摘要:

By numerical solution of the Orr–Sommerfeld equation for complex frequency and complex wavenumber for a wide range of Reynolds numbersRand by asymptotic analysis for largeR, it is shown that there is no absolute instability in a two‐dimensional plane Poiseuille flow for anyRand that the flow is convectively unstable forRc<R<∞, whereRcis the critical Reynolds number.

ISSN:0031-9171    

DOI:10.1063/1.866118

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Two questions are asked, and answered, concerning the dynamics of vortex filaments in a three‐dimensional slightly compressible fluid with constant sound speed: What is the flow (including the sound) generated by a vortex in prescribed motion? What is the response of a test vortex to an external flow? The first question is answered by a convolution of a Green’s function with a source localized at the filament; the second by a differential equation valid in the localized induction approximation. A variational principle encompassing both problems is also provided.

ISSN:0031-9171    

DOI:10.1063/1.866119

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Stokes flow past three spheres is solved analytically by use of (new) addition theorems that transform vector harmonics between different coordinate centers. The extension to other special configurations ofNspheres is indicated. The method is illustrated for uniform flow past three spheres in a triangular cluster, with good agreement with experimental sedimentation velocities.

ISSN:0031-9171    

DOI:10.1063/1.866120

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Two‐dimensional steady potential flow over a semicircular obstacle at the bottom of a channel is considered. The problem is solved numerically by using an integrodifferential equation formulation derived by Forbes and Schwartz [J. Fluid Mech.114, 299 (1982)]. This equation is reduced to a set of algebraic equations by a difference method and solved by Newton’s method together with parameter variation. The numerical results for subcritical flows agree with those of Forbes and Schwartz. However, it is found that supercritical solutions exist only for values of the Froude number greater than some particular value. Furthermore, for some values of the Froude number, there are two supercritical solutions. One is a perturbation of a uniform stream whereas the other is a perturbation of a solitary wave.

ISSN:0031-9171    

DOI:10.1063/1.866121

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

An analytic theory is presented for the linear stability of the Saffman–Taylor finger in a Hele–Shaw cell. Eigenvalues of the stability operator are determined in the limit of zero surface tension and it is found that all modes for the McLean–Saffman branch of solutions [J. Fluid Mech.102, 455 (1980)] are neutrally stable, whereas other branches first calculated by Romero (Ph.D. thesis, California Institute of Technology, 1982) and Vanden‐Broeck [Phys. Fluids26, 2033 (1983)] are unstable to arbitrary infinitesimal disturbances. It is also shown that the Saffman–Taylor discrete set of eigenvalues is a special case of a continuous unstable spectrum for zero surface tension. The introduction of any amount of surface tension perturbs the corresponding eigenmodes such that the finger boundary is a nonanalytic curve in general. Only transcendentally small terms in surface tension are responsible for the nonanalyticity of the finger boundary as in the case of Saffman–Taylor steady finger solutions of arbitrary finger width.

ISSN:0031-9171    

DOI:10.1063/1.866122

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The two‐surface dimensional dynamics of a periodically or soliton‐shaped modulated wave train on a water surface is investigated, using the Davey–Stewartson model. The depthhis taken to be uniform. The results obtained are twofold: the general behavior of the Benjamin–Feir (BF) instability is found for an arbitrary stationary envelope profile, thus generalizing Hayes’ analysis for uniform wave trains, and a new ‘‘Kdegeneracy’’ instability is found. The instability is always limited to ∼45° around the direction of propagation of the basic wave train and this critical angle decreases as the modulation becomes stronger. The new instability covers a narrow range of acute angles for 2&pgr;h/&lgr;≤1.363, where &lgr; is the wavelength of the carrier wave, and all angles for 2&pgr;h/&lgr;≥1.363. Thus our results add new significance to the famous critical number 1.363. A simple explanation of how the new instability comes about concludes the paper. Agreement with previous work is demonstrated.

ISSN:0031-9171    

DOI:10.1063/1.866123

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The recent theory describing 3‐D exact solutions of the Navier–Stokes equations is applied to the problem of stability of 2‐D viscous flow with elliptical streamlines. An intrinsically inviscid instability mechanism persists in all such flows provided the length scale of the disturbance is sufficiently large. Evidence is presented that this mechanism may be responsible for 3‐D instabilities in high Reynolds number flows whose vortex structures can be locally described by elliptical streamlines.

ISSN:0031-9171    

DOI:10.1063/1.866124

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The alignment between vorticity and eigenvectors of the strain‐rate tensor in numerical solutions of Navier–Stokes turbulence is studied. Solutions for isotropic flow and homogeneous shear flow from pseudospectral calculations using 1283grid points have been examined. The Taylor Reynolds number is 83 or greater. In both flows there is an increased probability for the vorticity to point in the intermediate strain direction and at three‐fourths of the sample points this strain is positive (extensive). This propensity for vorticity alignment with a positive intermediate strain is a consequence of angular momentum conservation, as shown by a restricted Euler model of the coupling between strain and vorticity. Probability distributions for intermediate strain, conditioned on total strain, change from a symmetric triangular form at small strain to an asymmetric one for large strain. The most probable value of the asymmetric distribution gives strains in the ratios of 3:1: −4. The evolution of the distribution from a symmetric to an asymmetric form as the strain magnitude increases is essentially the same in both flows, indicating a generic structure of intense turbulence. The alignment between the gradient of a passive scalar and eigenvectors of the strain‐rate tensor for Prandtl numbers of 0.1, 0.2, 0.5, and 1.0 has also been studied. There is an increased probability for the scalar gradient to align in the most compressive strain direction, and the average gradient is larger when it is pointing in that direction. Estimates for the scalar dissipation from the turbulent kinetic energy, its dissipation, and the root‐mean‐square scalar value are in reasonable agreement with calculated scalar dissipation if no explicit Prandtl number dependence is used in the estimate. Statistical analysis of scalar dissipation conditioned on energy dissipation yields a power‐law relation between conditioned mean values. Both simulated flows are found to obey the qualitative predictions of the Gurvich–Yaglom (lognormal) intermittency model. Energy and scalar intermittency exponents are estimated and compared to measured values.

ISSN:0031-9171    

DOI:10.1063/1.866513

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

An analysis is undertaken of a nominally two‐dimensional turbulent boundary layer in zero pressure gradient. In accord with Yajnik [J. Fluid Mech.42, 411 (1970)], the well known law‐of‐the‐wall similarity relationship for the mean velocity, Reynolds stress, and turbulence fields in the wall region is shown to be only the leading term in an expansion, the higher‐order terms of which are dependent upon streamwise Reynolds number. The asymptotic behavior of the streamwise velocity, Reynolds stress, and turbulence intensities is deduced to leading order for two parts of the wall region, one immediately next to the wall and the other far enough from it for the effects of viscosity to be unimportant. A continuous function is then deduced for the velocity that precisely satisfies and links the asymptotics in each region; the corresponding distributions of Reynolds stress and turbulence intensities follow. Agreement with experiment at high Reynolds number is excellent. Noadhocturbulence assumptions are made.

ISSN:0031-9171    

DOI:10.1063/1.866125

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

A model is used to study the viscous wall region of turbulent shear flows over rigid flat surfaces. Periodic boundary conditions are imposed in the horizontal directions with periodicity lengths that are several times larger than the experimental streak spacing. In order to sustain the turbulence in the viscous wall region, the averagedxcomponent of the velocity is set equal to a fixed profile outside the viscous wall region. Pseudospectral methods are used to solve the governing equations with the Marcus time splitting scheme. It is shown that a model of the viscous wall region can reproduce much of the behavior seen in direct simulations of turbulence that place greater demands on computer resources. The model is used to investigate the flow of energy in the viscous wall region and the relationship between low‐speed streaks and vortices in the viscous wall region.

ISSN:0031-9171    

DOI:10.1063/1.866126

出版商:AIP    

年代:1987

数据来源: AIP