Relationship between energy dissipation rate and channel morphology in the development of the model braided channel

A certain pattern of channel is the product of its self-adjustment under given boundary, discharge and sediment conditions. Based upon the principle of process-response model, an experimental study with 18 runs is carried out in LESRC. This paper is focused on the variation of the energy dissipation versus the channel morphology during and after the bedmaking process of braided channel. The results show that there exists a good empirical relationship between the energy dissipation rate and channel morphology. According to this relationship and the theory of minimum rate of energy dissipation, the authors explain the metamorphosis of the model channel with the development of the braided river.

EXPERIMENTAL STUDY OF MEASUREMENT FOR DISSIPATION RATE SCALING EXPONENT IN HEATED WALL TURBULENCE

Experimental investigations have been devoted to the study of scaling law of coarse-grained dissipation rate structure function for velocity and temperature fluctuation of non-isotropic and inhomogeneous turbulent flows at moderate Reynolds number. Much attention has been paid to the case of turbulent boundary layer, which is typically the non-istropic and inhomogeneous trubulence because of the dynamically important existence of organized coherent structure burst process in the near wall region . Longitudinal velocity and temperature have been measured at different vertical positions in turbulent boundary layer over a heated and unheated flat plate in a wind tunnel using hot wire anemometer. The influence of non-isotropy and inhomogeneity and heating the wall on the scaling law of the dissipation rate structure function is studied because of the existence of organized coherent structure burst process in the near wall region . The scaling law of coarse-grained dissipation rate structure function is foun

Estimation of Turbulent Kinetic Energy Dissipation Rate in the Bottom Boundary Layer of the Pearl River Estuary

A structure function approach is applied to estimate the turbulent kinetic energy （TKE） dissipation rate in the bottom boundary layer of the Pearl River Estuary （PRE）. Simultaneous measurements with an acoustic Doppler velocimeter （ADV） supplied independent data for the verification of the structure function method. The results show that, 1） the structure function approach is reliable and successfully applied method to estimate the TKE dissipation rate. The observed dissipation rates range between 8.3 ×10^-4 W/kg and 4.9× 10^-6 W/kg in YM01 and between 3.4×10^-4 W/kg and 4.8×10^-7 W/kg in YM03, respectively, while exhibiting a strong quarter-diurnal variation. 2） The balance between the shear production and viscous dissipation is better achieved in the straight river. This first-order balance is significantly broken in the estuary by non-shear production/dissipation due to wave-induced fluctuations.

Unit stream power,minimum energy dissipation rate,and river engineering

Unit stream power is the most important and dominant parameter for the determination of transport rate of sand,gravel,and hyper-concentrated sediment with wash load.Minimum energy dissipation rate theory,or its simplified minimum unit stream power and minimum stream power theories,can provide engineers the needed theoretical basis for river morphology and river engineering studies.The Generalized Sediment Transport model for Alluvial River Simulation computer mode series have been developed based on the above theories.The computer model series have been successfully applied in many countries.Examples will be used to illustrate the applications of the computer models to solving a wide range of river morphology and river engineering problems.

Improved Dissipation Rate Equation for Swirling and Rotating Pipe Flows

The nature of turbulent swirling and rotating flow in a straight pipe is investigated using a family of near-wall two-equation models. Specifically, the viability of three different near-wall two-equation models is assessed. These models are asymptotically consistent near the wall. The first two models, one with isotropic and another with anisotropic eddy viscosity invoked, solved a dissipation rate equation with no explicit correction made to account for swirl and flow rotation. The third model assumes an isotropic eddy viscosity but solves an improved dissipation rate equation that has explicit corrections made to account for swirl and flow rotation. Calculations of turbulent flows in the swirl number range 0.25 - 1.3 with and without a central recirculation region reveal that, with the exception of the third model, neither one of the other two models can replicate the mean field at the swirl numbers tested. Furthermore, taking stress anisotropy into account also fails to model swirl effect correctly. Significant improvements can be realized from the third model, which is based on an improved dissipation rate equation and the assumption of isotropic eddy viscosity. The predicted mean flow and turbulence statistics correlate well with measurements at low swirl. At high swirl, the two-equation model with an improved dissipation rate equation can still be used to model swirling and rotating pipe flows with a central recirculation region. However, its simulation of flows without a central recirculation region is not as satisfactory.

Constructal entransy dissipation rate minimization for umbrella-shaped assembly of cylindrical fins

Umbrella-shaped assembly of cylindrical fins is optimized by adopting analytical method and taking dimensionless mean thermal resistance (MTR) as performance index. The optimal construct of umbrella-shaped assembly is obtained. The results show that the heat conductance performance of the assembly becomes ever worse with ever greater number of elemental cylindrical fins,the umbrella-shaped assembly reduces to cylindrical fin in some values of design parameters,and the diameters’ dependence on design parameters is weak for the optimized assembly. An equivalent thermal resistance defined based on entransy dissipation rate (EDR) reflects an average heat transfer effect of the assembly. The constructal design corresponding to the minimum EDR (or MTR) should be adopted for designing an assembly of fins in engineering at the limit safe condition.

“Volume-point” heat conduction constructal optimization based on entransy dissipation rate minimization with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale

Based on constructal theory,the constructs of three "volume-point" heat conduction models with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale are optimized by taking minimum entransy dissipation rate as optimization objective.The optimal constructs of the three "volume-point" heat conduction models with minimum dimensionless equivalent thermal resistance are obtained.The results show that the optimal constructs of the three-dimensional cylindrical assembly based on the minimizations of dimensionless equivalent thermal resistance and dimensionless maximum thermal resistance are different,which is obviously different from the comparison between those of the corresponding two-dimensional rectangular assembly based on the minimizations of these two objectives.The optimal constructs based on rectangular and triangular elements on microscale and nanoscale when the size effect takes effect are obviously different from those when the size effect does not take effect.Because the thermal current density in the high conductivity channel of the rectangular and triangular second order assemblies are not linear with the length,the optimal constructs of these assemblies based on the minimization of entransy dissipation rate are different from those based on the minimization of maximum temperature difference.The dimensionless equivalent thermal resistance defined based on entransy dissipation rate reflects the average heat transfer performance of the construct.The studies on "volume-point" heat conduction constructal problems at three-dimensional conditions and microscale and nanoscale by taking minimum entransy dissipation rate as optimization objective extend the application range of the entransy dissipation extremum principle.

Constructal entransy dissipation rate minimization for leaf-like fins

Based on constructal theory,the constructs of the leaf-like fins are optimized by taking minimum entransy dissipation rate(for the fixed total thermal current,i.e.,the equivalent thermal resistance) as optimization objective.The optimal constructs of the leaf-like fins with minimum dimensionless equivalent thermal resistance are obtained.The results show that there exists an optimal elemental leaf-like fin number,which leads to an optimal global heat conduction performance of the first order leaf-like fin.The Biot number has little effects on the optimal elemental fin number,optimal ratios of length and width of the elemental and first order leaf-like fins;with the increase of the thermal conductivity ratio of the vein and blade,the optimal elemental fin number and optimal ratio of the length and width of the elemental leaf-like fin increase,and the optimal shape of the first order leaf-like fin becomes tubbier.The optimal construct based on entransy dissipation rate minimization is obviously different from that based on maximum temperature difference minimization.The dimensionless equivalent thermal resistance based on entransy dissipation rate minimization is reduced by 11.54% compared to that based on maximum temperature difference minimization,and the global heat conduction performance of the leaf-like fin is effectively improved.For the same volumes of the elemental and first order leaf-like fins,the minimum dimensionless equivalent thermal resistance of the first order of the leaf-like fin is reduced by 30.10% compared to that of the elemental leaf-like fin,and the global heat conduction performance of the first order leaf-like fin is obviously better than that of the elemental leaf-like fin.Essentially,this is because the temperature gradient field of the first order leaf-like fin based on entransy dissipation rate minimization is more homogenous than that of the elemental leaf-like fin.The dimensionless equivalent thermal resistance defined based on entransy dissipation rate reflects the average heat transfer performance of the leaf-like fin,and can provide some guidelines for the thermal design of the fins from the viewpoint of heat transfer optimization.

Constructal optimization of cylindrical heat sources with forced convection based on entransy dissipation rate minimization

Based on constructal theory and entransy theory,the optimal designs of constant-and variable-cross-sectional cylindrical heat sources are carried out by taking dimensionless equivalent resistance minimization as optimization objective.The effects of the cylindrical height,the cylindrical shape and the ratio of thermal conductivity of the fin to that of the heat source are analyzed.The results show that when the volume of the heat source is fixed,there exists an optimal ratio of the center-to-centre distance of the fin and the heat source to the cylinder radius which leads to the minimum dimensionless equivalent thermal resistance.With the increase in the height of the cylindrical heat source and the ratio of thermal conductivity,the minimum dimensionless equivalent thermal resistance decreases gradually.For the heat source model with inverted variable-cross-sectional cylinder,there exist an optimal ratio of the center-to-centre distance of the fin and the heat source to the cylinder radius and an optimal radius ratio of the smaller and bigger circles of the cylindrical fin which lead to a double minimum dimensionless equivalent thermal resistance.Therefore,the heat transfer performance of the cylindrical heat source is improved by adopting the cylindrical model with variable-cross-section.The optimal constructs of the cylindrical heat source based on the minimizations of dimensionless maximum thermal resistance and dimensionless equivalent thermal resistance are different.When the thermal security is ensured,the optimal construct of the cylindrical heat source based on minimum equivalent thermal resistance can provide a new alternative scheme for the practical design of heat source.The results obtained herein enrich the work of constructal theory and entransy theory in the optimal design field of the heat sources,and they can provide some guidelines for the designs of practical heat source systems.

ANALYSES OF TURBULENT MODELS WITH EXTREMUM LAW OF ENERGY DISSIPATION RATE

By introducing the extremum law of energy dissipation rate into the investigation of turbulent flow,the closure problem for the basic equations is briefly discussed in connection with a newly suggested semi-empirical turbulent flow model.As a result,several unknown functions which cannot be solved by the existed semi-empirical models are obtained in the present paper.It is shown that the turbulent flow models,as the constraints to the extremum problem, have direct influence on the final results of the primary parameters.

Minimax principle on energy dissipation of incompressible shear flow

The energy dissipation rate is an important concept in the theory of turbulence. Doering-Constantin＇s variational principle characterizes the upper bounds （maxi- mum） of the time-averaged rate of viscous energy dissipation. In the present study, an optimization theoretical point of view was adopted to recast Doering-Constantin＇s formu- lation into a minimax principle for the energy dissipation of an incompressible shear flow. Then, the Kakutani minimax theorem in the game theory is applied to obtain a set of conditions, under which the maximization and the minimization in the minimax principle are commutative. The results explain the spectral constraint of Doering-Constantin, and confirm the equivalence between Doering-Constantin＇s variational principle and Howard- Busse＇s statistical turbulence theory.

Research on the energy evolution characteristics and the failure intensity of rocks

It is pretty challenging and difficult to quantitatively evaluate the intensity of dynamic disasters in deep mining engineering.Based on the uniaxial loading-unloading experiments for five types of rocks,this paper investigated the energy evolution characteristics,and identified the damage and crack propagation thresholds.Also,the fragment size distributions of the rocks after failure were analyzed.The energy release rate(Ge)and energy dissipation rate(Gd)were then proposed to describe the change of energies per unit volume and per unit strain.Results demonstrated that the more brittle rocks had the shorter stage of unstable crack growth and the lower induced damage at crack damage thresholds.The evolution characteristics of the strain energy rates can be easily identified by the crack propagation thresholds.The failure intensity index(FId),which equals to the values of Ge/Gd at the failure point,was further put forth.It can account for the brittleness of the rocks,the intensity of rock failure as well as the degree of rock fragmentation.It was revealed that a higher FId corresponded to a lower fractal dimension and stronger dynamic failure.

Particle Image Velocimetry Study of Turbulence Characteristics in a Vessel Agitated by a Dual Rushton Impeller

Particle Image Velocimetry （PIV） has been used to investigate turbulence characteristics in a 0.48 m diameter stirred vessel filled to a liquid height （ H = 1.4T ） of 0.67 m. The agitator had dual Rushton impellers of 0.19 m diameter （ D = 0.4T ）. The developed flow patterns depend on the clearance of the lower impeller above the base of the vessel, the spacing between the two impellers, and the submergence of the upper impeller below the liq- uid surface. Their combinations can generate three basic flow patterns, named, parallel, merging and diverging flows. The results of velocity measurement show that the flow characteristics in the impeller jet flow region changes very little for different positions. Average velocity, trailing vortices and shear strain rate distributions for three flow patterns were measured by using PIV technique. The characteristics of trailing vortex and its trajectory were described in detail for those three flow patterns. Since the space-resolution of PIV can only reach the sub-grid rather than the Kolmogorov scale, a large-eddy PIV analysis has been used to estimate the distribution of the turbulent kinetic energy dissipation. Comparison of the distributions of turbulent kinetic energy and dissipation rate in merging flow shows that the highest turbulent kinetic energy and dissipation are both located in the vortex regions, but the maxima are at somewhat different lo- cations behind the blade. About 37% of the total energy is dissipated in dual impeller jet flow regions. The obtained distribution of shear strain rate for merging flow is similar to that of turbulence dissipation, with the shear strain rate around the trailing vortices much higher than in other areas.

Modeling of the eddy viscosity by breaking waves

Breaking wave induced nearsurface turbulence has important consequences for many physical and biochemical processes including water column and nutrients mixing, heat and gases exchange across air-sea interface. The energy loss from wave breaking and the bubble plume penetration depth are estimated. As a consequence, the vertical distribution of the turbulent kinetic energy （TKE）, the TKE dissipation rate and the eddy viscosity induced by wave breaking are also provided. It is indicated that model results are found to be consistent with the observational evidence that most TKE generated by wave breaking is lost within a depth of a few meters near the sea surface. High turbulence level with intensities of eddy viscosity induced by breaking is nearly four orders larger than vw1（ = κu ＊wz）, the value predicted for the wall layer scaling close to the surface, where u ＊w is the friction velocity in water, κ with 0. 4 is the yon Kármán constant, and z is the water depth, and the strength of the eddy viscosity depends both on wind speed and sea state, and decays rapidly through the depth. This leads to the conclusion that the breaking wave induced vertical mixing is mainly limited to the near surface layer, well above the classical values expected from the similarity theory. Deeper down, however, the effects of wave breaking on the vertical mixing become less important.

Response of cellular stoichiometry and phosphorus storage of the cyanobacteria A phanizomenon flos-aquae to smallscale turbulence

Turbulent mixing, in particular on a small scale, aff ects the growth of microalgae by changing diff usive sublayers and regulating nutrient fluxes of cells. We tested the nutrient flux hypothesis by evaluating the cellular stoichiometry and phosphorus storage of microalgae under dif ferent turbulent mixing conditions. A phanizomenon flos-aquae were cultivated in dif ferent stirring batch reactors with turbulent dissipation rates ranging from 0.001 51 m2/s 3 to 0.050 58 m 2/s 3, the latter being the highest range observed in natural aquatic systems. Samples were taken in the exponential growth phase and compared with samples taken when the reactor was completely stagnant. Results indicate that, within a certain range, turbulent mixing stimulates the growth of A. flos-aquae. An inhibitory ef fect on growth rate was observed at the higher range. Photosynthesis activity, in terms of maximum ef fective quantum yield of PSII(the ratio of F v/F m) and cellular chlorophyll a, did not change significantly in response to turbulence. However, Chl a/C mass ratio and C/N molar ratio, showed a unimodal response under a gradient of turbulent mixing, similar to growth rate. Moreover, we found that increases in turbulent mixing might stimulate respiration rates, which might lead to the use of polyphosphate for the synthesis of cellular constituents. More research is required to test and verify the hypothesis that turbulent mixing changes the dif fusive sublayer, regulating the nutrient flux of cells.

Observations of upper layer turbulent mixing in the southern South China Sea

A turbulent microstructure experiment was undertaken at a low latitude of 10°N in the South China Sea in late August 2012. The characteristics of the eddy diffusivity above 650 m were analyzed, which is one order of magnitude larger than that in the open ocean at that low latitude. Enhanced eddy diffusivities by strong shears and sharp changes in topography were observed. The strongest eddy diffusivity occurred in the mixed layer, and it reached O（10^-2 m^2/s）. Strong stratification in the thermocline inhibited the penetration of surface eddy diffusivities through the thermocline, where the mixing was weakest. Below the thermocline, where the background eddy diffusivity was approximately O（10^-6 m^2/s）, the eddy diffusivity increased with depth, and its largest value was O（10^-3 m^2/s）.

Turbulent mixing above the Atlantic Water around the Chukchi Borderland in 2014

This study presents an analysis of the CTD data and the turbulent microstructure data collected in 2014, the turbulent mixing environment above the Atlantic Water（AW） around the Chukchi Borderland region is studied.Surface wind becomes more efficient in driving the upper ocean movement along with the rapid decline of sea ice,thus results in a more restless interior of the Arctic Ocean. The turbulent dissipation rate is in the range of4.60×10–10（–3.31×10–9 W/kg with a mean value of 1.33×10–9 W/kg, while the diapycnal diffusivity is in the range of1.45×10–6–1.46×10–5m2/s with a mean value of 4.84×10–6 m2/s in 200–300 m（above the AW）. After investigating on the traditional factors（i.e., wind, topography and tides） that may contribute to the turbulent dissipation rate, the results show that the tidal kinetic energy plays a dominating role in the vertical mixing above the AW. Besides, the swing of the Beaufort Gyre（BG） has an impact on the vertical shear of the geostrophic current and may contribute to the regional difference of turbulent mixing. The parameterized method for the double-diffusive convection flux above the AW is validated by the direct turbulent microstructure results.

The cruise observation of turbulent mixing in the upwelling region east of Hainan Island in the summer of 2012

The turbulent mixing in the upwelling region east of Hainan Island in the South China Sea is analyzed based on in situ microstructure observations made in July 2012. During the observation, strong upwelling appears in the coastal waters, which are 3℃ cooler than the offshore waters and have a salinity 1.0 greater than that of the offshore waters. The magnitude of the dissipation rate of turbulent kinetic energy ε in the upwelling region is O（10–9 W/kg）, which is comparable to the general oceanic dissipation. The inferred eddy diffusivity Kρ is O（10–6 m2/s）, which is one order of magnitude lower than that in the open ocean. The values are elevated to Kρ≈O（10–4 m2/s） near the boundaries. Weak mixing in the upwelling region is consistent with weak instability as a result of moderate shears versus strong stratifications by the joint influence of surface heating and upwelling of cold water.The validity of two fine-scale structure mixing parameterization models are tested by comparison with the observed dissipation rates. The results indicate that the model developed by Mac Kinnon and Gregg in 2003 provides relatively better estimates with magnitudes close to the observations. Mixing parameterization models need to be further improved in the coastal upwelling region.

Robust Solution for Boundary Layer Height Detections with Coherent Doppler Wind Lidar

Although coherent Doppler wind lidar(CDWL)is promising in detecting boundary layer height(BLH),differences between BLH results are observed when different CDWL measurements are used as tracers.Here,a robust solution for BLH detections with CDWL is proposed and demonstrated:mixed layer height(MLH)is retrieved best from turbulent kinetic energy dissipation rate(TKEDR),while stable boundary layer height(SBLH)and residual layer height(RLH)can be retrieved from carrier-to-noise ratio(CNR).To study the cause of the BLH differences,an intercomparison experiment is designed with two identical CDWLs,where only one is equipped with a stability control subsystem.During the experiment,it is found that the CNR could be distorted by instrument instability because the coupling efficiency from free-space to the polarization-maintaining fiber of the telescope is sensitive to the surrounding environment.In the ML,a bias up to 2.13 km of the MLH from CNR is found,which is caused by the CNR deviation.In contrast,the MLH from TKEDR is robust as long as the accuracy of wind is guaranteed.In the SBL(RL),the CNR is found capable to retrieve SBLH and RLH simultaneously and robustly.This solution is tested during an observation period over one month.Statistical analysis shows that the root-mean-square errors(RMSE)in the MLH,SBLH,and RLH are 0.28 km,0.23 km,and 0.24 km,respectively.

Circulation Retrieval of Wake Vortices under Rainy Conditions with an X Band Radar

At airports, runway operation is the limiting factor for the overall throughput; specifically the fixed and overly conservative ICAO wake turbulence separation minima. The wake turbulence hazardous flows can dissipate quicker because of decay due to air turbulence or be transported out of the way on oncoming traffic by cross-wind, yet wake turbulence separation minima do not take into account wind conditions. Indeed, for safety reasons, most airports assume a worst-case scenario and use conservative separations; the interval between aircraft taking off or landing therefore often amounts to several minutes. However, with the aid of accurate wind data and precise measurements of wake vortex by radar sensors, more efficient intervals can be set, particularly when weather conditions are stable. Depending on traffic volume, these adjustments can generate capacity gains, which have major commercial benefits. This paper presents the use of Electronic scanning radar for detecting wake vortices. In this method, the raindrops Doppler spectrogram is used to retrieve the strength of the wake vortex. Numerical simulation are performed to establish an empirical model used during the retrieval method. This paper presents also the results obtained during the trials of the PARIS-CDG data set recorded from October 2014 to November 2015 with an X-band RADAR developed and deployed by THALES.