摘要:

The linear, inviscid, spatial instability of a mixing layer uniformly laden with a dilute concentration of heavy particles is studied numerically. The effect of the particles is modeled using an ensemble averaged Eulerian description of the velocity field and Stokes’ drag formula to compute an averaged force, and the carrier fluid and the particle motions are assumed to be fully coupled. The behavior of the linear instability (for a given mean shear) depends on two dimensionless parameters:Cf,representing the product of the inverse Stokes number and mass loading, andCp,representing the inverse Stokes number. For finite values ofCfand large values ofCp,the particles respond as fluid elements and the growth rate is equal to the one of the single-phase flow, while decreasingCpresults in a growth rate decrease. The growth rate also decreases with increasingCf.Beyond certain critical values of increasingCfand decreasingCp,a second unstable low-frequency mode appears which is distinct from the fundamental mode. The fully coupled character of the instability reveals three important aspects of the particle effect on the flow structure: (1) the particle concentration field is organized into alternating bands of increased and decreased concentration corresponding to the braid and core regions of the vortices, respectively, with peak perturbations occurring at intermediateCpvalues(0.01⩽Cp⩽0.1),(2) the streamwise particle velocity is higher than the streamwise fluid velocity for a substantial range ofCpvalues and every finiteCf,and (3) the modification of the fluid vorticity field structure with respect to the corresponding field in single-phase flow is driven by the divergence of the particle velocity field.©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869769

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The present paper deals with the stability properties of a planar channel flow driven by air injection through porous walls. Experimental investigations have been carried out in the so-called VECLA facility and a theoretical linear stability analysis has been performed. The nonparallel effects are studied by using three different stability approaches. They appear to be very significant for this particular flow. This study provides indeed an interesting example of an instability mechanism strongly related to the vertical component (usually negligible) of the mean flow. The obtained results finally agree very well with the measurements with respect to the amplified frequency range and to the streamwise amplification of the instability waves. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869770

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

This study is concerned with a fully nonlinear theoretical treatment of internal solitary waves in continuously stratified, incompressible, inviscid, shear-free Boussinesq fluids. Results are presented for wave propagation in both deep and shallow fluids with four different ambient stability profiles. Only the dominant mode with the greatest wave speed is considered. The morphology of finite-amplitude internal solitary waves in Boussinesq fluids is shown to be very sensitive to the precise form of the stability profile. The calculations indicate that a wave of maximum amplitude, which is less than the total fluid depth, exists for all internal solitary waves in continuously stratified Boussinesq fluids of finite depth. There is apparently no upper limit on the amplitude of internal solitary waves in many physically realistic unbounded fluids. Large amplitude waves of this type are mutually similar in form and the morphology of these waves appears to be independent of the ambient stability profile in the waveguide layer. It is shown that the properties of highly nonlinear waves with recirculating flow depend on the density distribution and vorticity of the trapped fluid inside the closed circulation cell. Fluid velocity components associated with the wave motion are evaluated and used to calculate the surface perturbation pressure. The surface perturbation pressure signature for internal solitary waves is found to change with the onset of recirculation from a single-crested profile at small wave amplitudes to a bimodal profile at large wave amplitudes. Results for solitary waves in finite-depth fluids differ from those found for deep fluids in that the surface perturbation pressure at the center of the wave eventually changes sign as wave amplitude increases. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869771

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Large-scale flows in the atmosphere and ocean are usually in a state of approximate momentum balance, the simplest form of which is geostrophy. Furthermore, balanced models have often been shown to be quite accurate in this regime, with the quasigeostrophic equations the simplest such model and the balance equations a more accurate one, even though such models exclude the rapidly oscillatory, unbalanced dynamics of acoustic, gravitational, and inertial oscillations. However, this behavior is not universal, and here we investigate the fluid dynamics on one of the margins of this regime. We solve for linearized, inviscid fluctuations about a horizontal shear flow with spatially uniform vorticity and strain rate in a rotating, stratified, incompressible fluid, without making any balanced approximations. In both parallel and elliptical shear flows, we find that a significant increase occurs in the growth of unbalanced fluctuations near the violation of a necessary condition for the time integrability of the balance equations. This condition is that the absolute vertical vorticity everywhere exceeds the modulus of the horizontal strain rate. Thus, we seemingly have found a new boundary to the regime of large-scale dynamics, with its approximate gradient-wind balance, anisotropic velocity field, and mostly “slow-manifold” evolutionary behavior. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869772

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Elongated streamwise structures are considered as a key element of the transition to turbulence in various wall flows. In pure plane Couette flow (pCf), longitudinal streaks originating from pairs of streamwise counter-rotating vortices are clearly identified surrounding growing turbulent spots or at late stages of spot relaxation. The same structures bifurcate subcritically from a slightly modified Couette flow where a thin spanwise wire has been introduced in the zero-velocity plane. The basic flow profile, as measured by laser Doppler velocimetry, is shown to approach continuously the original linear velocity profile as the radius of the wire is decreased. On the other hand, the vortices remain almost unchanged and the bifurcation threshold remains bounded from above by the global stability threshold below which turbulent spots relax spontaneously. This supports the conjecture that a related nontrivial nonlinear solution exists in the pure pCf limit. These observations are compared to numerical stability calculations of the modified flow and to finite amplitude solutions to pCf problems with a different tunable modification. ©1998 American Institute of Physics. 

ISSN:1070-6631    

DOI:10.1063/1.869773

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

We consider here the direct numerical simulation (DNS) of channel flow with two different surfaces: a no-slip, fixed wall and on the opposite side a free-slip, free surface. The simulated velocity field agrees well with the experimental data for a free-surface flow obtained by Komori &etal; [Int. J. Heat Mass Transf.25, 513 (1982)]. The DNS is used to simulate particle trajectories, which are computed with a dynamic particle equation in which only the drag force given by the Stokes law is taken into account. For the particle time scale, nondimensionalized in terms of the fixed-wall friction velocity and the kinematic viscosity, we use the values&tgr;+=5and&tgr;+=15.A statistically stationary condition is studied that is obtained by the introduction of a uniform distribution of particles at the beginning of the channel and by continuous removal through deposition at the two walls. The steady-state concentration distribution is nonuniform across the channel width, primarily due to the process whereby particles are trapped close to the surface. Moreover, we find that the wall–normal concentration profiles are self-similar. The deposition on both the no-slip and the free-slip wall can be described by a constant deposition coefficient, with for&tgr;+=5the larger value on the free-slip wall and for&tgr;+=15the opposite, i.e., the larger value over the no-slip wall. To study the deposition process in more detail we consider the cross channel particle fluxes and velocity statistics that are conditioned on deposition events. By means of instantaneous near-wall particle distributions we also consider the patterns of particles and their accumulation in certain areas of the flow. For a no-slip surface the well-known result that particles tend to collect in the low-speed streaks is confirmed. The patterns of particles near the free-slip surface are completely different, which can be explained in terms of the different types of coherent structures that are present near this surface. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869774

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

A number of statistical measures of the differential diffusion of multiple scalars driven by uniform mean gradients are studied by direct numerical simulation (DNS), in isotropic turbulence using up to5123grid points. Consistent with a gradient correlation given by a function of the molecular diffusivities alone, the coherency spectrum is found to be insensitive to the Reynolds number when scaled by Kolmogorov variables in wave number space. Analytical results based on joint Gaussianity assumptions are derived for important unclosed terms in the probability density function (PDF) and conditional moment closure (CMC) approaches, and shown to be successful in describing the behavior of conditional statistics extracted from DNS. The multiscalar conditional diffusion in the joint PDF equation is linear in the sample space variables and specified by the two-scalar correlation coefficients. A linear result is also derived for the term “ey,” which represents the transport of conditional fluctuations in the CMC method. The functional form obtained indicates that closure for this quantity remains an important issue at high Reynolds numbers. The transport of conditional fluctuations due to unsteady, convective and diffusive effects are analyzed separately; results for conditioning on the more diffusive versus less diffusive scalar differ in a manner traceable to the fact that less diffusive scalar fields carry more small-scale spectral content. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869775

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The triple velocity, the pressure–velocity, and the scalar–scalar–velocity correlations in incompressible turbulent shear flows and in passive scalar fields are studied by using the two-scale direct-interaction approximation, which satisfies the solenoidal condition of the velocity fields and systematically introduces the cutoff wave numbers. As a result, we obtain their expressions of the gradient diffusion type involving the effect of cross-diffusion. The model constants in the obtained expressions for the triple velocity and the pressure–velocity correlations are close to the values used in the turbulence models. The derived expression for the scalar–scalar–velocity correlation shows the complex dependence on the ratioRof the velocity length scale to the scalar one. As a special case ofR=1,we obtain its explicit expression whose model constant also agrees well with the numerically optimized value. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869776

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

A fundamental tenet of statistical mechanics is that the rate of collision of two objects is related to the expectation value of their relative velocities. In pioneering work by Saffman and Turner [J. Fluid Mech.1, 16 (1956)], two different formulations of this tenet are used to calculate the collision kernel &Ggr; between two arbitrary particle size groups in a turbulent flow. The first or spherical formulation is based on the radial componentwrof the relative velocitywbetween two particles:&Ggr;sph=2&pgr;R2⟨|wr|⟩,wherewr=w⋅R/R,Ris the separation vector, andR=|R|.The second or cylindrical formulation is based on the vector velocity itself:&Ggr;cyl=2&pgr;R2⟨|w|⟩,which is supported by molecular collision statistical mechanics. Saffman and Turner obtained different results from the two formulations and attributed the difference to the form of the probability function ofwused in their work. A more careful examination reveals that there is a fundamental difference between the two formulations. An underlying assumption in the second formulation is that the relative velocity at any instant is locally uniform over a spatial scale on the order of the collision radiusR, which is certainly not the case in turbulent flow. Therefore, the second formulation is not expected to be rigorously correct. In fact, both our analysis and numerical simulations show that the second formulation leads to a collision kernel about 25&percent; larger than the first formulation in isotropic turbulence. For a simple uniform shear flow, the second formulation is about 20&percent; too large. The two formulations, however, are equivalent for treating the collision rates among random molecules and the gravitational collision rates. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869777

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Experimental results for the spreading and centerline velocity decay rates for round, compressible jets, from a convergent and a convergent-divergent nozzle, are presented. The spreading rate is determined from the variation of streamwise mass flux obtained from Pitot probe surveys. Results for the far asymptotic region show that both spreading and centerline velocity decay rates, when nondimensionalized by parameters at the nozzle exit, decrease with increasing “jet Mach number”MJ.Dimensional analysis with the assumption of momentum conservation, together with compressible flow calculations for the conditions at the nozzle exit, predict this Mach number dependence well. The analysis also demonstrates that an increase in the “potential core length” of the jet occurring with increasingMJ,a commonly observed trend, is largely accounted for simply by the variations in the density and static pressure at the nozzle exit. The effect of decreasing mixing efficiency with increasing compressibility is inferred to contribute only partially to the latter trend.

ISSN:1070-6631    

DOI:10.1063/1.869778

出版商:AIP    

年代:1998

数据来源: AIP