摘要:

Three‐dimensional incompressible hydrodynamic turbulence is driven to a statistically steady state. A strong uniform rotation is then turned on. It is shown that the turbulence reduces to an approximate two‐dimensional state. Furthermore, the energy inverse cascades to longer length scales.

ISSN:1070-6631    

DOI:10.1063/1.868278

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Flow visualizations in a high Reynolds number, Mach 3, fully developed turbulent boundary layer indicate that the upper half of the boundary layer is populated with elongated longitudinal structures. These structures are robust with considerable streamwise but very limited spanwise extent, and are randomly distributed in space and time. Possible mechanisms for the generation of these structures are discussed.

ISSN:1070-6631    

DOI:10.1063/1.868279

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Consider a dilute, insoluble surfactant monolayer on the free surface of a thin viscous film. A gradient in surfactant concentration generates a gradient in surface tension, driving a flow that redistributes the surfactant so that these gradients decay. The nonlinear evolution equations governing such flows, derived using lubrication theory, have previously been shown to admit a set of simple similarity solutions representing the spreading of a monolayer over an uncontaminated interface. Here, a much more general class of similarity solutions is considered, and a transformation is identified reducing the governing partial differential equations to a set of nonlinear ordinary differential equations, the solutions of which correspond to integral curves in a two‐dimensional phase plane. This allows the construction of solutions to a wide range of problems. Many new solutions are revealed, including one that cannot be determined by simpler techniques, namely the closing of an axisymmetric hole in a monolayer, the radius of which is shown to be proportional to (−t)&dgr;ast→0−, where &dgr;≊0.807 41; this solution corresponds to a heteroclinic orbit in the phase plane.

ISSN:1070-6631    

DOI:10.1063/1.868280

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The oscillatory motion of a finite‐length, circular cylinder perpendicular to its symmetry axis in an incompressible, viscous fluid is described by the unsteady Stokes equations. Numerical calculations are performed using a first‐kind, boundary‐integral formulation for particle oscillation periods comparable to the viscous relaxation time. For high‐frequency oscillations, a two‐term, boundary layer solution is implemented that involves two, sequentially solved, second‐kind integral equations. Good agreement is obtained between the boundary layer solution and fully numerical solutions at moderate oscillation frequencies. At the edges, where the base joins the side of the cylinder, the pressure and both components of tangential stress exhibit distinct, singular behaviors that are characteristic of steady, two‐dimensional, viscous flow. Numerical calculations accurately capture the theoretically predicted singular behavior. The unsteady flow reversal process is initiated by a complex near‐field flow reversal process that is inferred from the tangential stress distribution. A qualitative picture is constructed that involves the formation of three viscous eddies during the decelerating portion of the oscillation cycle: two attached to the ends of a finite‐length cylinder, and a third that wraps around the cylinder centerline; the picture is similar to the results for axisymmetric flow. As deceleration proceeds, the eddies grow and coalesce at the cylinder edges to form a single eddy that encloses the entire particle. The remainder of the oscillatory flow cycle is insensitive to particle geometry and orientation. The macroscopic effect of the sharp edges is illustrated by considering ultrasonic, viscous dissipation in a dilute suspension. For a fixed particle‐to‐fluid density ratio, four different frequency regimes are identified. Four distinct viscous dissipation spectra are shown for different particle‐to‐fluid density ratios. The results indicate that particle geometry is important only for particles considerably less dense than the suspending fluid. The effect of edges is most apparent for disk‐ and rod‐shaped particles.

ISSN:1070-6631    

DOI:10.1063/1.868281

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

An experiment to measure the properties of the collisions between two small spheres or between a small sphere and a semi‐infinite flat wall are described. The apparatus releases the particles in a free‐fall without initial spin. The impacts are modeled in terms of three coefficients. The first is the coefficient of normal restitution. The second represents the frictional properties of the contact surfaces. The last characterizes the restitution of the tangential components of the velocity of the contact point for impacts that do not involve sliding. The coefficients are calculated from stroboscopic photographs of the ballistics of the particles near the collision. The results establish that the collision model provides an accurate description of the dynamics of the impacts.

ISSN:1070-6631    

DOI:10.1063/1.868282

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

This paper presents detailed computational results for the dispersion of heavy particles in transitional mixing layers forced at both the fundamental and subharmonic frequencies. The results confirm earlier observations of particle streaks forming in the braid region between successive vortices. A scaling argument based on the idealization of the spatially periodic mixing layer as a row of point vortices shows that the formation of these concentrated particle streaks proceeds with optimum efficiency for St&bartil;1. It thereby provides a quantitative basis for experimental and numerical observations of preferential particle dispersion at Stokes numbers of order unity. Both the model and full simulation furthermore exhibit oscillatory particle motion, as well as the formation of two bands of high particle concentrations, for larger Stokes numbers. The particle dispersion as a function of time and the Stokes number is quantified by means of two different integral scales. These show that the number of dispersed particles does not reach a maximum for intermediate Stokes number. However, when the distance is weighted, optimum dispersion is observed for Stokes numbers around unity. By tracing the dispersed particles backwards in time, they are found to originate in inclined, narrow bands that initially stretch from the braid region into the seeded free stream. This suggests that particle dispersion can be optimized by phase coupling the injection device with the forcing signal for the continuous phase. In the presence of a subharmonic perturbation, enhanced particle dispersion is observed as a result of the motion of the vortices, whereby a larger part of the flow field is swept out.

ISSN:1070-6631    

DOI:10.1063/1.868283

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The initial evolution of a wave packet in a laminar boundary layer is examined. By comparing the experimental streamwise growth of individual modes with the prediction of a linear model, two kinds of nonlinearities are explored. The first of which is associated with oblique waves with a frequency range centered around half the frequency of the most amplified linear mode. This type of nonlinear growth of subharmonic waves has been observed in the past in cases in which artificial excitations of a single two‐dimensional (2‐D) fundamental wave, with or without simultaneous excitations of three‐dimensional (3‐D) subharmonic waves were used, and in the case in which the disturbance was generated by a continuous harmonic point source disturbance. However, unlike all the cases mentioned above, the nonlinear growth of subharmonic waves in the present case begins well upstream of the neutral point of the fundamental wave at branch II, long before the streamwise position, where the amplitudes of the fundamental Tollmien–Schlichting (TS) waves (in the previous cases), attained a saturation level. The second type of nonlinear growth is associated with waves having shorter wavelengths than the wavelengths of the most amplified waves. In this case the nonlinear growth of the waves is first observed at their neutral points (at branch II), characterized by an enhanced streamwise growth rate of their amplitudes. The linear model, which includes the solution of the vertical vorticity equation in addition to the Orr–Sommerfeld equation and accounts for the effect of the mean flow divergence, is found to be very successful in predicting the downstream growth of the most amplified modes and the normalized cross‐stream distributions of the various modes of all three velocity components.

ISSN:1070-6631    

DOI:10.1063/1.868284

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The transient flow of an Oldroyd‐B fluid over an infinite disk set in rotation impulsively is studied under the similarity assumption. The unsteady velocity and stress field is calculated exactly for short times by a power series expansion in time. The order of magnitude of the velocity and stress components is found to depend on the relative magnitude of the Deborah number (De) and the ratio of solvent to polymeric viscosities (&mgr;r). When either one becomes very small, a solution using singular perturbations and Laplace transforms is developed. It is found that the diffusive mechanism for momentum transfer, which exists for about &mgr;r≳0.1 (depending on De) dramatically changes and turns into a propagating wave for &mgr;r<0.1. Numerical calculations are used to determine the extent of validity of the present results.

ISSN:1070-6631    

DOI:10.1063/1.868285

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The system of Rossby waves is unstable with respect to modulations. This instability results in the generation of a large‐scale zonal flow with zero mean vorticity. It is shown that in both stable and unstable situations, a finite‐time singularity formation takes place in the system. Such a singularity has the form of peaks on the vorticity profile of the zonal flow. The situation is also considered when some zonal flow with nonzero mean vorticity is initially present. Solitary‐wave solutions appropriate for the description of nonlinear behavior of such systems are found. In the case of weak mean vorticity of the zonal flow, the solitons break and the singularities develop. If the mean vorticity is strong, then the evolution of the system can be considered as the dynamics of a soliton gas. Soliton dynamics possesses some interesting properties, such as formation of soliton pairs and annihilation of solitons during collision.

ISSN:1070-6631    

DOI:10.1063/1.868286

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

A comparison is made between numerical and experimental results for spin‐up from rest in a rectangular container. The numerical results were obtained by using a three‐dimensional finite volume method on a supercomputer. The experiments were performed with water, using tracer particles floating at the free surface in order to visualize the flow field. The numerical and experimental results are in good agreement. They show the formation of a stable three‐cell pattern. In contrast to similar experiments performed at higher angular velocities, the center cell of this pattern appears to be anticyclonic. Initially, the relation between vorticity &ohgr; and streamfunction &psgr; of this organized flow is linear, but it is seen to evolve slowly into a relation with ∂2&ohgr;/∂&psgr;2<0.

ISSN:1070-6631    

DOI:10.1063/1.868287

出版商:AIP    

年代:1994

数据来源: AIP