摘要:

The transition to three‐dimensionality in the near wake of a circular cylinder involves two successive transitions, each of which corresponds with a discontinuity in the Strouhal–Reynolds number relationship. The first discontinuity [between Reynolds numbers (Re) of 170 to 180] is associated with the inception of vortex loops, and it is hysteretic. The second discontinuity (between Re=230 to 260) corresponds with a change to a finer‐scale streamwise vortex structure. At this discontinuity there is no hysteresis, and it is suggested that two modes of vortex shedding alternate in time.

ISSN:0031-9171    

DOI:10.1063/1.866925

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

A novel method is applied to the Lorenz system that deals directly with the power spectrum of the turbulent solutions. Analytic predictions are produced as to the level of turbulence and the spread in frequency space of the solution that are in good agreement with numerical computations. The method involves manipulation of the Fourier transformed Lorenz equations and their tempered distribution solutions.

ISSN:0031-9171    

DOI:10.1063/1.866926

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

In the cyclotron autoresonance maser, an electromagnetic wave is amplified by interaction with an electron beam. Because of the copropagating electron beam, the refractive index seen by the wave is modified from the vacuum index and the dielectric properties of the electron beam can alter the propagation of the radiation beam. This phenomenon is studied through the use of a source‐dependent modal expansion of the fully three‐dimensional radiation field. In the exponential gain regime, the natural tendency of the radiation beam to spread diffractively is overcome and the beam is focused. The nature of the focusing is found to depend on the relative magnitude of the Doppler‐shifted wave frequency and the gyrofrequency.

ISSN:0031-9171    

DOI:10.1063/1.866927

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

Exact periodic solutions are found for the relative motion of three spheres sedimenting in a Stokes fluid. Nearby solutions are found to be nearly periodic for a long time. Existence of the exact periodic solutions is proved using the point‐particle approximation and symmetry properties of Stokes equations. Numerical simulations for finite‐sized particles are performed using a method of multipole expansions.

ISSN:0031-9171    

DOI:10.1063/1.866928

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The fluid mechanics of viscous fluid injection into a fracture embedded in a permeable rock formation is studied. Coupling between flow in the fracture and flow in the rock is retained. The analysis is based on a perturbation scheme that assumes the depth of penetration of the fluid into the rock is small compared to the characteristic lengthw30/k, wherew0is the characteristic crack width andkis the permeability. This restriction, however, is shown to be minor. The spatial dependence of the leakage rate per unit length from the fracture is found to be linear, decreasing from the well bore to the fracture tip where it vanishes. The magnitude of the leakage rate per unit length is found to decay in time ast−1/3if the injection rate at the well bore is constant, and ast−1/2if the well bore pressure is held constant. The results cast considerable doubt on the validity of Carter’s well‐known leakage formula (Drilling Prod. Prac. API1957, 261) derived from a one‐dimensional theory. Using the simple fracture propagation model made popular by Carter, the present work also predicts that the fracture grows at a rate proportional tot1/3for a fixed well bore injection rate and a rate proportional tot1/4for a fixed well bore pressure.

ISSN:0031-9171    

DOI:10.1063/1.866929

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The linear stability of a steadily moving bubble or a finger in a Hele–Shaw cell is considered in the case when gravity and the ratio between the viscosities of the less and more viscous fluids are nonzero. The effect of gravity is easily incorporated by a transformation of parameters introduced previously by Saffman and Taylor [Proc. R. Soc. London Ser. A245, 312 (1958)] for the steady flow, which makes the time‐dependent flows with and without gravity equivalent. For the nonzero viscosity ratio, the transformation of parameters introduced by Saffman and Taylor also makes steady finger and bubble flows with nonzero and zero viscosity ratios equivalent. However, for the unsteady case, there is no such equivalence and so a complete calculation is carried out to investigate the effect of the nonzero viscosity ratio on the stability of fingers and bubbles. The incorporation of the finite viscosity ratio is found not to qualitatively alter the linear stability features obtained in earlier work for the zero viscosity ratio, although there are quantitative differences in the growth or decay rate of various modes. For any surface tension, numerical calculation suggests that the McLean–Saffman branch of bubbles [Phys. Fluids30, 651 (1987)] of arbitrary size is stable, whereas all the other branches are unstable. For a small bubble that is circular, the eigenvalues of the stability operator are found explicitly. The previous analytic theory for the stability of the finger in the limit of zero surface tension is extended to include the case of the finite viscosity ratio. It is found that, as in the case of bubbles, the finite viscosity ratio does not alter qualitatively any of the features obtained previously for the zero viscosity ratio.

ISSN:0031-9171    

DOI:10.1063/1.866930

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The penetration of a front of light fluid into a heavy fluid in a Rayleigh–Taylor unstable flow is studied by using a vortex‐in‐cell numerical algorithm. The algorithm is used to simulate the competition among the bubbles that are formed in the interface when the density ratio of the two fluids is very large. Several multifrequency initial conditions and the effect of surface tension have been considered. It is found that the front moves with constant acceleration. The values obtained for the acceleration of the front are in very good agreement with experimental results obtained by Read [Phys. D12, 45 (1984)] and with the results obtained by using Zufiria’s [Phys. Fluids31, 440 (1988)] model.

ISSN:0031-9171    

DOI:10.1063/1.866931

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The evolution of a viscous vortex pair is investigated through the use of a heuristic model. The model is based on the linear superposition of two Oseen vortices of opposite circulation spaced a distance 2bapart. The vortices are allowed to evolve through viscous diffusion and their mutual induction. The motion is unforced and as a consequence the total hydrodynamic impulse is exactly conserved for all time. In the model the total circulation in the upper half plane is assumed to remain initially constant. This constraint is applied up to a finite time when the model solution reaches its asymptotic form corresponding to a drifting Stokes dipole dominated by interdiffusion of vorticity across the plane of symmetry. The drift velocity of the vortex pair is determined by the condition that the integrated pressure force vanishes on the line of symmetry at all times. At large time this leads to an asymptotic value of the drift velocity which scales with the similarity properties of the Stokes solution. To provide a more rigorous foundation for the drift, the asymptotic behavior of the flow for large time is investigated through an expansion of the solution in inverse powers of the time. First the second‐order pressure is determined as a solution of a Poisson equation with the source term generated by the first‐order flow field. Surprisingly, the solution turns out to be independent of the drift. Nevertheless, an exact condition for the drift is found by considering the limiting form of the second‐order pressure at infinity where the flow is irrotational and the pressure can be computed directly from the first‐order velocity field using Bernoulli’s equation. In this latter approach the far field pressure is determined up to an unknown function of time which upon comparison with the Poisson solution is identified as the drift. The exact drift obtained in this fashion differs by only 10% from the value obtained using the pressure field of the heuristic model. Finally, it is shown that the existence of the complete second‐order asymptotic solution of the Navier–Stokes equations requires the inclusion of the same drift in the first‐order solution that was found from the examination of the pressure. The second‐order vorticity and streamfunction are determined; the latter contains afree constant to accommodate conditions at earlier times. Prospects for the existence of higher‐order asymptotic terms are discussed.

ISSN:0031-9171    

DOI:10.1063/1.866932

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

Stability of two superposed fluids of different viscosity in plane Poiseuille flow is studied numerically. Conditions for the growth of an interfacial wave are identified. The analysis extends Yih’s results [J. Fluid Mech.27, 337 (1967)] for small wavenumbers to large wavenumbers and accounts for differences in density and thickness ratios, as well as the effects of interfacial tension and gravity. Neutral stability diagrams for the interfacial mode are reported for a wide range of the physical parameters describing the flow. The analysis shows also that the flow is linearly unstable to a shear mode instability. The dependence of the critical Reynolds number for the shear mode on the viscosity ratio is reported. Theoretical predictions of critical Reynolds numbers for both modes of instability are compared with available experimental data.

ISSN:0031-9171    

DOI:10.1063/1.866933

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The linear stability of inviscid, compressible shear flows is studied. Some previous results for homentropic flows are extended to include adiabatic flows with variable temperature. Specific neutral solutions are obtained for both a shear layer and a wake in the subsonic regime that are stability boundaries. Unstable solutions are calculated for both streamwise and oblique disturbances in the shear layer flow. Other neutrally stable solutions are presented, which do not correspond to stability boundaries, describing stationary oscillations of supersonic shear flows.

ISSN:0031-9171    

DOI:10.1063/1.866934

出版商:AIP    

年代:1988

数据来源: AIP