摘要:

The traditional Smagorinsky subgrid‐scale viscosity (CS&lgr;)2Shas been supplemented by the addition of stochastic backscatter. The random acceleration is derived from a vector potentialCb‖S &dgr;t‖3/2(&lgr;/&dgr;t)2g. HereSis the local strain rate, &lgr; is the grid resolution length scale, &dgr;tis the time step, andgis a unit random Gaussian. It is found that valuesCS=0.2 for the Smagorinsky constant andCb=0.4 for the backscatter constant give a robust calculation of the two‐dimensional shear mixing layer with the observed growth rate and with realistic emergence of random coherent eddy structures.

ISSN:0899-8213    

DOI:10.1063/1.857779

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

For comparison with recent experimental results, a concise analytical method is presented for the sedimentation of a disk moving toward a plane wall in the presence of a parallel free surface or axisymmetric cylindrical container. In each case the problem is reduced to the numerical solution of dual integral equations and computed values of the normalized drag coefficient are displayed. The method is also applied to an array of sedimenting disks, possibly within a circular pipe, and then there is usually a larger number of integral equations to be solved. However, a clear pattern for the construction of the kernels emerges from the sample cases considered.

ISSN:0899-8213    

DOI:10.1063/1.857780

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

A thin liquid layer rests on a horizontal plane that is subject to a two‐dimensional spatially periodic temperature distribution. Thermocapillary forces on the free surface result in a dimpling interface and a steady viscous flow. Long‐wave theory is used to study this system and to determine whether or not there is film dryout locally, and how such dimpling and/or dryout is affected by London–van der Waals forces, surface tension, and hydrostatic effects.

ISSN:0899-8213    

DOI:10.1063/1.857781

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The steady thermocapillary flow of nonvolatile layers, nonuniformly heated from below, is examined. The interactions among viscous forces, thermocapillarity, and hydrostatic effects give rise to the steady‐state dimpling of the interface. The steady dimpling of nonuniformly heated silicone–oil layers with mean thicknesses ranging from 0.125 to 1.684 mm is studied experimentally. The temperature distribution in the substrate is monitored by thermocouples and the interface shapes by a mechanical impedance probe. Measured steady shapes and theoretical predictions agree within 20% for moderate heating when the film is not close to rupture. When the heating rate causes the film to ‘‘dry out’’ above the hottest point on the substrate, the long‐wave theory delivers a parametric index, involving thermocapillary and hydrostatic effects, which is an excellent predictor of rupture. Nonlinear long‐wave theories of the type discussed here have never been tested experimentally, until now. The confirmation of this thermocapillary theory is suggestive of the validity of the previous long‐wave analysis [Phys. Fluids A2, 313 (1990)] of unsteady, evaporating/condensing liquid layers.

ISSN:0899-8213    

DOI:10.1063/1.857782

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The transition from thermal convection in the form of rolls in a fluid layer heated from below to traveling wave convection occurs at the Rayleigh numberRII=1854 in the limit of low Prandtl numbers and in the presence of no‐slip boundaries. While the traveling wave convection exhibits similar properties at moderately low and very low Prandtl numbers, the tertiary transition to asymmetric waves experiences a qualitative change at a Prandtl number of about 0.02. Instead of the double frequency asymmetric waves that occur at higher Prandtl numbers the traveling wave convection becomes just asymmetric, but remains stationary with respect to the moving frame of reference. The heat transport carried by the new form of convection is larger than for symmetric traveling wave convection.

ISSN:0899-8213    

DOI:10.1063/1.857783

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

In this paper the weakly nonlinear stability of two‐phase core‐annular film flows in the limit of small film thickness and in the presence of both viscosity stratification and interfacial tension is examined. Rational asymptotic expansions are used to derive some novel nonlinear evolution equations for the interface between the phases. The novel feature of the equations is that they include a coupling between core and film dynamics thus enabling a study of its effect on the nonlinear evolution of the interface. The nonlinear interfacial evolution is governed by modified Kuramoto–Sivashinsky equations in the cases of slow and moderate flow [the former also developed by Frenkel,SixthSymposiumonEnergyEngineeringSciences(Argonne Lab. Pub. CONF‐8805106, 1988), p.100, using different asymptotic methods], which include new nonlocal terms that reflect core dynamics. These equations are solved numerically for given initial conditions and a range of parameters. Some interesting behavior results, such as transition (in parameter space) of chaotic solutions into traveling‐wave pulses with more than one characteristic length scale.

ISSN:0899-8213    

DOI:10.1063/1.857784

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Small‐amplitude steady thermal convection is a horizontal layer of fluid with finite conducting boundaries and rotating about a vertical axis is investigated. Both analytical and numerical techniques are used to solve the nonlinear and stability problems. Conditions on the parameters &ggr;b, &ggr;t, and &tgr; are determined under which either square cells or two‐dimensional rolls can be the preferred form of convection (&ggr;band &ggr;tare the ratios of the thermal conductivities of the lower and upper boundaries to that of the fluid and &tgr; is the rotation parameter). Transition from steady rolls to time‐dependent flow occurs for &tgr; beyond some value, which decreases with decreasing &ggr;bor &ggr;t. Square cell convection is not subject to such transition, but there is a transition from steady squares to steady rolls for &tgr; beyond a critical value. The dependence on &ggr;b, &ggr;t, and &tgr; of the time‐dependent transition and of the heat transported by convection are also discussed.

ISSN:0899-8213    

DOI:10.1063/1.857785

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Long solitary waves in incompressible density stratified fluids are described, to the first order in wave amplitude by the Korteweg–de Vries equation. A well‐known solution of this equation represents a single solitary wave that has the familiar ‘‘sech2 ’’ profile and a phase speed that varies linearly with the wave amplitude. In the present paper the modifications of these waves resulting from the compressibility are investigated. Solitary waves are again described by the Korteweg–de Vries equation. Three special cases are discussed and results are compared with the results of incompressible solitary wave theory. This shows that qualitative and quantitative differences may be profound, especially for an isothermal shearless fluid.

ISSN:0899-8213    

DOI:10.1063/1.857786

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The three‐dimensional development of the wake behind a flat plate separating two laminar streams of equal velocity, subjected to perturbations in its initial conditions, is studied experimentally and numerically at moderate Reynolds numbers. The effect of single waves as well as subharmonic streamwise forcing is discussed. For the case of a single wave, streamwise forcing combined with a sinusoidal spanwise perturbation, the two distinct three‐dimensional vorticity modes found in an early study [J. Fluid Mech.190, 1 (1988)], are further studied and their symmetry properties analyzed. Depending on the orientation of the spanwise perturbation, the counter‐rotating pairs of streamwise vortex tubes forming in the braids are shown to induce undulations in the cores of the Karman‐like vortices, resulting in either anin‐phaseor avaricoseconfiguration. Furthermore, when the wake is subjected to subharmonic streamwise forcing, additional modes of the topology of the vorticity field are shown to exist. The evolution of these subharmonic three‐dimensional modes is analyzed as a function of the initial conditions.

ISSN:0899-8213    

DOI:10.1063/1.857787

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The effect of wall cooling on the two‐dimensional linear stability of subsonic flows over two‐dimensional surface imperfections is investigated. Results are presented for flows over smooth humps and backward‐facing steps with Mach numbers up to 0.8. The results show that, whereas cooling reduces the viscous instability, it increases the shear‐layer instability and hence it increases the growth rates in the separation region. The coexistence of more than one instability mechanism makes a certain degree of wall cooling most effective. For the Mach numbers 0.5 and 0.8, the optimum wall temperature is about 80% of the adiabatic wall temperature.

ISSN:0899-8213    

DOI:10.1063/1.857788

出版商:AIP    

年代:1990

数据来源: AIP