Wall-bounded turbulent flow involves the development of multi-scale turbulent eddies, as well as a sharply varying boundary layer. Its theoretical descriptions are yet phenomenological. We present here a new framework...Wall-bounded turbulent flow involves the development of multi-scale turbulent eddies, as well as a sharply varying boundary layer. Its theoretical descriptions are yet phenomenological. We present here a new framework called structural ensemble dynamics （SED）, which aims at using systematically all relevant statistical properties of turbulent structures for a quantitative description of ensemble means. A new set of closure equations based on the SED approach for a turbulent channel flow is presented. SED order functions are defined, and numerically determined from data of direct numerical simulations （DNS）. Computational results show that the new closure model reproduces accurately the solution of the original Navier-Stokes simulation, including the mean velocity profile, the kinetic energy of the streamwise velocity component, and every term in the energy budget equation. It is suggested that the SED-based studies of turbulent structure builds a bridge between the studies of physical mechanisms of turbulence and the development of accurate model equations for engineering predictions.展开更多
Based on the equations of motion and the assumption that ocean turbulence is of isotropy or quasi-isotropy, we derived the closure equations of the second-order moments and the variation equations for characteristic q...Based on the equations of motion and the assumption that ocean turbulence is of isotropy or quasi-isotropy, we derived the closure equations of the second-order moments and the variation equations for characteristic quantities, which describe the mechanisms of advection transport and shear instability by the sum of wave-like and eddy-like motions and circulation. Given that ocean turbulence generated by wave breaking is dominant at the ocean surface, we presented the boundary conditions of the turbulence kinetic energy and its dissipation rate, which are determined by energy loss from wave breaking and entrainment depth respectively. According to the equilibrium solution of the variation equations and available data of the dissipation rate, we obtained an analytical estimation of the characteristic quantities of surface-wave-generated turbulence in the upper ocean and its related mixing coefficient. The derived kinetic dissipation rate was validated by field measurements qualitatively and quantitatively, and the mixing coefficient had fairly good consistency with previous results based on the Prandtl mixing length theory.展开更多
A three-dimensional, first order turbulence closure, thermal diffusion model is described in this paper. The governing equations consist of an equation of continuity, three components of momentum, conservation equatio...A three-dimensional, first order turbulence closure, thermal diffusion model is described in this paper. The governing equations consist of an equation of continuity, three components of momentum, conservation equations for salt, temperature and subgridscale energy, and an equation of state. In the model, according to the hypothesis of Kolmogorov and Prandtl, the viscosity coefficient of turbulent flow of homogeneous fluid is related to the local turbulent energy, and the horizontal and vertical exchange coefficients of mass, heat and momentum are computed with the introduction of subgridscale turbulence energy. The governing equations are solved by finite difference techniques. This model is applied to the Jiaozhou bay to predict thermal pollution by the Huangdao power plant. An instantaneous tidal current field is computed, then the distribution of temperature increment is predicted, and finally the effect of wind stress on thermal discharge is discussed.展开更多
In this paper the system of Reynolds equations of the multi-scaled atmospheric motions is set up based on the con- cept of decomposing the meteorological elements into multi-scale disturbances.It is proved to be true ...In this paper the system of Reynolds equations of the multi-scaled atmospheric motions is set up based on the con- cept of decomposing the meteorological elements into multi-scale disturbances.It is proved to be true that the Reynolds exchange term in the averaged motion is equal to the sum of averaged nonlinear terms in all sub-averaged motions.In order to avoid the higher order closure in Eulerian approaches,a new K-theory based on the multi-scaled Reynolds equations is given in which the subscale motions are described by Langevin equation as the air particles are moving in the Eulerian average background.From the new K-theory are derived the momentum,heat and mass exchange coefficients as the functions of statistical variables such as variances and Lagrangian time scales of velocity,temperature and other meteorological elements in disturbances.The new K-theory also expounds the causes for the differences be- tween the exchange coefficients of one element and another and gives the ambient conditions in which the buoyancy and/or Coriolis force Will build the chaotic disturbances into the orderly gradient of mean values of the corresponding elements.In consequence the K-theory can be used to explain some of negative viscosity phenomena in atmospheric mo- tions.展开更多
Closure models started from Chou＇s work have been developed for more than 70 years, aiming at providing analytical tools to describe turbulent flows in the spectral space. In this study, a preliminary attempt is pres...Closure models started from Chou＇s work have been developed for more than 70 years, aiming at providing analytical tools to describe turbulent flows in the spectral space. In this study, a preliminary attempt is presented to introduce a closure model in the physical space, using the velocity structure functions as key parameters. The present closure model appears to qualitatively reproduce the asymptotic scaling behav- iors at small and large scales, despite some inappropriate behaviors such as oscillations. Therefore, further improvements of the present model are expected to provide appropriate descriptions of turbulent flows in the physical space.展开更多
Turbulent nonpremixed CH4/H2 flame has been simulated using several typical differential secondmoment turbulence closure (SMTC) models. To clarify the applicability of the various models, the LRR-IP model,JM model, SS...Turbulent nonpremixed CH4/H2 flame has been simulated using several typical differential secondmoment turbulence closure (SMTC) models. To clarify the applicability of the various models, the LRR-IP model,JM model, SSG model as well as two modified LRR-IP models were tested. Some of above-mentioned SMTC models cannot provide the overall satisfactory predictions of this challenging case. It is confirmed again that the standard LRR-IP model considerably overpredict the centerline velocity decay rate, and therefore performs not well. Also it is interesting to observe that the JM model does not perform well in this challenging test case, although it has already been proved successful in other cases. The SSG model produces quite satisfactory prediction and performs equally well or better than the two modified LRR-IP models in the reacting case. It can be concluded that the modified LRR-IP models as well as the SSG model are superior to the other SMTC models in the turbulent nonpremixed CH4/H2 flame.展开更多
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. U...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.展开更多
The structures and the vertical profiles of turbulent variance and covariance of the stably stratified boundary layer (SBL) are simulated with a second-order closure turbulence model. The results confirm that the ver... The structures and the vertical profiles of turbulent variance and covariance of the stably stratified boundary layer (SBL) are simulated with a second-order closure turbulence model. The results confirm that the vertical profiles of the dimensionless turbulence variance and covariance can be well represented by the form F = A(1 - Z / h)x. Here h is the height of SBL. and both exponent a and coefficient A are the functions of terrain, baroclinicity, radiation cooling and the state of temporal development of SBL. Comparing with Minnesota and Cabauw experiment data, we have analysed the value of a and expounded the main reasons that great difference in a exists among different literatures.展开更多
基金supported by the National Natural Science Foundation of China (90716008)the MOST under 973 project (2009CB724100)
文摘Wall-bounded turbulent flow involves the development of multi-scale turbulent eddies, as well as a sharply varying boundary layer. Its theoretical descriptions are yet phenomenological. We present here a new framework called structural ensemble dynamics （SED）, which aims at using systematically all relevant statistical properties of turbulent structures for a quantitative description of ensemble means. A new set of closure equations based on the SED approach for a turbulent channel flow is presented. SED order functions are defined, and numerically determined from data of direct numerical simulations （DNS）. Computational results show that the new closure model reproduces accurately the solution of the original Navier-Stokes simulation, including the mean velocity profile, the kinetic energy of the streamwise velocity component, and every term in the energy budget equation. It is suggested that the SED-based studies of turbulent structure builds a bridge between the studies of physical mechanisms of turbulence and the development of accurate model equations for engineering predictions.
基金supported by National Natural Science Foundation of China(Grant Nos. 40776020, 41106032 and 40531005)National Basic Research Program of China (Grant Nos. G1999043800, 2006CB403600,2010CB950300 and 2010CB950404)
文摘Based on the equations of motion and the assumption that ocean turbulence is of isotropy or quasi-isotropy, we derived the closure equations of the second-order moments and the variation equations for characteristic quantities, which describe the mechanisms of advection transport and shear instability by the sum of wave-like and eddy-like motions and circulation. Given that ocean turbulence generated by wave breaking is dominant at the ocean surface, we presented the boundary conditions of the turbulence kinetic energy and its dissipation rate, which are determined by energy loss from wave breaking and entrainment depth respectively. According to the equilibrium solution of the variation equations and available data of the dissipation rate, we obtained an analytical estimation of the characteristic quantities of surface-wave-generated turbulence in the upper ocean and its related mixing coefficient. The derived kinetic dissipation rate was validated by field measurements qualitatively and quantitatively, and the mixing coefficient had fairly good consistency with previous results based on the Prandtl mixing length theory.
基金This project was financially supported by the National Committee of Science and Technology Grants/903-85-08-05
文摘A three-dimensional, first order turbulence closure, thermal diffusion model is described in this paper. The governing equations consist of an equation of continuity, three components of momentum, conservation equations for salt, temperature and subgridscale energy, and an equation of state. In the model, according to the hypothesis of Kolmogorov and Prandtl, the viscosity coefficient of turbulent flow of homogeneous fluid is related to the local turbulent energy, and the horizontal and vertical exchange coefficients of mass, heat and momentum are computed with the introduction of subgridscale turbulence energy. The governing equations are solved by finite difference techniques. This model is applied to the Jiaozhou bay to predict thermal pollution by the Huangdao power plant. An instantaneous tidal current field is computed, then the distribution of temperature increment is predicted, and finally the effect of wind stress on thermal discharge is discussed.
文摘In this paper the system of Reynolds equations of the multi-scaled atmospheric motions is set up based on the con- cept of decomposing the meteorological elements into multi-scale disturbances.It is proved to be true that the Reynolds exchange term in the averaged motion is equal to the sum of averaged nonlinear terms in all sub-averaged motions.In order to avoid the higher order closure in Eulerian approaches,a new K-theory based on the multi-scaled Reynolds equations is given in which the subscale motions are described by Langevin equation as the air particles are moving in the Eulerian average background.From the new K-theory are derived the momentum,heat and mass exchange coefficients as the functions of statistical variables such as variances and Lagrangian time scales of velocity,temperature and other meteorological elements in disturbances.The new K-theory also expounds the causes for the differences be- tween the exchange coefficients of one element and another and gives the ambient conditions in which the buoyancy and/or Coriolis force Will build the chaotic disturbances into the orderly gradient of mean values of the corresponding elements.In consequence the K-theory can be used to explain some of negative viscosity phenomena in atmospheric mo- tions.
基金supported by the National Natural Science Foundation of China(Nos.11572025,11202013,and 51420105008)
文摘Closure models started from Chou＇s work have been developed for more than 70 years, aiming at providing analytical tools to describe turbulent flows in the spectral space. In this study, a preliminary attempt is presented to introduce a closure model in the physical space, using the velocity structure functions as key parameters. The present closure model appears to qualitatively reproduce the asymptotic scaling behav- iors at small and large scales, despite some inappropriate behaviors such as oscillations. Therefore, further improvements of the present model are expected to provide appropriate descriptions of turbulent flows in the physical space.
文摘Turbulent nonpremixed CH4/H2 flame has been simulated using several typical differential secondmoment turbulence closure (SMTC) models. To clarify the applicability of the various models, the LRR-IP model,JM model, SSG model as well as two modified LRR-IP models were tested. Some of above-mentioned SMTC models cannot provide the overall satisfactory predictions of this challenging case. It is confirmed again that the standard LRR-IP model considerably overpredict the centerline velocity decay rate, and therefore performs not well. Also it is interesting to observe that the JM model does not perform well in this challenging test case, although it has already been proved successful in other cases. The SSG model produces quite satisfactory prediction and performs equally well or better than the two modified LRR-IP models in the reacting case. It can be concluded that the modified LRR-IP models as well as the SSG model are superior to the other SMTC models in the turbulent nonpremixed CH4/H2 flame.
基金supported by the National Natural Science Foundation of China(Grant Nos.41006017,41476006)the Natural Science Foundation of Fujian Province of China(Grant No.2015J06010)
文摘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.
文摘 The structures and the vertical profiles of turbulent variance and covariance of the stably stratified boundary layer (SBL) are simulated with a second-order closure turbulence model. The results confirm that the vertical profiles of the dimensionless turbulence variance and covariance can be well represented by the form F = A(1 - Z / h)x. Here h is the height of SBL. and both exponent a and coefficient A are the functions of terrain, baroclinicity, radiation cooling and the state of temporal development of SBL. Comparing with Minnesota and Cabauw experiment data, we have analysed the value of a and expounded the main reasons that great difference in a exists among different literatures.
