Evolution of global enstrophy in cylinder wake controlled by Lorentz force

The Okubo-Weiss function is correlated with the fluid particle compression, deformation and vorticity, which provides a simple way to characterize different regions of a flow-field. In the present paper, it shows mathematically that the global integration of Okubo-Weiss function is always equal to zero for a two dimensional incompressible flow with no-slip boundaries. To validate the conclusion, a flow passing a circular cylinder con- trolled by the electromagnetic force is calculated numerically as an example. Distributions of global enstrophy, total squared strain and Okubo-Weiss function in the controlled flow field are discussed. The influence of Lorentz force on the distribution is analyzed.

Transient response of enstrophy transport to opposition control in turbulent channel flow

The transient response of the turbulent enstrophy transport to opposition control in the turbulent channel flow is studied with the aid of direct numerical simulation. It is found that the streamwise enstrophy and the spanwise enstrophy are suppressed by the attenuation of the stretching terms at first, while the vertical enstrophy is reduced by inhibiting the tilt of the mean shear. In the initial period of the control, the streamwise enstrophy evolves much slower than the other two components. The vertical vorticity component exhibits a rapid monotonic decrease and also plays an important role in the attenuation of the other two components.

BAROTROPIC AND BAROCLINIC ENSTROPHY EQUATIONS WITH THEIR APPLICATIONS TO A BLOCKING CIRCULATION

After the manner for studying atmospheric kinetic energy,concepts of atmospheric enstrophy (ζ~2/2)_m and barotropic and baroclinic enstrophy (ζ_m^2/2,ζ_s^2/2) are developed with their relations investigated,whereupon are established,separately,equations for the 1000- 100 hPa extent- averaged ζ_m^2/2 and ζ_s^2/2 over a limited area and on a local basis.Study shows that controlling their changes are the following factors:the terms of their fluxes (viz.,divergences).β effect,their mutual conversions,production and dissipation.Analysis is undertaken of these terms-dependent physical mechanisms for the variations in barotropic and baroclinic enstrophy and by means of the equations,calculation is conducted of the terms during the development of an Okhotsk blocking circulation,indicating that the total,harotropic and haroclinic enstrophies experience noticeable variations,from which we see that the latter two factors can really characterize the development as a whole,thus revealing the mechanisms at different stages of the circulation history.

Subgrid-scale contributions to Lagrangian time correlations in isotropic turbulence

The application of large-eddy simulation （LES） to particle-laden turbulence raises such a fundamental question as whether the LES with a subgrid scale （SGS） model can correctly predict Lagrangian time correlations （LTCs）. Most of the currently existing SGS models are constructed based on the energy budget equations. Therefore, they are able to correctly predict energy spectra, but they may not ensure the correct prediction on the LTCs. Previous researches investigated the effect of the SGS modeling on the Eulerian time correlations. This paper is devoted to study the LTCs in LES. A direct numerical simulation （DNS） and the LES with a spectral eddy viscosity model are performed for isotropic turbulence and the LTCs are calculated using the passive vector method. Both a priori and a posteriori tests are carried out. It is observed that the subgrid;scale contributions to the LTCs cannot be simply ignored and the LES overpredicts the LTCs than the DNS. It is concluded from the straining hypothesis that an accurate prediction of enstrophy spectra is most critical to the prediction of the LTCs.

Numerical simulation on evolution of subharmonic low-speed streaks in minimal channel turbulent flow

The evolution of low-speed streaks in the turbulent boundary layer of the minimum channel flow unit at a low Reynolds number is simulated by the direct numer- ical simulation （DNS） based on the standard Fourier-Chebyshev spectral method. The subharmonic sinuous （SS） mode for two spanwise-aligned low-speed streaks is excited by imposing the initial perturbations. The possibilities and the physical realities of the turbulent sustaining in the minimal channel unit are examined. Based on such a flow field environment, the evolution of the low-speed streaks during a cycle of turbulent sus- taining, including lift-up, oscillation, and breakdown, is investigated. The development of streamwise vortices and the dynamics of vortex structures are examined. The results show that the vortices generated from the same streak are staggered along the streamwise direction, while the vortices induced by different streaks tilt toward the normal direction due to the mutual induction effect. It is the spatial variations of the streamwise vortices that cause the lift-up of the streaks. By resolving the transport dynamics of enstrophy, the strength of the vortices is found to continuously grow in the logarithmic layer through the vortex stretching mechanism during the evolution of streaks. The enhancement of the vortices contributes to the spanwise oscillation and the following breakdown of the low-speed streaks.

A DISCUSSION OF NON-LINEAR MECHANISM ON SUBTROPICAL ANTICYCLONE'S EXTENDING/SHRINKING OVER EAST-ASIA IN SUMMER

Based on the actual circulation structure as well as weather characters over East_Asia subtropical region in summer, by using three_dimension non_linear forced/dissipated dynamic model, the activities of subtropical anticyclone over East_Asia have been studied and discussed. The potential enstrophy criteria of system stability have been derived and also been analysed. The criterion can provide useful reference for analysing and predicting subtropical anticyclone's extending/shrinking as well as corresponding weather over East_Asia in summer.

Evaluation of the Momentum Closure Schemes in MPAS-Ocean

In order to compare and evaluate the performances of the Laplacian viscosity closure, the biharmonic viscosity closure, and the Leith closure momentum schemes in the MPAS-Ocean model, a variety of physical quantities, such as the relative reference potential energy(RPE) change, the RPE time change rate(RPETCR), the grid Reynolds number, the root mean square(RMS) of kinetic energy, and the spectra of kinetic energy and enstrophy, are calculated on the basis of results of a 3D baroclinic periodic channel. Results indicate that: 1) The RPETCR demonstrates a saturation phenomenon in baroclinic eddy tests. The critical grid Reynolds number corresponding to RPETCR saturation differs between the three closures: the largest value is in the biharmonic viscosity closure, followed by that in the Laplacian viscosity closure, and that in the Leith closure is the smallest. 2) All three closures can effectively suppress spurious dianeutral mixing by reducing the grid Reynolds number under sub-saturation conditions of the RPETCR, but they can also damage certain physical processes. Generally, the damage to the rotation process is greater than that to the advection process. 3) The dissipation in the biharmonic viscosity closure is strongly dependent on scales. Most dissipation concentrates on small scales, and the energy of small-scale eddies is often transferred to large-scale kinetic energy. The viscous dissipation in the Laplacian viscosity closure is the strongest on various scales, followed by that in the Leith closure. Note that part of the small-scale kinetic energy is also transferred to large-scale kinetic energy in the Leith closure. 4) The characteristic length scale L and the dimensionless parameter Г in the Leith closure are inherently coupled. The RPETCR is inversely proportional to the product of Г and L. When the product of Г and L is constant, both the simulated RPETCR and the inhibition of spurious dianeutral mixing are the same in all tests using the Leith closure. The dissipative scale in the Leith closure depends on the parameter L, and the dissipative intensity depends on the parameter Г. 5) Although optimal results may not be achieved by using the optimal parameters obtained from the 2D barotropic model in the 3D baroclinic simulation, the total energies are dissipative in all three closures. Dissipation is the strongest in the biharmonic viscosity closure, followed by that in the Leith closure, and that in the Laplacian viscosity closure is the weakest. Mesoscale eddies develop the fastest in the biharmonic viscosity closure after the baroclinic adjustment process finishes, and the kinetic energy reaches its maximum, which is attributed to the smallest dissipation of enstrophy in the biharmonic viscosity closure. Mesoscale eddies develop the slowest, and the kinetic energy peak value is the smallest in the Laplacian viscosity closure. Results in the Leith closure are between that in the biharmonic viscosity closure and the Laplacian viscosity closure.

PULLBACK EXPONENTIAL ATTRACTORS FOR THE NON-AUTONOMOUS MICROPOLAR FLUID FLOWS

This paper investigates the pullback asymptotic behaviors for the non-autonomous micropolar fluid flows in 2D bounded domains. We use the energy method, combining with some important properties of the generated processes, to prove the existence of pullback exponential attractors and global pullback attractors and show that they both with finite fractal dimension. Further, we give the relationship between global pullback attractors and pullback exponential attractors.

Potential enstrophical diagnostic analyses on the mechanism of change of tropical cyclone intensity

It is indicated that the change of mean potential enstrophy within tropical cyclone (TC) corresponds tothe change of TC intensity. A series of factors influencing the intensity change have been discussed by calculating budget of potential enstrophy in tangential wave-number domain in cylindric coordinates. The results indicate thatthe vertical distribution of mean diabatic heating is an important factor that influences the change of TC intensitythrough transformation mechanism of the Coriolis effect and cyclonic vorticity, especially in the sudden intensifyingstage of TC. It is favourable to the intensification when the diabatic heating is largest in upper-middle troposphere,while TC weakens when this kind of role of heating become small or the heating is largest in lower troposphere. Therole of the axisymmetric fields of TC is different from that of the non-axisymmetric fields. In addition,we have analysed some other factors that influence TC intensity.

ALow-order Model of Two-dimensional Fluid Dynamics on the Surface of a Sphere

Without any other approximations apart from the spectral method which is employed,the energy spectra corresponding to two kinds of'negative temperatures'are simulated with a symmetric trapezium truncation.The simulated results with either of the two negative temperatures are reasonably consistent with those from the statistical theory of turbulence.The more usual case for two positive temperatures evolves differently from the theoretical prediction.The viscosity influence on the ergodicity is discussed. It is shown that two--dimensional(2D)ideal flows on thesphere have a less pronounced tendency to be ergodic than those on planar geometry due to the curvature of thespherical surface that weakens the interaction between different parts of the flow,enabling these parts to behave inmore relative isolation. The expressions for the standard deviations from a canonical ensemble for the two differentoptions of coefficients are shown to be proportional to in(N is the total number of independent modes in the system),independent of the initial conditions of the system.

Numerical investigation on compressible flow around a cylinder in proximity to the heated wall

In this study,direct numerical simulations were conducted to investigate the compressible flow around a circular cylinder near a heated wall at a Reynolds number(Re)of 500 and a Mach number(Ma)of 0.4.The heating ratio T^(*)ranging from 1.0 to 1.6 represents the different situations of a heated wall,whereas the gap ratio ranges from 0.3 to 1.0.This study analyzed the impact of heating effect and wall proximity on flow characteristics and aerodynamic forces.The results indicated that the stability of the flow was enhanced as the gap ratio decreased or the heating ratio increased.Through the calculation of enstrophy,it was found that the strength of shedding vortices weakens with a decrease in gap ratio or an increase in heating ratio.Furthermore,the mean drag coefficient decreases as the heating ratio increases or the gap ratio decreases.In contrast,the mean lift coefficient initially decreases and then increases as the gap ratio decreases.Finally,the drag reduction mechanism was analyzed by examining the pressure distribution on the surface of the cylinder.

Can lift be generated in a steady inviscid flow?

This paper presents a critical evaluation of the physical aspects of lift generation to prove that no lift can be generated in a steady inviscid flow.Hence,the answer to the recurring question in the paper title is negative.In other words,the fluid viscosity is necessary in lift generation.The relevant topics include D’Alembert’s paradox of lift and drag,the Kutta condition,the force expression based on the boundary enstrophy flux(BEF),the vortex lift,and the generation of the vorticity and circulation.The physi-cal meanings of the variational formulations to determine the circulation and lift are discussed.In particular,in the variational formulation based on the continuity equation with the first-order Tikhonov regularization functional,an incompressible flow with the artificial viscosity(the Lagrange multiplier)is simulated,elucidating the role of the artifi-cial viscosity in lift generation.The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.

Reconstruction of skin friction topology in complex separated flows

This paper describes a theoretical method for reconstruction of the skin friction topology in complex separated flows,which is developed based on the exact relation between skin friction and surface pressure through the boundary enstrophy flux(BEF).The key of this method is that a skin friction field is reconstructed from a surface pressure field as an inverse problem by applying a variational method.For applications,the approximate method is proposed,where the composite surface pressure field is given by a linear superposition of the base-flow surface pressure field and the surface pressure variation field and the base-flow BEF field is used as the first-order approximation.This approximate method is constructive in a mathematical sense since a complex skin friction field in separated flows can be reconstructed from some elemental skin friction structures(skin friction source/sink,vortex and their combinations)by a linear superposition of some simple surface pressure structures.The distinct topological features,such as critical points,separation lines and attachment lines,naturally occur as a result of such reconstruction.As examples,some elemental skin friction structures in separated flows are reconstructed in simulations,and the skin friction fields in shock-wave/boundary-layer interactions(SWBLIs)are reconstructed from pressure sensitive paint(PSP)images obtained in wind tunnel experiments.

Investigation on the relationship between hydraulic loss and vortex evolution in pump mode of a pump-turbine

Hydraulic loss and vorticity are two most common methods in analyzing the flow characteristics in hydro-machine,i.e.,centrifugal pump,Francis turbine,etc.While the relationship and correlation between hydraulic loss and vortex evolution are not uncovered yet.In this study,hydraulic loss is regarded as the combination of dissipation effect and transportation effect in flow domains.Meanwhile,vorticityωcan be decomposed into two parts,namely the Liutex partω_(R),the shear partωs,of whichω_(R)is regarded as the third-generation vortex identification method for its precise and rigorous definition of local rigid rotation part of fluid.Based on the dimensional analysis,two new physical quantities related to vorticity(ω,ω_(R)andωS),namely enstrophyΩ,vorticity transport intensity T are adopted to express the energy characteristic in vortex evolution process.Finally,operating points at pump mode of an ultra-high head reversible pump-turbine are selected as the research object and the numerical results calculated using SST k-ωturbulence model are consistent well with the experimental data.Pearson correlation coefficient is adopted to evaluate the correlation between hydraulic loss and vortex evolution in main flow regions.Results show that apart from the spiral casing domain,the enstrophy of shear partΩs has very strong correlation with dissipation effect and Liutex transport intensity TR has stronger correlation with transportation effect when compared with other forms of vorticity.The correlation between Liutex transport intensity TR and transportation effect is strong in stay/guide vanes(SGVs)while reduce to medium level in runner and draft tube domains.In spiral casing domain,all forms of vorticity show weak or very weak correlation with transportation effect.Based on the proposed method,we believe that the relationship and correlation between hydraulic loss and vortex evolution in other hydraulic machineries can also be clearly investigated.

Evolutionary understanding of airfoil lift

This review attempts to elucidate the physical origin of aerodynamic lift of an airfoil using simple formulations and notations,particularly focusing on the critical effect of the fluid viscosity.The evolutionary development of the lift problem of a flat-plate airfoil is reviewed as a canonical case from the classical inviscid circulation theory to the viscous-flow model.In particular,the physical aspects of the analytical expressions for the lift coefficient of the plate-plate airfoil are discussed,including Newton’s sine-squared law,Rayleigh’s lift formula,thin-airfoil theory and viscous-flow lift formula.The vortex-force theory is described to provide a solid foundation for consistent treatment of lift,form drag,Kutta condition,and downwash.The formation of the circulation and generation of lift are discussed based on numerical simulations of a viscous starting flow over an airfoil,and the evolution of the flow topology near the trailing edge is well correlated with the realization of the Kutta condition.The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.