摘要:

The influence of a ‘‘nonscale invariant’’ forcing is investigated in the renormalization group theory of stirred fluids. It is shown that such forcings introduce a free parameter in the theory. However, the difficulties inherent in the use of the &egr; expansion remain when the results are applied to real turbulence.    

ISSN:0899-8213    

DOI:10.1063/1.858711

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Numerical evidence is presented that the motion of a solid body through incompressible, inviscid fluid, moving irrotationally and otherwise at rest, is chaotic.

ISSN:0899-8213    

DOI:10.1063/1.858712

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Two‐ and three‐dimensional models of the fluid motion through a junction are described for Stokes flow. It is found that for both models separation of the streamlines can occur on the branch of the outer channel wall with smaller flow rate. The relevance of the results for flow at higher Reynolds numbers is also described.

ISSN:0899-8213    

DOI:10.1063/1.858713

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Wave formation in the gravity‐driven low‐Reynolds number flow of two liquid films down an inclined plane is studied by a linear stability analysis. Wavy motion can appear due to an instability of either the fluid–fluid interface or the fluid‐air free surface. It is shown that the flow is always unstable and wavy motion can occur when the less viscous layer is in the region next to the wall for any Reynolds number and any finite interface and surface tensions. Stability can be achieved for the configuration with the more viscous component adjacent to the wall in the presence of interfacial tension when Reynolds number is small enough.

ISSN:0899-8213    

DOI:10.1063/1.858714

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Experiments were carried out to study the sedimentation of a two‐dimensional particle cloud. When a large number of particles (glass beads) of uniform size are released from a two‐dimensional opening into a column of fresh water, the mixture initially descends as a thermal; however, after some time, the particles start settling individually, thus leaving the parent fluid behind. For a given type of particle, the critical depthzcat which this transition occurs, measured from a virtual origin, was found to change aszcws/&ngr;∼(Q/&ngr;ws)&agr;, with &agr;&bartil;0.3, wherewsis the terminal velocity of a single particle, &ngr; is the kinematic viscosity, andQis the total buoyancy of the released particles per unit length. The descending velocity and the spatial growth of the particle cloud were found to depend on its sedimentation characteristics.

ISSN:0899-8213    

DOI:10.1063/1.858715

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

This paper uses a fluid‐mechanical model of a granular medium to calculate the hydrodynamic modes of a spatially uniform basic state. These modes are the granular analogs of the heat, sound, and shear modes of the standard fluid. Attention is focused on the possibility of an unstable mode that might result in the spontaneous development of inhomogeneities in density. Two cases are considered: the cooling medium which loses energy without replenishment, and the heated medium which reaches a steady state when an energy source balances the loss of energy through particle collisions. The spatially uniform state of the cooling granular medium is unstable. Two modes, analogous to the shear and heat conduction modes of a standard fluid, are unstable at long wavelengths. The growth of these modes is algebraic, rather than exponential, in time. The shear mode does not involve the formation of density inhomogeneities, but the heat mode does. At long wavelengths the heat mode can be visualized by imagining a converging velocity increasing the density of particles in a certain region. The increased collisional dissipation of granular thermal energy reduces the pressure, and prevents it from reversing the convergent velocities, so the condensation is not checked. The stability of the heated granular medium depends on the energy source. If the energy source selectively deposits energy in hot regions of a disturbance, the diffusion and collisional damping can be overwhelmed, and the disturbance grows exponentially. The standard fluid (completely elastic particles) can be recovered as a special case of the heated granular medium. In all cases, waves analogous to the sound and heat conduction modes are present. In some cases, a second type of sound wave is present at long wavelengths with the peculiar property of being damped more quickly for more elastic particles.  

ISSN:0899-8213    

DOI:10.1063/1.858716

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The steady perturbation caused in a longshore flow by a bottom undulation is considered. The bedforms are assumed to be alongshore periodic, with crests in the cross‐shore direction and with a small amplitude in order for linear theory to be applicable. The inviscid shallow‐water equations are considered in order to investigate topographic resonance, that is, the condition under which the perturbation in the flow reaches a maximum. Since upstream edge waves held stationary by the mean flow are solutions to the homogeneous resonance equations, the existence of such flows gives rise to the existence of resonances of infinite amplitude (linear, inviscid theory). For a maximum local Froude number of the basic flowFof less than 1, the flow is found to behave subcritically according to classic channel flow theory. In addition, neither steady edge waves nor infinite amplitude resonances exist in this case. However, by numerical simulation, a finite maximum in the flow perturbation as a function of bedform wavelength is found. This topographic resonance is rather weak and wide banded. For a bedform height of 1% the local water depth, the perturbation on the flow may typically be 4% of the mean current. The resonant wavelength is between two and three times the distance of the peak longshore current to the shoreline,lV, when the current profile has a maximum at some distance offshore, or nearly four times the cross‐shore length scale of the sandbars,l, for a flow profile monotonically increasing to a constant current far offshore. ForF≳1 resonances of infinite amplitude are found. For everyF,lV, andl, there is an infinite set of resonant modes with an increasing cross‐shore complexity when the mode number increases, similarly to edge waves. The resonant wavelength increases withFand withlV. Some implications on the growth of transverse sandbar families and cuspidal coast are discussed.  

ISSN:0899-8213    

DOI:10.1063/1.858717

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A shear layer formed by two unidirectional gas streams of different velocities with a multisize (polydisperse) spray of evaporating droplets suspended in one of the gas streams is considered here. Similarity solutions are presented for the evolution in droplet size distributions across the shear layer and the effects of various initial droplet size distributions on the profiles of vapor concentrations are examined. A qualitative comparison between the present results for typical computed total mass distributions of the liquid phase and experimental data reported by Lazaro and Lasheras [Phys. Fluids A1, 1035 (1989);Proceedingsofthe22ndSymposium(International)onCombustion(The Combustion Institute, Pittsburgh, 1988), pp. 1991–1998; J. Fluid Mech.235, 143 (1992)] shows strong similarity between the two sets of profiles. This supports the assumptions and boundary conditions employed in the present theoretical study. The general behavior of the theoretical SMD (Sauter mean diameter) distribution of the spray across the shear layer also compares well with the reported experimental results of Lazaro and Lasheras.

ISSN:0899-8213    

DOI:10.1063/1.858718

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The two‐dimensional unsteady incompressible Navier–Stokes equations, solved by a fractional time‐step method, were used to investigate separation due to the application of an adverse pressure gradient to a low‐Reynolds number boundary layer flow. The inviscid pressure distribution of Gaster [AGARD CP4, 813 (1966)] was applied in the present computations to study the development of a laminar separation bubble. In all cases studied, periodic vortex shedding occurred from the primary separation region. The shed vortices initially lifted from the boundary layer and then returned towards the surface downstream. The shedding frequency nondimensionalized by the momentum thickness was found to be independent of Reynolds number. The value of the nondimensional Strouhal number, however, was found to differ from the results of Pauleyetal. [J. Fluid Mech.220, 397 (1990)], indicating that the shedding frequency varies with the nondimensional pressure distribution,Cp. The computational results were time averaged over several shedding cycles and the results were compared with Gaster. The numerical study accurately reproduced the major characteristics of the separation found in Gaster’s study such as the separation point, the pressure plateau within the upstream portion of the separation bubble, and the reattachment point. The similarity between the experimental results and the time‐averaged two‐dimensional computational results indicates that the low‐frequency velocity fluctuations detected by Gaster are primarily due to the motion of large vortex structures. This suggests that large‐scale two‐dimensional structures control bubble reattachment and small‐scale turbulence contributes a secondary role.

ISSN:0899-8213    

DOI:10.1063/1.858719

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The spatial stability of multiple solutions for fully developed laminar flow through a curved tube and through a straight tube in the presence of buoyant effects was studied using a three‐dimensional numerical representation of the fully elliptic Navier–Stokes and energy equations. Several recent numerical studies have reported the existence of multiple solutions for fully developed laminar flow in curved tubes; see, for example, Yang and Keller [Appl. Numer. Math.2, 257 (1986)] or Daskopoulos and Lenhoff [J. Fluid Mech.203, 125 (1989)]. A similar solution multiplicity for the case of fully developed laminar flow in a heated straight tube has been discussed by Nandakumaretal. [J. Fluid Mech.152, 145 (1985)]. Each of these studies has reported solutions of a two‐ and four‐cell type, which are symmetric about the midplane of the tube and invariant in the axial (streamwise) flow direction. In addition, the flow visualization study of Cheng and Yuen [J. Heat Trans.109, 55 (1987)] indicates that two‐ and four‐cell solutions can be obtained experimentally for the flow developing in a curved tube with a 180° bend. The present study investigates the stability of two‐ and four‐cell solutions with respect to perturbations that are asymmetric about the midplane of the tube. Perturbed two‐ and four‐cell solutions are imposed as entrance boundary conditions for three‐dimensional simulations of the full tube cross section and the evolution of the flow is observed as it progresses downstream from the entrance plane. For the conditions explored, present results indicate that the two‐cell solutions are stable, and asymmetric perturbations are observed to decay as the flow travels downstream. Four‐cell solutions are unstable when asymmetric perturbations are introduced, and growth of the perturbations eventually results in a complex three‐dimensional transition from four‐cell to two‐cell flow. Details of the transition flow are described and transition mechanisms are identified.

ISSN:0899-8213    

DOI:10.1063/1.858720

出版商:AIP    

年代:1993

数据来源: AIP