Coherent Structures in Transition of a Flat-Plate Boundary Layer at Ma = 0.7

Direct numerical simulation （DNS） of a spatially evolving fiat-plate boundary layer transition process at free stream Mach number 0. 7 is performed. Tollmien-Schlichting （T-S） waves are added on the inlet boundary as the disturbances before transition. Typical coherent structures in the transition process are investigated based on the second invariant of velocity gradient tensor. The instantaneous shear stress and the mean velocity profile in the transition region are studied. In our view, the fact that the peak value of shear stress in the stress concentration area increases and exceeds a threshold value during the later stage of the trallsition process plays an important role in the laminar breakdown process.     

Two Phases of Coherent Structure Motions in Turbulent Boundary Layer

Two phases of coherent structure motion are acquired after obtaining conditional phase-averaged waveforms for longitudinal velocity of coherent structures in turbulent boundary layer based on Harr wavelet transfer. The correspondences of the two phases to the two processes （i.e. ejection and sweep） during a burst are determined.     

Frequency Response of Near-Wall Coherent Structures to Localized Periodic Blowing and Suction in Turbulent Boundary Layer

We experimentally investigate the frequency response of near-wall coherent structures to localized periodic blow- ing and suction through a spanwise slot in a turbulent boundary layer by changing the frequency of periodic disturbance at similar velocities of free stream. The effects of blowing and suction disturbance on energy redistri- bution, turbulent intensity U^＋ rums over y^＋ and waveforms of phase-averaged velocity during sweeping process are respectively discussed under three frequencies of periodic blowing and suction in near-wall region of turbulent boundary layer, compared with those in a standard turbulent boundary layer. The most effective disturbance frequency is figured out in this system.     

Turbulence Modulations in the Boundary Layer of a Horizontal Particle-Laden Channel Flow

Turbulence modulations are experimentally investigated using particle image velocimetry （PIV） in the lower boundary layer of a fully developed horizontal channel flow. A simultaneous two-phase PIV measurement technique is adopted to acquire the turbulent statistics quantities and to examine the coherent structures in the near-wall region. Polythene beads with diameters of 60 μm are used as dispersed phases, and the PIV measurements have been performed at three mass loadings varying from 2.5 ×10^-4 to 5 × 10^-3. All the experiments are performed at a wall shear Reynolds number of Reτ = 430. The results show that the presence of the particles suppresses the coherent structures, with shorter streamwise extent of the quasistrearnwise structures, and then, the wall-normal velocity fluctuations and shear Reynolds stresses are both decreased in the near-core region. In addition, as a result of the particle wake, the turbulence intensity and shear Reynolds stress both increase in the vicinity of the wall. Due to the drag effects of the particles on the gas, the streamwise velocity gradients decrease in the outer region and increase in the viscous sublayer, meanwhile the thickness of the viscous sublayer also decreases. These results cause the peak values of the streamwise velocity fluctuations adjacent to the wall to increase, and the peak positions shift to the wall. This is the reason for decreasing the near-wall region and increasing the near-core region of the streamwise velocity fluctuations in appearance.     

Supersonic Turbulent Boundary Layer： DNS and RANS

We assess the performance of a few turbulence models for Reynolds averaged Navier-Stokes （RANS） simulation of supersonic boundary layers, compared to the direct numerical simulations （DNS） of supersonic flat-plate turbulent boundary layers, carried out by Gao et al. [Chin. Phys. Lett. 22（2005）1709] and Huang et al. [Sci. Chin. 48 （2005） 614], as well as some available experimental data. The assessment is made for two test cases, with incoming Mach numbers and Reynolds numbers M = 2.25, Re = 365, 000//in, and M = 4.5, Re = 1.7 × 10^7/m, respectively. It is found that in the first case the prediction of RANS models agrees well with the DNS and the experimental data, while for the second case the agreement of the DNS models with experiment is less satisfactory. The compressibility effect on the RANS models is discussed.     

Wavelet Cross-Spectrum Analysis of Multi-Scale Disturbance Instability and Transition on Sharp Cone Hypersonic Boundary Layer

Experimental measurement of hypersonic boundary layer stability and transition on a sharp cone with a half angle of 5° is carried out at free-coming stream Mach number 6 in a hypersonic wind tunnel. Mean andfluctuation surface-thermal-flux characteristics of the hypersonic boundary layer flow are measured by Pt-thin-film thermocouple temperature sensors installed at 28 stations on the cone surface along longitudinal direction. At hypersonic speeds, the dominant flow instabilities demonstrate that the growth rate of the second mode tends to exceed that of the low-frequency mode. Wavelet-based cross-spectrum technique is introduced to obtain the multi-scale cross-spectral characteristics of the fluctuating signals in thefrequency range of the second mode. Nonlinear interactions both of the second mode disturbance and the first mode disturbance are demonstrated to be dominant instabilities in the initial stage of laminar-turbulence transition for hypersonic shear flow.     

Turbulent Boundary Layer Control via a Streamwise Travelling Wave Induced by an External Force

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.     

Direct Numerical Simulation of a Spatially Evolving Supersonic Turbulent Boundary Layer at Ma = 6

Direct numerical simulation is carried out for a spatially evolving supersonic turbulent boundary layer at freestream Mach number 6. To overcome numerical instability, the seventh-order WENO scheme is used for the convection terms of Navier-Stokes equations, and fine mesh is adopted to minimize numerical dissipation. Compressibility effects on the near-wall turbulent kinetic energy budget are studied. The cross-stream extended self-similarity and scaling exponents including the near-wall region are studied. In high Mach number flows, the coherence vortex structures are arranged to be smoother and streamwised, and the hair-pin vortices are less likely tO OCCUr.     

Large Eddy Simulation of Turbulent Channel Flow with 3D Roughness Using a Roughness Element Model

Large eddy simulation of turbulent channel flow with dense and small 3D roughness elements is carried out using a roughness element model Profiles of mean Reynolds stress, mean velocity and rms velocity as well as turbulent structures near the wall are obtained. The shear stress in the rough wall is larger than that in the smooth wall side and the rough wall has a larger influence on the channel flow. Profiles of mean streamwise velocity near the wall have logarithmic velocity distributions for both smooth and roughness walls, while there is a velocity decrease for the rough wall due to larger fractional drag. All the three components of rms velocities in the rough wall region are larger than that in the smooth wall region, and the roughness elements on the wall increase turbulent intensity in all directions. The s~reak spacing and average diameter of near wall quasi-s~reamwise vortices increase with the presence of roughness elements on the wall and it is shown that the rough wall induces complex and strong streamwise vortices. Results of dense and small 3D roughness elements in both turbulent statistics and structure, obtained with a relatively simple method, are found to be comparable to related experiments.     

Effect of Surface Roughness and Reynolds Number on Self-Similarity of Velocity Profile in the Atmospheric Boundary Layer

Self-similarity of power law velocity profile of a simulated atmospheric boundary layer is studied experimentally. The results demonstrate that the self-similarity maintains very well along the streamwise direction for the same rough surface but changes significantly with the surface roughness at the same position. The self-similarity of the vertical velocity profiles is affected by enhancement of the free stream velocity when the roughness concentration is relatively denser.     

Convective heat transport in a fluid layer of infinite Prandtl number: upper bounds for the case of rigid lower boundary and stress-free upper boundary

We present the theory of the multi--solutions of the variational problem for the upper bounds on the convective heat transport in a heated from below horizontal fluid layer with rigid lower boundary and stress-free upper boundary. A sequence of upper bounds on the convective heat transport is obtained. The highest bound is between the bounds for the case of a fluid layer with two rigid boundaries and for the case of a fluid layer with two stress-free boundaries. As an additional result of the presented theory we obtain small corrections of the boundary layer thicknesses of the optimum fields for the case of fluid layer with two rigid boundaries. These corrections lead to systematically lower upper bounds on the convective heat transport in comparison to the bounds obtained in [5]. Received 29 September 1999     

Compressibility Effects in Turbulent Boundary Layers

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.     

Numerical tests of a new molecule-dependent momentum transport equation

It is shown that a new incompressible fluid equation is obtained by inclusion of a new dimensionless coupling parameter in the momentum transport equation derived in [L. Jirkovsky, L. Bo-ot, Momentum transport equation for the fluids using projection-perturbation formalism and onset of turbulence, Physica A 352 (2005) 241-251] from the Boltzmann kinetic equation where the Boltzmann collision integral includes inelastic interactions of quantum origin among the particles of the fluid. Numerical results from the equation for the plane and circular Poiseuille flows are consistent with the observations. The numerical tests also manifest a difference in the onset of turbulence between the flat plates and the circular pipe flow systems. Although all obtained velocity profiles are flattened at the center-a feature of turbulence-the results demonstrate greater stability of the velocity profiles in the circular pipe flow.     

Transition to Chaos in the Floating Half Zone Convection

The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge. The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos. The measured Feigenbaum numbers are δ2 =4.69 and δ4 = 4.6, which are comparable with the theoretical asymptotic value δ=4.669.     

Turbulence in diffusion replicator equation

Dynamical behaviors in the diffusion replicator equation of three species are numerically studied. We point out the significant role of the heteroclinic cycle in the equation, and analyze the details of the turbulent solution that appeared in this system. Firstly, the bifurcation diagram for a certain parameter setting is drawn. Then it is shown that the turbulence appears with the supercritical Hopf bifurcation of a stationary uniform solution and it disappears under a subcritical-type bifurcation. Secondly, the statistical property of the turbulence near the supercritical Hopf onset point is analyzed precisely. Further, the correlation lengths and correlation times obey some characteristic scaling laws.     

Upper bounds on the convective heat transport in a rotating fluid layer of infinite Prandtl number: case of large Taylor numbers

By means of the Howard-Busse method of the optimum theory of turbulence we obtain upper bounds on the convective heat transport in a horizontal fluid layer heated from below and rotating about a vertical axis. We consider the interval of large Taylor numbers where the intermediate layers of the optimum fields expand in the direction of the corresponding internal layers. We consider the 1 - α-solution of the arising variational problem for the cases of rigid-stress-free, stress-free, and rigid boundary conditions. For each kind of boundary condition we discuss four cases: two cases where the boundary layers are thinner than the Ekman layers of the optimum field and two cases where the boundary layers are thicker than the Ekman layers. In most cases we use an improved solution of the Euler-Lagrange equations of the variational problem for the intermediate layers of the optimum fields. This solution leads to corrections of the thicknesses of the boundary layers of the optimum fields and to lower upper bounds on the convective heat transport in comparison to the bounds obtained by Chan [J. Fluid Mech. 64, 477 (1974)] and Hunter and Riahi [J. Fluid Mech. 72, 433 (1975)]. Compared to the existing experimental data for the case of a fluid layer with rigid boundaries the corresponding upper bounds on the convective heat transport is less than two times larger than the experimental results, the corresponding upper bound on the convective heat transport, obtained by Hunter and Riahi is about 10% higher than the bound obtained in this article. When Rayleigh number and Taylor number are high enough the upper bound on the convective heat transport ceases to depend on the boundary conditions. Received 30 January 2001 and Received in final form 28 May 2001     

Finite-Size Scaling Analysis of a Three-Dimensional Blume--Capel Model in the Presence of External Magnetic Field

The Blume-Capel model in the presence of external magnetic field H has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton in three-dimension lattice. The field critical exponent 5 is estimated using the power law relations and the finite size scaling functions for the magnetization and the susceptibility in the range -0.1≤ h = H/J ≤0. The estimated value of the field critical exponent 5 is in good agreement with the universal value （δ = 5） in three dimensions. The simulations are carried out on a simple cubic lattice under periodic boundary conditions.     

MHD Boundary Layer Flow of a Non-Newtonian Fluid on a Moving Surface with a Power-Law Velocity

A theoretical analysis for MHD boundary layer flow on a moving surface with the power-law velocity is presented. An accurate expression of the skin friction coefficient is derived. The analytical approximate solution is obtained by means of Adomian decomposition methods. The reliability and efficiency of the approximate solutions are verified by numerical ones in the literature.     

On the Doppler distortion of the sea-wave spectra

Discussions on a form of a frequency spectrum of wind-driven sea waves just above the spectral maximum have continued for the last three decades. In 1958 Phillips made a conjecture that wave breaking is the main mechanism responsible for the spectrum formation [O.M. Phillips, J. Fluid Mech. 4 (1958) 426]. That leads to the spectrum decay ∼ω⁻⁵, where ω is the frequency of waves. There is a contradiction between the numerous experimental data and this spectrum. Experiments frequently show decay ∼ω⁻⁴ [Y. Toba, J. Oceanogr. Soc. Japan 29 (1973) 209; M.A. Donelan, J. Hamilton, W.H. Hui, Phil. Trans. R. Soc. London A315 (1985) 509; P.A. Hwang, et al., J. Phys. Oceanogr. 30 (1999) 2753]. There are several ways of the explanation of this phenomenon. One of them (proposed by Banner [M.L. Banner, J. Phys. Oceanogr. 20 (1990) 966]) takes into account the Doppler effect due to surface circular currents generated by underlying waves in the Phillips model.In this article the influence of the Doppler effect on an arbitrary averaged spectrum is considered using both analytic and numerical approaches. Although we mostly concentrated on the very important case of Phillips model, the developed technique and general formula can be used for the analysis of other spectra.For the particular case of Phillips spectra we got analytic asymptotics in the vicinity of spectral maximum and for high frequencies. Results were obtained for two most important angular dependences of the spectra: isotropic and strongly anisotropic. Together with the analytic investigation we performed numerical calculations in a wide range of frequencies. Both high and low frequency asymptotics are in very good agreement with the numerical results.It was shown that at least at low frequencies, the correction to the spectrum due to the Doppler shift is negligible. At high frequencies there is an asymptotic with tail ∼ω⁻³.