摘要:

McLean and Saffman’s model for the fingering in a Hele–Shaw cell is solved numerically. The results suggests that a countably infinite number of solutions exist for nonzero surface tension. This set of solutions contains the solution previously obtained by McLean and Saffman.

ISSN:0031-9171    

DOI:10.1063/1.864406

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

A solution to the problem posed when a rigid sphere normally approaches an interface between immiscible viscous fluids is presented when the deformation of the interface is small compared with the sphere radius or its minimum clearance from the undistorted interface. The complete boundary conditions at the interface of continuity of velocity and tangential stress together with discontinuity of normal stress by the surface tension times the mean curvature are applied in the first‐order analysis of a perturbation scheme in which the interface has small distortion from planar. This results in a finite force on the sphere being predicted as the sphere approaches the interface.

ISSN:0031-9171    

DOI:10.1063/1.864407

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

The conditions for wave formation and growth during sedimentation in inclined channels is investigated using a linear stability analysis in the limit of large sedimentation Grashof number with the Reynolds number remainingO(1). An asymptotic solution for long waves reveals that the critical Reynolds number is proportional to the tangent of the angle of inclination of the channel times the ratio of the thickness of the thin pure‐fluid layer, which forms beneath the downward‐facing surface of the channel, to the width of the channel. Hence, the critical Reynolds number is very small unless the channel is extremely long and narrow. Numerical calculations indicate, however, that the maximum amplification rates are often so small that the disturbances may be convected out of the channel before they reach an observable size. This conclusion is consistent with experiments performed in our laboratory, and the observed wave inception point and the calculated maximum amplification rates exhibit remarkably similar dependence on the angle of inclination and the suspension concentration.

ISSN:0031-9171    

DOI:10.1063/1.864408

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

A linear‐stability analysis is performed to investigate in detail the conditions for wave formation and growth during sedimentation in long, narrow channels that are inclined from the vertical. The maximum amplification rates of such waves are predicted by solving the equations governing the instabilities both asymptotically for long‐wavelength disturbances and also numerically for disturbances with moderate wavelengths. The general trends set forth by the linear theory are found to be consistent with experimental observations. In particular, it is shown that very tall and narrow vessels not only give the largest enhancement in the settling rate but also significantly increase the stability of inclined settling systems.

ISSN:0031-9171    

DOI:10.1063/1.864409

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

Numerical solutions via Newton’s method of the Reynolds‐averaged Navier–Stokes equations for steady flow over a two‐dimensional wavy surface indicates that by using a simple algebraic eddy‐viscosity model, the distribution of wall pressure and shear stresses and the corresponding drag coefficients can be predicted. Computations are compared with experimental results over rigid wavy surfaces and moving flexible boundaries. For small‐amplitude wavy surfaces, computed values of the wall stresses agree well with the experimental measurements. For larger‐amplitude waves, regions of reverse flow in the trough of the wave are predicted.

ISSN:0031-9171    

DOI:10.1063/1.864410

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

Application of speckle velocimetry in a round jet (Re=2300) provides instantaneous 2‐D velocity fields and vorticity maps of the interaction between unstable vortices. Detailed descriptions of the pairing process and of the large‐scale structures observed near the end of the potential core are obtained without excitation of the jet and without the smearing effects of the conditional sampling method.

ISSN:0031-9171    

DOI:10.1063/1.864411

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

The kinematic problem of calculating second‐order velocity moments from given values of the vorticity covariance is examined. Integral representation formulas for second‐order velocity moments in terms of the two‐point vorticity correlation tensor are derived. The special relationships existing between velocity moments in isotropic turbulence are expressed in terms of the integral formulas yielding several kinematic constraints on the two‐point vorticity correlation tensor in isotropic turbulence. Numerical evaluation of these constraints suggests that a Gaussian curve may be the only form of the longitudinal velocity correlation coefficient which is consistent with the requirement of isotropy. It is shown that if this is the case, then a family of exact solutions to the decay of isotropic turbulence may be obtained which contains Batchelor’s final period solution as a special case. In addition, the computed results suggest a method of approximating the integral representation formulas in general turbulent shear flows.

ISSN:0031-9171    

DOI:10.1063/1.864412

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

The variable‐interval time‐averaging (VITA) technique developed by Blackwelder and Kaplan [J. Fluid Mech.76, 89 (1976)] is applied to data obtained from large‐eddy simulation of turbulent channel flow in an investigation of the organized structures associated with the bursting phenomenon in the near‐wall region. Conditionally averaged velocities, shear stress, pressure, and vorticity are discussed in conjunction with the bursting phenomenon detected by the VITA technique. The conditionally averaged pressure reveals that the ejection process is associated with a localized adverse pressure gradient. In the plane perpendicular to the flow direction, the conditionally averaged vorticity field indicates that a pair of counterrotating streamwise vortices is being lifted through the ejection process.

ISSN:0031-9171    

DOI:10.1063/1.864413

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin–Fokker–Planck (LFP) model. The dynamic damping coefficient &eegr; of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for &eegr; to replace the divergent response equation of Kraichnan’s direct‐interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko=1.2, which is compatible with the experimental data given by Gibson and Schwartz.

ISSN:0031-9171    

DOI:10.1063/1.864414

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

The frequency dependence of a turbulent Prandtl number, defined using the Reynolds shear stress and normal heat flux co‐spectra, in various turbulent shear flows accentuates the inadequacy of the Reynolds analogy from a spectral point of view. For the same flows, the analogy between spectral distributions of the kinetic energy and the temperature variance is validated over a significant frequency domain. This analogy suggests a spectral parameter which is very close to unity in this frequency range for all the flows considered.

ISSN:0031-9171    

DOI:10.1063/1.864415

出版商:AIP    

年代:1983

数据来源: AIP