by a row of inlet guide vanes, are investigated experimentally in a refractive-index-matched facility that provides unobstructed view of the entire flowfield. Stereoscopic particle image velocimetry measurements, performed in closely spaced radial planes, enable measurements of all the components of the phase-averaged strain rate, Reynolds stress, and triple correlation tensors. The rotor wake is bent and compressed as a result of exposure to regions with high axial momentum (jets), which fill the gaps between inlet guide vanes wakes. As the rotor wake propagates away from the blade, this process of bending and compression by the jets leads to formation of distinct wake kinks containing regions of high turbulence (turbulent hot spots). We focus on an early stage of hot-spot formation. On the suction side of the wake, compression by a jet increases turbulence production, causing nonuniform and asymmetric distribution of Reynolds stresses. In a curvilinear coordinate system aligned with the wake centerline, all the Reynolds stresses are higher on the suction side of the wake where the decay rate of turbulence is much slower than that expected in wakes. The production rate of streamwise stress is dominated by interactions of the shear stress with the cross-stream gradients of the phase-averaged streamwise velocity. The latter also interact with the cross-stream stress to cause high production of shear stress, especially on the suction side. The locations of peak streamwise and shear stresses are consistent with those of the corresponding production rates. The similar locations of peak streamwise and cross-stream stresses, together with low production rate of the latter, suggest a significant contribution by intercomponent transfer from the streamwise to the cross-stream stress. The effects of streamwise curvature and rotation on the evolution of turbulent stresses are marginal. The paper also provides distributions of advection by phase-averaged flow and turbulent diffusion components. The diffusion terms oppose the peaks of production rates, but also have high values along the perimeter of the wake. We compare the distribution of diffusion of turbulent kinetic energy to a model based on the gradient-diffusion hypothesis. The model predicts the diffusion peak that opposes the production rate maximum quite well, but underpredicts the diffusion along the perimeter of the wake and overpredicts it near the wake center.

Analysis and Modeling of the Turbulent Diffusion of Turbulent Kinetic Energy in Natural Convection

Buoyant flows often contain regions with unstable and stable thermal stratification from which counter gradient turbulent fluxes are resulting, e.g. fluxes of heat or of any turbulence quantity. Basing on investigations in meteorology an improvement in the standard gradient-diffusion model for turbulent diffusion of turbulent kinetic energy is discussed. The two closure terms of the turbulent diffusion, the velocity-fluctuation triple correlation and the velocity-pressure fluctuation correlation, are investigated based on Direct Numerical Simulation (DNS) data for an internally heated fluid layer and for Rayleigh–Benard convection. As a result it is decided to extend the standard gradient-diffusion model for the turbulent energy diffusion by modeling its closure terms separately. Coupling of two models leads to an extended RANS model for the turbulent energy diffusion. The involved closure term, the turbulent diffusion of heat flux, is studied based on its transport equation. This results in a buoyancy-extended version of the Daly and Harlow model. The models for all closure terms and for the turbulent energy diffusion are validated with the help of DNS data for internally heated fluid layers with Prandtl number Pr = 7 and for Rayleigh–Benard convection with Pr = 0.71. It is found that the buoyancy-extended diffusion model which involves also a transport equation for the variance of the vertical velocity fluctuation gives improved turbulent energy diffusion data for the combined case with local stable and unstable stratification and that it allows for the required counter gradient energy flux.

Vertical mixing schemes in the coastal ocean: Comparison of the level 2.5 Mellor‐Yamada scheme with an enhanced version of the K profile parameterization

The performance of two vertical mixing parameterizations in idealized continental shelf settings is analyzed to assess in what aspects and under what conditions they differ. The level 2.5 Mellor‐Yamada turbulence closure (M‐Y) is compared with an enhanced version of the K profile parameterization (KPP), which has been appended to include a representation of the bottom boundary layer. The two schemes are compared in wind‐driven one‐ and two‐dimensional shallow ocean settings to examine differences in (1) the surface boundary layer response, (2) the response when surface and bottom boundary layers are in close proximity, and (3) the response when the horizontal advective effects of a coastal upwelling circulation compete with the vertical mixing processes. The surface boundary layer experiments reveal that M‐Y mixes deeper and entrains more than KPP when the pycnocline beneath the wind‐mixed layer is highly stratified and mixes less when it is weaker. This is related to the role of vertical diffusion of turbulent kinetic energy in M‐Y and the nature of the interior shear mixing parameterization of KPP. In shallow water when surface and bottom boundary layers impinge on each other, the stronger mixing at the interface produced by KPP can lead to much more rapid disintegration of the pycnocline. The two‐dimensional upwelling circulation experiments show that the two schemes can produce quite similar or significantly different solutions in the nearshore region dependent on the initial stratification. The differences relate to the stronger suppression of turbulence by M‐Y under the restratifying influence of horizontal advection of denser water in the bottom boundary layer.