Despite dedicated effort for many decades,statistical description of highly technologically important wall turbulence remains a great challenge.Current models are unfortunately incomplete,or empirical,or qualitative.A...Despite dedicated effort for many decades,statistical description of highly technologically important wall turbulence remains a great challenge.Current models are unfortunately incomplete,or empirical,or qualitative.After a review of the existing theories of wall turbulence,we present a new framework,called the structure ensemble dynamics （SED）,which aims at integrating the turbulence dynamics into a quantitative description of the mean flow.The SED theory naturally evolves from a statistical physics understanding of non-equilibrium open systems,such as fluid turbulence, for which mean quantities are intimately coupled with the fluctuation dynamics.Starting from the ensemble-averaged Navier-Stokes（EANS） equations,the theory postulates the existence of a finite number of statistical states yielding a multi-layer picture for wall turbulence.Then,it uses order functions（ratios of terms in the mean momentum as well as energy equations） to characterize the states and transitions between states.Application of the SED analysis to an incompressible channel flow and a compressible turbulent boundary layer shows that the order functions successfully reveal the multi-layer structure for wall-bounded turbulence, which arises as a quantitative extension of the traditional view in terms of sub-layer,buffer layer,log layer and wake. Furthermore,an idea of using a set of hyperbolic functions for modeling transitions between layers is proposed for a quantitative model of order functions across the entire flow domain.We conclude that the SED provides a theoretical framework for expressing the yet-unknown effects of fluctuation structures on the mean quantities,and offers new methods to analyze experimental and simulation data.Combined with asymptotic analysis,it also offers a way to evaluate convergence of simulations.The SED approach successfully describes the dynamics at both momentum and energy levels, in contrast with all prevalent approaches describing the mean velocity profile only.Moreover,the SED theoretical framework is general,independent of the flow system to study, while the actual functional form of the order functions may vary from flow to flow.We assert that as the knowledge of order functions is accumulated and as more flows are analyzed, new principles（such as hierarchy,symmetry,group invariance,etc.） governing the role of turbulent structures in the mean flow properties will be clarified and a viable theory of turbulence might emerge.展开更多
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and ...The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion function. The generalized Fourier transform approach is the extension of the Fourier transform method used for the normal diffusion equation. The feasibility of the approach is validated by comparing the numerical result with the exact solution for a point-source. The merit of the numerical method is that it provides a way to calculate anomalous diffusion with an arbitrary initial condition.展开更多
Classical Mach-number(M) scaling in compressible wall turbulence was suggested by van Driest(Van Driest E R.Turbulent boundary layers in compressible fluids.J Aerodynamics Science,1951,18(3):145-160) and Huang et al.(...Classical Mach-number(M) scaling in compressible wall turbulence was suggested by van Driest(Van Driest E R.Turbulent boundary layers in compressible fluids.J Aerodynamics Science,1951,18(3):145-160) and Huang et al.(Huang P G,Coleman G N,Bradshaw P.Compressible turbulent channel flows:DNS results and modeling.J Fluid Mech,1995,305:185-218).Using a concept of velocity-vorticity correlation structure(VVCS),defined by high correlation regions in a field of two-point cross-correlation coefficient between a velocity and a vorticity component,we have discovered a limiting VVCS as the closest streamwise vortex structure to the wall,which provides a concrete Morkovin scaling summarizing all compressibility effects.Specifically,when the height and mean velocity of the limiting VVCS are used as the units for the length scale and the velocity,all geometrical measures in the spanwise and normal directions,as well as the mean velocity and fluctuation(r.m.s) profiles become M-independent.The results are validated by direct numerical simulations(DNS) of compressible channel flows with M up to 3.Furthermore,a quantitative model is found for the M-scaling in terms of the wall density,which is also validated by the DNS data.These findings yield a geometrical interpretation of the semi-local transformation(Huang et al.,1995),and a conclusion that the location and the thermodynamic properties associated with the limiting VVCS determine the M-effects on supersonic wall-bounded flows.展开更多
基金supported by the National Natural Science Foundation of China(90716008)the National Basic Research Program of China(2009CB724100).
文摘Despite dedicated effort for many decades,statistical description of highly technologically important wall turbulence remains a great challenge.Current models are unfortunately incomplete,or empirical,or qualitative.After a review of the existing theories of wall turbulence,we present a new framework,called the structure ensemble dynamics （SED）,which aims at integrating the turbulence dynamics into a quantitative description of the mean flow.The SED theory naturally evolves from a statistical physics understanding of non-equilibrium open systems,such as fluid turbulence, for which mean quantities are intimately coupled with the fluctuation dynamics.Starting from the ensemble-averaged Navier-Stokes（EANS） equations,the theory postulates the existence of a finite number of statistical states yielding a multi-layer picture for wall turbulence.Then,it uses order functions（ratios of terms in the mean momentum as well as energy equations） to characterize the states and transitions between states.Application of the SED analysis to an incompressible channel flow and a compressible turbulent boundary layer shows that the order functions successfully reveal the multi-layer structure for wall-bounded turbulence, which arises as a quantitative extension of the traditional view in terms of sub-layer,buffer layer,log layer and wake. Furthermore,an idea of using a set of hyperbolic functions for modeling transitions between layers is proposed for a quantitative model of order functions across the entire flow domain.We conclude that the SED provides a theoretical framework for expressing the yet-unknown effects of fluctuation structures on the mean quantities,and offers new methods to analyze experimental and simulation data.Combined with asymptotic analysis,it also offers a way to evaluate convergence of simulations.The SED approach successfully describes the dynamics at both momentum and energy levels, in contrast with all prevalent approaches describing the mean velocity profile only.Moreover,the SED theoretical framework is general,independent of the flow system to study, while the actual functional form of the order functions may vary from flow to flow.We assert that as the knowledge of order functions is accumulated and as more flows are analyzed, new principles（such as hierarchy,symmetry,group invariance,etc.） governing the role of turbulent structures in the mean flow properties will be clarified and a viable theory of turbulence might emerge.
文摘The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion function. The generalized Fourier transform approach is the extension of the Fourier transform method used for the normal diffusion equation. The feasibility of the approach is validated by comparing the numerical result with the exact solution for a point-source. The merit of the numerical method is that it provides a way to calculate anomalous diffusion with an arbitrary initial condition.
基金supported by the National Nature Science Foundation of China (Grant Nos.90716008,10572004 and 11172006)the National Basic Research Program of China (Grant No.2009CB724100)
文摘Classical Mach-number(M) scaling in compressible wall turbulence was suggested by van Driest(Van Driest E R.Turbulent boundary layers in compressible fluids.J Aerodynamics Science,1951,18(3):145-160) and Huang et al.(Huang P G,Coleman G N,Bradshaw P.Compressible turbulent channel flows:DNS results and modeling.J Fluid Mech,1995,305:185-218).Using a concept of velocity-vorticity correlation structure(VVCS),defined by high correlation regions in a field of two-point cross-correlation coefficient between a velocity and a vorticity component,we have discovered a limiting VVCS as the closest streamwise vortex structure to the wall,which provides a concrete Morkovin scaling summarizing all compressibility effects.Specifically,when the height and mean velocity of the limiting VVCS are used as the units for the length scale and the velocity,all geometrical measures in the spanwise and normal directions,as well as the mean velocity and fluctuation(r.m.s) profiles become M-independent.The results are validated by direct numerical simulations(DNS) of compressible channel flows with M up to 3.Furthermore,a quantitative model is found for the M-scaling in terms of the wall density,which is also validated by the DNS data.These findings yield a geometrical interpretation of the semi-local transformation(Huang et al.,1995),and a conclusion that the location and the thermodynamic properties associated with the limiting VVCS determine the M-effects on supersonic wall-bounded flows.
