The relationship between stabilities of the buoyancy boundary layers along an inclined plate and a vertical plate immersed in a stratified medium is studied theoretically and numerically. The eigenvalue problem of ene...The relationship between stabilities of the buoyancy boundary layers along an inclined plate and a vertical plate immersed in a stratified medium is studied theoretically and numerically. The eigenvalue problem of energy stability is solved with the method of descending exponentials. The disturbance energy is found to be able to grow to 11.62 times as large as the initial disturbance energy for Pr = 0.72 when the Grashof number is between the critical Grashof numbers of the energy stability and the linear stability. We prove that, with a weighted energy method, the basic flow of the vertical buoyancy boundary layer is stable to finite-amplitude streamwise-independent disturbances.展开更多
This study develops a direct optimal growth algorithm for three-dimensional transient growth analysis of perturbations in channel flows which are globally stable but locally unstable. Different from traditional non-mo...This study develops a direct optimal growth algorithm for three-dimensional transient growth analysis of perturbations in channel flows which are globally stable but locally unstable. Different from traditional non-modal methods based on the Orr- Somrnerfeld and Squire （OSS） equations that assume simple base flows, this algorithm can be applied to arbitrarily complex base flows. In the proposed algorithm, a re- orthogonalization Arnoldi method is used to improve orthogonality of the orthogonal basis of the Krylov subspace generated by solving the linearized forward and adjoint Navier-Stokes （N-S） equations. The linearized adjoint N-S equations with the specific boundary conditions for the channel are derived, and a new convergence criterion is pro- posed. The algorithm is then applied to a one-dimensional base flow （the plane Poiseuille flow） and a two-dimensional base flow （the plane Poiseuille flow with a low-speed streak） in a channel. For one-dimensional cases, the effects of the spanwise width of the chan- nel and the Reynolds number on the transient growth of perturbations are studied. For two-dimensional cases, the effect of strength of initial low-speed streak is discussed. The presence of the streak in the plane Poiseuille flow leads to a larger and quicker growth of the perturbations than that in the one-dimensional case. For both cases, the results show that an optimal flow field leading to the largest growth of perturbations is character- ized by high- and low-speed streaks and the corresponding streamwise vortical structures. The lift-up mechanism that induces the transient growth of perturbations is discussed. The performance of the re-orthogonalization Arnoldi technique in the algorithm for both one- and two-dimensional base flows is demonstrated, and the algorithm is validated by comparing the results with those obtained from the OSS equations method and the cross- check method.展开更多
The transient growth due to non-normMity is investigated for the Poiseuille- Rayleigh-Benard problem of binary fluids with the Soret effect. For negative separation factors such as ψ = -0.1, it is found that a large ...The transient growth due to non-normMity is investigated for the Poiseuille- Rayleigh-Benard problem of binary fluids with the Soret effect. For negative separation factors such as ψ = -0.1, it is found that a large transient growth can be obtained by the non-normal interaction of the two least-stable-modes, i.e., the upstream and downstream modes, which determine the linear critical boundary curves for small Reynolds numbers. The transient growth is so strong that the optimal energy amplification factor G（t） is up to 10^2 - 10^3. While for positive separation factors such as ψ = 0.1, the transient growth is weak with the order O（I） of the amplification factor, which can even be computed by the least-stable-mode. However, for both cases, the least-stable-mode can govern the long-term behavior of the amplification factor for large time. The results also show that large Reynolds numbers have stabilization effects for the maximum amplification within moderate wave number regions. Meanwhile, much small negative or large positive separation factors and large Rayleigh numbers can enlarge the maximum transient growth of the pure streamwise disturbance with the wavenumber α= 3.14. Moreover, the initial and evolutionary two-dimensional spatial patterns of the large transient growth for the pure streamwise disturbance are exhibited with a plot of the velocity vector, spanwise vorticity, temperature, and concentration field. The initial three-layer cell vorticity struc- ture is revealed. When the amplification factor reaches the maximum Gmax, it develops into one cell structure with large amplification for the vorticity strength.展开更多
The optimal transient growth process of perturbations driven by the pressure gradient is studied in a turbulent pipe flow. A new computational method is proposed, based on the projection operators which project the go...The optimal transient growth process of perturbations driven by the pressure gradient is studied in a turbulent pipe flow. A new computational method is proposed, based on the projection operators which project the governing equations onto the sub- space spanned by the radial vorticity and radial velocity. The method is validated by comparing with the previous studies. Two peaks of the maximum transient growth am- plification curve are found at different Reynolds numbers ranging from 20 000 to 250 000. The optimal flow structures are obtained and compared with the experiments and DNS results. The location of the outer peak is at the azimuthal wave number n = 1, while the location of the inner peak is varying with the Reynolds number. It is observed that the velocity streaks in the buffer layer with a spacing of 100δv are the most amplified flow structures. Finally, we consider the optimal transient growth time and its dependence on the azimuthal wave length. It shows a self-similar behavior for perturbations of different scales in the optimal transient growth process.展开更多
Linear transient growth of optimal perturbations in particle-laden turbulent channel flow is investigated in this work.The problem is formulated in the framework of a Eulerian-Eulerian approach,employing two-way coupl...Linear transient growth of optimal perturbations in particle-laden turbulent channel flow is investigated in this work.The problem is formulated in the framework of a Eulerian-Eulerian approach,employing two-way coupling between fine particles and fluid flow.The model is first validated in laminar cases,after which the transient growth of coherent perturbations in turbulent channel flow is investigated,where the mean particle concentration distribution is obtained by direct numerical simulation.It is shown that the optimal small-scale structures for particles are streamwise streaks just below the optimal streamwise velocity streaks,as was previously found in numerical simulations of particle-laden channel flow.This indicates that the optimal growth of perturbations is a dominant mechanism for the distribution of particles in the near-wall region.The current study also considers the transient growth of small-and large-scale perturbations at relatively high Reynolds numbers,which reveals that the optimal large-scale structures for particles are in the near-wall region while the optimal large-scale structures for fluid enter the outer region.展开更多
Previous studies show that transient axonal glycoprotein-1, a ligand of amyloid precursor pro- tein, increases the secretion of amyloid precursor protein intracellular domain and is involved in apoptosis in Alzheimer...Previous studies show that transient axonal glycoprotein-1, a ligand of amyloid precursor pro- tein, increases the secretion of amyloid precursor protein intracellular domain and is involved in apoptosis in Alzheimer＇s disease. In this study, we examined the effects of transient axonal glyco- protein-1 on U251 glioma cells. 3-（4,5-Dimethylthiazol-2-yl）-2,5-diphenyltetrazolium bromide assay showed that transient axonal glycoprotein-1 did not inhibit the proliferation of U251 cells, but promoted cell viability. The terminal deoxynucleotidyl transferase dUTP nick end labeling assay showed that transient axonal glycoprotein-1 did not induce U251 cell apoptosis. Real-time PCR revealed that transient axonal glycoprotein-1 substantially upregulated levels of amyloid precursor protein intracellular C-terminal domain, and p53 and epidermal growth factor recep- tor mRNA expression. Thus, transient axonal glycoprotein-1 increased apoptosis-related gene expression in U251 cells without inducing apoptosis. Instead, transient axonal glycoprotein-1 promoted the proliferation of these glioma cells.展开更多
The generation of a hairpin vortex from near-wall streamwise vortices is studied via the direct numerical simulation（DNS） of the streak transient growth in the minimal channel flow at Re_τ- 400.The streak profile i...The generation of a hairpin vortex from near-wall streamwise vortices is studied via the direct numerical simulation（DNS） of the streak transient growth in the minimal channel flow at Re_τ- 400.The streak profile is obtained by conditionally averaging the DNS data of the fully developed turbulent channel flow at the same Reynolds number.The near-wall streamwise vortices are produced by the transient growth of the streak which is initially subjected to the sinuous perturbation of the spanwise velocity.It is shown that the arch head of the hairpin vortex first grows from the downstream end of the stronger streamwise vortex and then connects with the weaker,opposite-signed streamwise vortex in their overlap region,forming a complete individual hairpin structure.The vorticity transport along the vortex lines indicates that the strength increase and the spatial expansion of the arch head are due to the stretching and the turning of the vorticity vector,respectively.The hairpin packets could be further produced from the generated individual hairpin vortex following the parent-offspring process.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11225209,11490553,and 11521091)
文摘The relationship between stabilities of the buoyancy boundary layers along an inclined plate and a vertical plate immersed in a stratified medium is studied theoretically and numerically. The eigenvalue problem of energy stability is solved with the method of descending exponentials. The disturbance energy is found to be able to grow to 11.62 times as large as the initial disturbance energy for Pr = 0.72 when the Grashof number is between the critical Grashof numbers of the energy stability and the linear stability. We prove that, with a weighted energy method, the basic flow of the vertical buoyancy boundary layer is stable to finite-amplitude streamwise-independent disturbances.
基金supported by the National Natural Science Foundation of China(No.11372140)
文摘This study develops a direct optimal growth algorithm for three-dimensional transient growth analysis of perturbations in channel flows which are globally stable but locally unstable. Different from traditional non-modal methods based on the Orr- Somrnerfeld and Squire （OSS） equations that assume simple base flows, this algorithm can be applied to arbitrarily complex base flows. In the proposed algorithm, a re- orthogonalization Arnoldi method is used to improve orthogonality of the orthogonal basis of the Krylov subspace generated by solving the linearized forward and adjoint Navier-Stokes （N-S） equations. The linearized adjoint N-S equations with the specific boundary conditions for the channel are derived, and a new convergence criterion is pro- posed. The algorithm is then applied to a one-dimensional base flow （the plane Poiseuille flow） and a two-dimensional base flow （the plane Poiseuille flow with a low-speed streak） in a channel. For one-dimensional cases, the effects of the spanwise width of the chan- nel and the Reynolds number on the transient growth of perturbations are studied. For two-dimensional cases, the effect of strength of initial low-speed streak is discussed. The presence of the streak in the plane Poiseuille flow leads to a larger and quicker growth of the perturbations than that in the one-dimensional case. For both cases, the results show that an optimal flow field leading to the largest growth of perturbations is character- ized by high- and low-speed streaks and the corresponding streamwise vortical structures. The lift-up mechanism that induces the transient growth of perturbations is discussed. The performance of the re-orthogonalization Arnoldi technique in the algorithm for both one- and two-dimensional base flows is demonstrated, and the algorithm is validated by comparing the results with those obtained from the OSS equations method and the cross- check method.
基金Project supported by the National Natural Science Foundation of China(Nos.11172049 and11472060)
文摘The transient growth due to non-normMity is investigated for the Poiseuille- Rayleigh-Benard problem of binary fluids with the Soret effect. For negative separation factors such as ψ = -0.1, it is found that a large transient growth can be obtained by the non-normal interaction of the two least-stable-modes, i.e., the upstream and downstream modes, which determine the linear critical boundary curves for small Reynolds numbers. The transient growth is so strong that the optimal energy amplification factor G（t） is up to 10^2 - 10^3. While for positive separation factors such as ψ = 0.1, the transient growth is weak with the order O（I） of the amplification factor, which can even be computed by the least-stable-mode. However, for both cases, the least-stable-mode can govern the long-term behavior of the amplification factor for large time. The results also show that large Reynolds numbers have stabilization effects for the maximum amplification within moderate wave number regions. Meanwhile, much small negative or large positive separation factors and large Rayleigh numbers can enlarge the maximum transient growth of the pure streamwise disturbance with the wavenumber α= 3.14. Moreover, the initial and evolutionary two-dimensional spatial patterns of the large transient growth for the pure streamwise disturbance are exhibited with a plot of the velocity vector, spanwise vorticity, temperature, and concentration field. The initial three-layer cell vorticity struc- ture is revealed. When the amplification factor reaches the maximum Gmax, it develops into one cell structure with large amplification for the vorticity strength.
基金Project supported by the National Natural Science Foundation of China(Nos.11322221,11132005,and 11490551)
文摘The optimal transient growth process of perturbations driven by the pressure gradient is studied in a turbulent pipe flow. A new computational method is proposed, based on the projection operators which project the governing equations onto the sub- space spanned by the radial vorticity and radial velocity. The method is validated by comparing with the previous studies. Two peaks of the maximum transient growth am- plification curve are found at different Reynolds numbers ranging from 20 000 to 250 000. The optimal flow structures are obtained and compared with the experiments and DNS results. The location of the outer peak is at the azimuthal wave number n = 1, while the location of the inner peak is varying with the Reynolds number. It is observed that the velocity streaks in the buffer layer with a spacing of 100δv are the most amplified flow structures. Finally, we consider the optimal transient growth time and its dependence on the azimuthal wave length. It shows a self-similar behavior for perturbations of different scales in the optimal transient growth process.
文摘Linear transient growth of optimal perturbations in particle-laden turbulent channel flow is investigated in this work.The problem is formulated in the framework of a Eulerian-Eulerian approach,employing two-way coupling between fine particles and fluid flow.The model is first validated in laminar cases,after which the transient growth of coherent perturbations in turbulent channel flow is investigated,where the mean particle concentration distribution is obtained by direct numerical simulation.It is shown that the optimal small-scale structures for particles are streamwise streaks just below the optimal streamwise velocity streaks,as was previously found in numerical simulations of particle-laden channel flow.This indicates that the optimal growth of perturbations is a dominant mechanism for the distribution of particles in the near-wall region.The current study also considers the transient growth of small-and large-scale perturbations at relatively high Reynolds numbers,which reveals that the optimal large-scale structures for particles are in the near-wall region while the optimal large-scale structures for fluid enter the outer region.
基金supported by grants from the National Natural Science Foundation of China,No.81171179,81272439the Key Sci-Tech Research Projects of Guangdong Province in China,No.2008A030201019the Guangzhou Municipal Science and Technology Project in China,No.09B52120112-2009J1-C418-2,No.2008A1-E4011-6
文摘Previous studies show that transient axonal glycoprotein-1, a ligand of amyloid precursor pro- tein, increases the secretion of amyloid precursor protein intracellular domain and is involved in apoptosis in Alzheimer＇s disease. In this study, we examined the effects of transient axonal glyco- protein-1 on U251 glioma cells. 3-（4,5-Dimethylthiazol-2-yl）-2,5-diphenyltetrazolium bromide assay showed that transient axonal glycoprotein-1 did not inhibit the proliferation of U251 cells, but promoted cell viability. The terminal deoxynucleotidyl transferase dUTP nick end labeling assay showed that transient axonal glycoprotein-1 did not induce U251 cell apoptosis. Real-time PCR revealed that transient axonal glycoprotein-1 substantially upregulated levels of amyloid precursor protein intracellular C-terminal domain, and p53 and epidermal growth factor recep- tor mRNA expression. Thus, transient axonal glycoprotein-1 increased apoptosis-related gene expression in U251 cells without inducing apoptosis. Instead, transient axonal glycoprotein-1 promoted the proliferation of these glioma cells.
基金supported by the National Natural Science Foundation of China(Grants 11490551,11472154, 11132005,and 11322221)
文摘The generation of a hairpin vortex from near-wall streamwise vortices is studied via the direct numerical simulation（DNS） of the streak transient growth in the minimal channel flow at Re_τ- 400.The streak profile is obtained by conditionally averaging the DNS data of the fully developed turbulent channel flow at the same Reynolds number.The near-wall streamwise vortices are produced by the transient growth of the streak which is initially subjected to the sinuous perturbation of the spanwise velocity.It is shown that the arch head of the hairpin vortex first grows from the downstream end of the stronger streamwise vortex and then connects with the weaker,opposite-signed streamwise vortex in their overlap region,forming a complete individual hairpin structure.The vorticity transport along the vortex lines indicates that the strength increase and the spatial expansion of the arch head are due to the stretching and the turning of the vorticity vector,respectively.The hairpin packets could be further produced from the generated individual hairpin vortex following the parent-offspring process.
