摘要:

A swirling jet, emerging normal to a plane, serves as a model of a tornado and is characterized by its flow force and outer circulation. This model is examined here using the full Navier–Stokes equations. Three branches of solutions are found which form a hysteresis loop and a cusp catastrophe that means jump transitions between flow regimes. One of the jumps relates to vortex breakdown and the other relates to a new (opposite) effect: abrupt vortex consolidation. These results are compared with those of Long [J. Fluid Mech.11, 611 (1961)], who considered a near‐axis jet in the boundary layer approximation. More detailed analysis made here for high circulation values allows discovery of two new types of asymptotic solutions corresponding to a near‐plane fan jet and a two‐cell flow. It was also found that the boundary layer approach for the near‐axis jet fails to accurately yield the total flow force because the outer flow contributes a share of the momentum flux of comparable magnitude to that of the inner flow. The prediction of the jump transitions between one‐ and two‐cell flow patterns agrees with observations of abrupt changes in tornado patterns in nature.

ISSN:0899-8213    

DOI:10.1063/1.858888

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Vortex pairs interacting with a circular cylinder have been simulated by the numerical simulation of the two‐dimensional Navier–Stokes equation in the vorticity streamfunction formulation. The interaction with a cylinder with a diameter equal to the diameter of the dipole has been simulated in the inviscid case with free‐slip boundaries. This case has been considered as a way to perturb the initial dipole, which splits into two vortices that rejoin at a different location on the cylinder depending on the initial displacement of the cylinder from the centerline of the primary vortex pair. By the scatter plots it was shown that the Lamb dipole after the perturbation relaxes to its initialk2&psgr; functional relationship. The case of no‐slip interaction has been considered when the cylinder is two orders of magnitude smaller than the dipole. The same features observed in the experiment of Homaetal. [J. Fluid Mech.197, 571 (1988)] are obtained by the numerical simulations, that is a thin vorticity layer is generated at the cylinder, it rolls up and forms dipolar and tripolar structures, depending on the initial displacement of the cylinder from the centerline of the incoming dipole. Scatter plots of the vortex pair formed by the primary and secondary vorticity show a linear distribution similar to that of the Lamb dipole. The dependence on the Reynolds number has been investigated.

ISSN:0899-8213    

DOI:10.1063/1.858557

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A mathematical framework is proposed in which it seems possible to justify the computationally‐observed relaxation of a two‐dimensional Navier–Stokes fluid to a ‘‘most probable,’’ or maximum entropy, state. The relaxation occurs at large but finite Reynolds numbers, and involves substantial decay of higher‐order ideal invariants such as enstrophy. A two‐fluid formulation, involving interpenetrating positive and negative vorticity fluxes (continuous and square integrable) is developed, and is shown to be intimately related to the passive scalar decay problem. Increasing interpenetration of the two fluids corresponds to the decay of vorticity flux due to viscosity. It is demonstrated numerically that, in two dimensions, passive scalars decay rapidly, relative to mean‐square vorticity (enstrophy). This observation provides a basis for assigning initial data to the two‐fluid field variables.

ISSN:0899-8213    

DOI:10.1063/1.858558

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A theoretical study is carried out for investigating spatial instabilities of a supersonic vortex sheet inside a circular duct. The sheet is cylindrical in shape, separating the flow into an inner region and an outer one of uniform properties. It is found that there is one family of subsonic (Kelvin–Helmholtz) instability waves which are accompanied by two families of neutral modes. Two families of supersonic instability waves can be identified to be associated with two other families of neutral modes. A mathematical analogy indicates that instability modes at high frequencies bear resemblance to those obtained by Tam and Hu [J. Fluid. Mech.203, 51 (1989).] for plane mixing layers inside a rectangular channel. Geometric effects of both the vortex sheet and the outer confinement are significant only at relatively low frequencies of disturbances. In addition, extensive parametric study reveals interesting features of the dependence of the instability waves on the density ratio, velocity ratio, radius ratio of the inner and outer regions, and three‐dimensional disturbances.

ISSN:0899-8213    

DOI:10.1063/1.858559

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The instability of the von Ka´rma´n vortex streets and the existence of a global Lyapunov function at the special aspect ratioh/l=(1/&pgr;)sinh−1(1), are some of the difficulties with the well‐known von Ka´rma´n model. By consistently applying the principle of genericity, its shown that a new family of near‐equilibrium periodic solutions of the von Ka´rma´n model for aspect ratios near 0.281... supplies numerous theoretical candidates for observed vortex trails. This set of solutions implies that there is no global Lyapunov functions whenh/l≠(1/&pgr;)sinh−1(1) which in turn leads to a rich variety of near‐equilibrium solutions for the model.

ISSN:0899-8213    

DOI:10.1063/1.858560

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A nonlinear random differential equation describing the magnitude of vorticity is given for fine vortex tube in locally isotropic turbulence. From this vortex dynamics model, the asymptotic expressions of the probability density function of the dissipation rate in locally isotropic turbulence are obtained. In particular, several physical mechanisms behind turbulence statistics are explored.

ISSN:0899-8213    

DOI:10.1063/1.858561

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Experiments have been carried out in which a cylindrical volume of a gas, that is either lighter or heavier than its surroundings, is impulsively accelerated by a weak shock wave. Laminar jets of helium or sulphur hexafluoride (SF6) are used to produce the cylinders, and planar laser‐induced fluorescence is used to visualize the flow. It is found that the vorticity deposited on the boundary of the SF6cylinder by the interaction with the shock wave, separates from the heavy gas to form a pair of vortices, which subsequently wrap the SF6around them. This process is quite different from what is observed in the light gas experiments, which showed a small amount of helium to remain with the vorticity, eventually becoming part of the vortex cores. Centrifugal forces combined with differences in the rates of the diffusion of vorticity in the two gases are given as possible reasons for these differences. Measurement of the initial downstream velocity for a heavy gas cylinder is found to agree well with a theory based on two simple models. But, because diffusion causes the light gas jet density to be significantly greater than that of pure helium, the theory overpredicts the measured velocity of the light gas experiments. The final translational velocities for both light and heavy gas experiments are not accurately predicted by the model, and measurements of the vortex spacing are found to be significantly larger than those indicated by this theory. These differences are likely caused by the theory’s inability to accurately describe the viscous nonuniform flow.

ISSN:0899-8213    

DOI:10.1063/1.858562

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The variational approach to the closure problem of turbulence theory with particular attention to the perturbation–variation method of Qian [Phys. Fluids26, 2098 (1983)] is studied. It is shown that although the method is based on a clear physical idea, it is not self‐consistent. The procedure to obtain the equation for the dynamic damping coefficient does contain arbitrariness, which leads to the dependence of this equation on the choice of variables. This ambiguity is illustrated by numerical evaluations of the Kolmogorov constant in two‐dimensional and three‐dimensional cases. The equation for the dynamic damping coefficient, which is invariant, with respect to the change of variables, is obtained and analyzed. The principal inevitability of arbitrariness in closure methods is discussed.

ISSN:0899-8213    

DOI:10.1063/1.858563

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Recent theoretical proposals concerning non‐Gaussian statistics of passive scalars in random velocity fields are tested experimentally, by measuring the probability distributions of fluctuating temperature in an oscillating grid flow across which a steady temperature gradient is maintained. Pronounced exponential tails occur at sufficiently high Reynolds numberR, and predominantly Gaussian statistics at lowR. When the extended tails are present for the passive scalar, the corresponding velocity power spectrum shows reasonable scaling, and the velocity distribution is not far from Gaussian. The present paper provides a more complete characterization of the flow field than an earlier brief report [Phys. Rev. Lett.67, 3507 (1991)], and also contains a description of additional features, such as the skewness of the distributions. Finally, the effective or eddy diffusivity of both heat and a molecular impurity are measured and compared.  

ISSN:0899-8213    

DOI:10.1063/1.858564

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

An elementary argument shows that non‐Gaussian fluctuations in the temperature at a point in space are induced by random advection of a passive temperature field that has a nonlinear mean gradient, whether or not there is molecular diffusion. This is corroborated by exact analysis for the nondiffusive case and by direct numerical simulation for diffusive cases. Eulerian mapping closure gives results close to the simulation data. Non‐Gaussian fluctuations of temperature at a point also are induced by a more subtle mechanism that requires both advection and molecular diffusion and is effective even when the statistics are strictly homogeneous. It operates through selectively strong dissipation of regions where intense temperature gradients have been induced by advective straining. This phenomenon is demonstrated by simulations and explored by means of an idealized analytical model.

ISSN:0899-8213    

DOI:10.1063/1.858530

出版商:AIP    

年代:1993

数据来源: AIP