Theoretical results on the scaling properties of turbulent velocity fields are reported in this letter.Based on the Kolmogorov equation and typical models of the second-order statistical moments (energy spectrum and t...Theoretical results on the scaling properties of turbulent velocity fields are reported in this letter.Based on the Kolmogorov equation and typical models of the second-order statistical moments (energy spectrum and the second-order structure function),we have studied the relative scaling using the ESS method.It is found that the relative EES scaling exponent Sis greater than the real or theoretical inertial range scaling exponentξ,which is attributed to an evident bump in the ESS range.展开更多
Time-resolved particle image velocimetry（TRPIV） experiments are performed to investigate the coherent structure＇s performance of riblets in a turbulent boundary layer（TBL） at a friction Reynolds number of 185. To...Time-resolved particle image velocimetry（TRPIV） experiments are performed to investigate the coherent structure＇s performance of riblets in a turbulent boundary layer（TBL） at a friction Reynolds number of 185. To visualize the energetic large-scale coherent structures（CSs） over a smooth surface and riblets, the proper orthogonal decomposition（POD） and finite-time Lyapunov exponent（FTLE） are used to identify the CSs in the TBL. Spatial-temporal correlation is implemented to obtain the characters and transport properties of typical CSs in the FTLE fields. The results demonstrate that the generic flow structures, such as hairpin-like vortices, are also observed in the boundary layer flow over the riblets, consistent with its smooth counterpart. Low-order POD modes are more sensitive to the riblets in comparison with the high-order ones,and the wall-normal movement of the most energy-containing structures are suppressed over riblets. The spatial correlation analysis of the FTLE fields indicates that the evolution process of the hairpin vortex over riblets are inhibited. An apparent decrease of the convection velocity over riblets is noted, which is believed to reduce the ejection/sweep motions associated with high shear stress from the viscous sublayer. These reductions exhibit inhibition of momentum transfer among the structures near the wall in the TBL flows.展开更多
Precipitation sequence is a typical nonlinear and chaotic observational series, and studies on precipitation forecasts are restricted to the use of traditional linear statistical methods, especially when analysing the...Precipitation sequence is a typical nonlinear and chaotic observational series, and studies on precipitation forecasts are restricted to the use of traditional linear statistical methods, especially when analysing the regional characteristics of precipitation. In the context of 20 stations＇ daily precipitation series （from 1956 to 2000） in South China （SC） and North China （NC）, we divide each precipitation series into many self-stationary segments by using the heuristic segmentation algorithm （briefly BG algorithm）. For each station＇s precipitation series, we calculate the exponent of power-law tall （EPT） of the cumulative probability distribution of segments with a length larger than l for precipitation and temperature series. Our results show that the power-law decay of the cumulative probability distribution of stationary segments might be a common attribution for precipitation and other nonstationary time series; the EPT somewhat indicates the precipitation duration and its spatial distribution that might be different from area to area. The EPT in NC is larger than in SC; Meanwhile, EPT might be another effective way to study the abrupt changes in nonlinear and nonstationary time series.展开更多
Wavelet analysis is applied to study the global and local scaling exponents in fully developed asymmetric channel flow. Global exponents are calculated by orthogonal wavelets and Extended Scaling Similarity(ESS). The ...Wavelet analysis is applied to study the global and local scaling exponents in fully developed asymmetric channel flow. Global exponents are calculated by orthogonal wavelets and Extended Scaling Similarity(ESS). The results show that the flow in an asymmetric channel flow exhibits different characteristics of intermittency from that in a symmetric flow. It is also shown that the intermittency property of the streamwise fluctuations is different from that of vertical fluctuations, and the intermittency does not decay with the increase of the distance from the wall. In addition, the Continuous Wavelet Transform(CWT) method is found to be unreliable to calculate the local scaling components. Finally, it is pointed out that the existence and the significance of negative local scaling components need further study.展开更多
Using complete orthonormal sets of ψ^α-exponential type orbitals in single exponent approximation the new approach has been suggested for construction of different kinds of functions which can be useful in the theor...Using complete orthonormal sets of ψ^α-exponential type orbitals in single exponent approximation the new approach has been suggested for construction of different kinds of functions which can be useful in the theory of linear combination of atomic orbitals. These functions can be chosen properly according to the nature of the problems under consideration. This is rather important because the choice of the basis set may be play a crucial role in applications to atomic and molecular problems. As an example of application, different atomic orbitals for the ground states of the neutral and the first ten cationic members of the isoelectronic series of He atom are constructed by the solution of Hartree-Fock-Roothaan equations using ψ^1, ψ^0 and ψ^-1 basis sets. The cMculated results are close to the numerical Hartree-Fock values. The total energy, expansion coefficients, orbital exponents and virial ratio for each atom are presented.展开更多
Streamwise evolution of longitudinal and transverse velocity structure functions in a decaying homogeneous and nearly isotropic turbulence is reported for Reynolds numbers Reλ up to 720. First, two theoretical relati...Streamwise evolution of longitudinal and transverse velocity structure functions in a decaying homogeneous and nearly isotropic turbulence is reported for Reynolds numbers Reλ up to 720. First, two theoretical relations between longitudinal and transverse structure functions are examined in the light of recently derived relations and the results show that the low-order transverse structure functions can be well approximated by longitudinal ones within the sub-inertial range. Reconstruction of fourth-order transverse structure functions with a recently proposed relation by Grauer et al. is comparatively less valid than the relation already proposed by Antonia et al. Secondly, extended self-similarity methods are used to measure the scaling exponents up to order eight and the streamwise evolution of scaling exponents is explored. The scaling exponents of longitudinal structure functions are, at first location, close to Zybin's model, and at the fourth location, close to She–Leveque model. No obvious trend is found for the streamwise evolution of longitudinal scaling exponents, whereas, on the contrary, transverse scaling exponents become slightly smaller with the development of a steamwise direction. Finally, the stremwise variation of the order-dependent isotropy ratio indicates the turbulence at the last location is closer to isotropic than the other three locations.展开更多
Local cascade （LC） scheme and space-time correlations are used to study turbulent structures and their convection behaviour in the near-wall region of compressible boundaxy layers at Ma = 0.8 and 1.3. The convection...Local cascade （LC） scheme and space-time correlations are used to study turbulent structures and their convection behaviour in the near-wall region of compressible boundaxy layers at Ma = 0.8 and 1.3. The convection velocities of fluctuating velocity components u （streamwise） and v （vertical） are investigated by statistically analysing scale-dependent ensembles of LC structures. The results suggest that u is convected with entropy perturbations while v with an isentropic process. An abnormal thin layer distinct from the conventional viscous sub-layer is discovered in the immediate vicinity of the wall （y^＋ ≤ 1） in supersonic flows. While in the region 1 〈 y^＋ 〈 30, streamwise streaks dominate velocity, density and temperature fluctuations, the abnormal thin layer is dominated by spanwise streaks in vertical velocity and density fluctuations, where pressure and density fluctuations are strongly correlated. The LC scheme is proven to be effective in studying the nature of supersonic flows and compressibility effects on wall-bounded motions.展开更多
Turbulent boundary layer control via a streamwise travelling wave is investigated based on direct numerical simulation of an incompressible turbulent channel flow. The streamwise travelling wave is induced on one side...Turbulent boundary layer control via a streamwise travelling wave is investigated based on direct numerical simulation of an incompressible turbulent channel flow. The streamwise travelling wave is induced on one side wall of the channel by a spanwise external force, e.g., Lorenz force, which is con^ned in the viscous sublayer. As the control strategy used in this study has never been examined, we pay our attention to its efficiency of drag control. It is revealed that the propagating direction of the travelling wave, i.e., the downstream or upstream propagating direction with respect to the streamwise flow, has an important role on the drag control, leading to a significant drag reduction or enhancement for the parameters considered. The coherent structures of turbulent boundary layer are altered and the underlying mechanisms are analysed. The results obtained provide physical insight into the understanding of turbulent boundary layer control.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 vert...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
In the present study, a high Reynolds number version of a turbulence model was proposed by using drag reduction to analyze the turbulent flows of power-law fluid for engineering applications. In order to determine the...In the present study, a high Reynolds number version of a turbulence model was proposed by using drag reduction to analyze the turbulent flows of power-law fluid for engineering applications. In order to determine the model constants in the constitutive equation, numerical simulation was conducted under the same conditions that were applied to obtain the experiment re- suits and previous turbulence models. For validation of the modified turbulence model, numerical simulations were performed for power-law fluids of different viscosities. The results of the modified k-ε turbulence model showed better agreement with the experimental results than those of the standard k-ε turbulence model. In addition, computation time and computer resource of the modified k-ε turbulence model were reduced by about one third as compared to the low Reynolds number model for power-law fluids.展开更多
基金supported by the National Natural Science Foundation of China(90816013,10572083)also supported by State Key Laboratory for Turbulence and Complex System
文摘Theoretical results on the scaling properties of turbulent velocity fields are reported in this letter.Based on the Kolmogorov equation and typical models of the second-order statistical moments (energy spectrum and the second-order structure function),we have studied the relative scaling using the ESS method.It is found that the relative EES scaling exponent Sis greater than the real or theoretical inertial range scaling exponentξ,which is attributed to an evident bump in the ESS range.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11332006,11732010,11572221,and 11502066)the Natural Science Foundation of Tianjin City(Grant No.18JCQNJC5100)
文摘Time-resolved particle image velocimetry（TRPIV） experiments are performed to investigate the coherent structure＇s performance of riblets in a turbulent boundary layer（TBL） at a friction Reynolds number of 185. To visualize the energetic large-scale coherent structures（CSs） over a smooth surface and riblets, the proper orthogonal decomposition（POD） and finite-time Lyapunov exponent（FTLE） are used to identify the CSs in the TBL. Spatial-temporal correlation is implemented to obtain the characters and transport properties of typical CSs in the FTLE fields. The results demonstrate that the generic flow structures, such as hairpin-like vortices, are also observed in the boundary layer flow over the riblets, consistent with its smooth counterpart. Low-order POD modes are more sensitive to the riblets in comparison with the high-order ones,and the wall-normal movement of the most energy-containing structures are suppressed over riblets. The spatial correlation analysis of the FTLE fields indicates that the evolution process of the hairpin vortex over riblets are inhibited. An apparent decrease of the convection velocity over riblets is noted, which is believed to reduce the ejection/sweep motions associated with high shear stress from the viscous sublayer. These reductions exhibit inhibition of momentum transfer among the structures near the wall in the TBL flows.
基金supported by the National Natural Science Foundation of China (Grant No 40675044)the State Key development program for Basic Research (Grant No 2006CB400503)
文摘Precipitation sequence is a typical nonlinear and chaotic observational series, and studies on precipitation forecasts are restricted to the use of traditional linear statistical methods, especially when analysing the regional characteristics of precipitation. In the context of 20 stations＇ daily precipitation series （from 1956 to 2000） in South China （SC） and North China （NC）, we divide each precipitation series into many self-stationary segments by using the heuristic segmentation algorithm （briefly BG algorithm）. For each station＇s precipitation series, we calculate the exponent of power-law tall （EPT） of the cumulative probability distribution of segments with a length larger than l for precipitation and temperature series. Our results show that the power-law decay of the cumulative probability distribution of stationary segments might be a common attribution for precipitation and other nonstationary time series; the EPT somewhat indicates the precipitation duration and its spatial distribution that might be different from area to area. The EPT in NC is larger than in SC; Meanwhile, EPT might be another effective way to study the abrupt changes in nonlinear and nonstationary time series.
文摘Wavelet analysis is applied to study the global and local scaling exponents in fully developed asymmetric channel flow. Global exponents are calculated by orthogonal wavelets and Extended Scaling Similarity(ESS). The results show that the flow in an asymmetric channel flow exhibits different characteristics of intermittency from that in a symmetric flow. It is also shown that the intermittency property of the streamwise fluctuations is different from that of vertical fluctuations, and the intermittency does not decay with the increase of the distance from the wall. In addition, the Continuous Wavelet Transform(CWT) method is found to be unreliable to calculate the local scaling components. Finally, it is pointed out that the existence and the significance of negative local scaling components need further study.
文摘Using complete orthonormal sets of ψ^α-exponential type orbitals in single exponent approximation the new approach has been suggested for construction of different kinds of functions which can be useful in the theory of linear combination of atomic orbitals. These functions can be chosen properly according to the nature of the problems under consideration. This is rather important because the choice of the basis set may be play a crucial role in applications to atomic and molecular problems. As an example of application, different atomic orbitals for the ground states of the neutral and the first ten cationic members of the isoelectronic series of He atom are constructed by the solution of Hartree-Fock-Roothaan equations using ψ^1, ψ^0 and ψ^-1 basis sets. The cMculated results are close to the numerical Hartree-Fock values. The total energy, expansion coefficients, orbital exponents and virial ratio for each atom are presented.
基金Project supported by the National Natural Science Foundation of China （Grant Nos. 11272196, 11002085, and 11032007） and the Key Project of Education Commission of Shanghai Municipal, China （Grant No. 11ZZ87）.
文摘Streamwise evolution of longitudinal and transverse velocity structure functions in a decaying homogeneous and nearly isotropic turbulence is reported for Reynolds numbers Reλ up to 720. First, two theoretical relations between longitudinal and transverse structure functions are examined in the light of recently derived relations and the results show that the low-order transverse structure functions can be well approximated by longitudinal ones within the sub-inertial range. Reconstruction of fourth-order transverse structure functions with a recently proposed relation by Grauer et al. is comparatively less valid than the relation already proposed by Antonia et al. Secondly, extended self-similarity methods are used to measure the scaling exponents up to order eight and the streamwise evolution of scaling exponents is explored. The scaling exponents of longitudinal structure functions are, at first location, close to Zybin's model, and at the fourth location, close to She–Leveque model. No obvious trend is found for the streamwise evolution of longitudinal scaling exponents, whereas, on the contrary, transverse scaling exponents become slightly smaller with the development of a steamwise direction. Finally, the stremwise variation of the order-dependent isotropy ratio indicates the turbulence at the last location is closer to isotropic than the other three locations.
基金Supported by the National Natural Science Foundation of China under Grant Nos 90716008 and 10572004.
文摘Local cascade （LC） scheme and space-time correlations are used to study turbulent structures and their convection behaviour in the near-wall region of compressible boundaxy layers at Ma = 0.8 and 1.3. The convection velocities of fluctuating velocity components u （streamwise） and v （vertical） are investigated by statistically analysing scale-dependent ensembles of LC structures. The results suggest that u is convected with entropy perturbations while v with an isentropic process. An abnormal thin layer distinct from the conventional viscous sub-layer is discovered in the immediate vicinity of the wall （y^＋ ≤ 1） in supersonic flows. While in the region 1 〈 y^＋ 〈 30, streamwise streaks dominate velocity, density and temperature fluctuations, the abnormal thin layer is dominated by spanwise streaks in vertical velocity and density fluctuations, where pressure and density fluctuations are strongly correlated. The LC scheme is proven to be effective in studying the nature of supersonic flows and compressibility effects on wall-bounded motions.
基金Supported by the National Natural Science Foundation of China under Grant Nos 90405007, 90605005 and 10772173, the Programme for Changjiang Scholars and Innovative Research Team in the University under Grant No IRT0538, the Science and Technology Innovative Foundation of Chinese Academy of Sciences （CXJJ-237）, and the Anhui Province Excellent Young Scholars Foundation under Grant No 08040106826.
文摘Turbulent boundary layer control via a streamwise travelling wave is investigated based on direct numerical simulation of an incompressible turbulent channel flow. The streamwise travelling wave is induced on one side wall of the channel by a spanwise external force, e.g., Lorenz force, which is con^ned in the viscous sublayer. As the control strategy used in this study has never been examined, we pay our attention to its efficiency of drag control. It is revealed that the propagating direction of the travelling wave, i.e., the downstream or upstream propagating direction with respect to the streamwise flow, has an important role on the drag control, leading to a significant drag reduction or enhancement for the parameters considered. The coherent structures of turbulent boundary layer are altered and the underlying mechanisms are analysed. The results obtained provide physical insight into the understanding of turbulent boundary layer control.
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.
基金supported by the Chung-Ang University Research Grant in 2008
文摘In the present study, a high Reynolds number version of a turbulence model was proposed by using drag reduction to analyze the turbulent flows of power-law fluid for engineering applications. In order to determine the model constants in the constitutive equation, numerical simulation was conducted under the same conditions that were applied to obtain the experiment re- suits and previous turbulence models. For validation of the modified turbulence model, numerical simulations were performed for power-law fluids of different viscosities. The results of the modified k-ε turbulence model showed better agreement with the experimental results than those of the standard k-ε turbulence model. In addition, computation time and computer resource of the modified k-ε turbulence model were reduced by about one third as compared to the low Reynolds number model for power-law fluids.
