摘要:

A simple equation is derived for the nonlinear evolution of a front (a potential‐vorticity discontinuity) in the rotating shallow‐water equations, assuming weak along‐front variations relative to the internal radius of deformation. This equation can be transformed into the modified Korteweg–de Vries equation, which is integrable and possesses exact, time‐dependent solutions.

ISSN:0899-8213    

DOI:10.1063/1.858592

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Recent interpretations of direct numerical simulation (DNS) measurements have led some authors to suggest that energy is largely transferred downscale locally, supporting a basic concept of the Kolmogorov phenomenology that leads to the universal inertial subrange. However, these authors conclude that the local energy transfer results from nonlocal triad interactions. This claim brings into question the validity of the assumption of the statistical independence of the large‐ and small‐scale motions in the Kolmogorov universal theory of turbulence. In this Letter, the measured raw transfer interactions have been summed in a way that directly indicates the scale disparity (s) of contributions to the net energy flux across the spectrum. It is found that the dependence uponsclosely follows thes−4/3form predicted by classical arguments. As a result, it is concluded that DNS measurements, in fact, lend support to the classical Kolmogorov phenomenology of local interactions and local transfer in an inertial range.

ISSN:0899-8213    

DOI:10.1063/1.858593

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Some simple solutions are presented to the unsteady Stokes flow equations which describe the development of the slow viscous flow due to a line rotlet. Four different geometries are considered, with the rotlet (a) in front of a plane wall, (b) inside a circular cylinder, (c) outside a circular cylinder, (d) between two parallel walls; also, the development is considered (i) after the impulsive introduction of a potential vortex, and (ii) after the impulsive introduction of a line source of angular momentum. Separation occurs in all these situations, and one is able to trace the movement of the separation points, and the formation of eddies, for different times. A number of distinctive physical phenomena are detected.  

ISSN:0899-8213    

DOI:10.1063/1.858594

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A viscous incompressible fluid occupying the space &thgr;≤&pgr;/2 and bounded by the wall &thgr;=&pgr;/2 of a spherical polar coordinate system (r,&thgr;,&fgr;), is stirred by a line vortex along the line &thgr;=0 which is switched on at timet=0. The line vortex is perpendicular to the wall. The development of the flow configuration is considered for the case where the poloidal flow is weak and does not affect the structure of the inducing azimuthal flow. The problem is formulated in terms of the similarity variabler/2(&ngr;t)1/2and the polar angle &thgr;, where &ngr; is the kinematic viscosity of the fluid. An analytical solution is constructed for the azimuthal flow. At any given stationrthe steady azimuthal velocity field is, practically, reached within timer2/&ngr;. The equations governing the poloidal flow are coupled partial differential equations of mixed elliptic–parabolic type which are transformed to equations that are elliptic throughout the solution domain. These equations are solved numerically using the methods of successive overrelaxation and fast Fourier transform. The results show that the poloidal flow in a meridional plane at timetforms closed loops about the pointr≊1.58(&ngr;t)1/2, &thgr;=&pgr;/4, where the velocity has only an azimuthal component. The case of a diffusing configuration from the steady state, due to switching off att=0 of the agent generating the flow, is also considered. For this case the poloidal field consists of open streamlines and att=2r2/&ngr; its intensity is a very small fraction of that associated with the steady state.  

ISSN:0899-8213    

DOI:10.1063/1.858595

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A simple eigenfunction expansion and matching method is used to solve the slow viscous flow through a wall with two‐dimensional periodic gaps. The normalized pressure drop is determined as a function of the geometric parameters.

ISSN:0899-8213    

DOI:10.1063/1.858596

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A free viscous film is subject to van der Waals attractions that lead to film rupture. Long‐wave asymptotics is used to derive approximate equations that govern the unstable evolution of the film. The solution of the nonlinear evolution equation is then considered using bifurcation techniques leading to an estimate for the nonlinear rupture time.  

ISSN:0899-8213    

DOI:10.1063/1.858597

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The hydrodynamic interaction between a pair of nondeformable bubbles (low Weber number limit) in potential flow (high Reynolds number limit) was analyzed. The velocity potential was determined using twin spherical expansions, and the equations of motion were calculated by enforcing the zero net force condition on the surface of the bubbles. The acceleration due to the interaction is expressed in a perturbation series in the parameter (ai/R), whereaiis the radius of bubblei,Ris the distance between the bubbles, and the leading‐order acceleration was found to decrease as (ai/R)4. The effect of potential flow interactions on the trajectory of a pair of bubbles of different sizes (size ratio greater than 1.07 at a Reynolds number of 200) rising due to gravity was studied. A salient feature of the trajectories is that the surfaces of the bubble do not come into contact during the interaction, except when the smaller bubble radius is less than 0.233 times the larger bubble radius when the Reynolds number based on the larger bubble is 200. In the latter case, however, the Reynolds number based on the radius of the smaller bubble is not large enough to justify the potential flow approximation. For interactions where collisions do not occur, the mean‐square fluctuating velocity in a uniform suspension and the hydrodynamic diffusivities in a nonuniform suspension were calculated by performing an ensemble average over pair interactions. The pair averaging procedure is valid for dilute suspensions (V≪18/Re, whereVis the volume fraction of the bubbles and Re is the Reynolds number based on the bubble radius and its terminal velocity).

ISSN:0899-8213    

DOI:10.1063/1.858598

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The interactions between bubbles of nearly equal size (size ratio less than 1.1 at Re=100, and size ratio less than 1.07 at Re=200) in a suspension of bubbles rising due to gravity were analyzed under high Reynolds number, low Weber number conditions. The potential flow interaction between a pair of bubbles was studied using the equations of motion derived by Kumaran and Koch [Phys. Fluids A5, 1123 (1993)]. If the horizontal distance between the bubbles is smaller than a critical value, the bubbles approach each other along the horizontal plane and collide. Previous studies suggest that in a collision, the bubbles could either coalesce or bounce off each other. If it is assumed that the bubbles bounce when they collide, they continue to collide repeatedly. The amplitude of the oscillations decrease due to viscous drag, and ultimately the bubbles rise as a horizontally aligned pair. In this configuration, scaling arguments indicate the bubbles coalesce in finite time. The coalescence frequency in a suspension of bubbles was calculated by averaging over pair interactions. This procedure is valid forV≪18/Re, whereVis the volume fraction of the bubbles. The coalescence frequency is proportional toV Re−2/5in this limit.

ISSN:0899-8213    

DOI:10.1063/1.858599

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The hydrodynamic diffusion of particles or bubbles sedimenting in a liquid is considered for moderate particle Reynolds numbers, Re∼O(1), and small particle volume fractions, &fgr;≪1. Here, Re≡&rgr;Uta/&mgr;,Utis the mean terminal velocity of the particles,ais their mean radius, and &rgr; and &mgr; are the density and viscosity of the fluid. The interactions that control the diffusion occur when one particle is in the wake of another particle with a separation that is large compared with the particle radiusa. The conditionally averaged velocity disturbance in the wake of a particle is screened at anO(a&fgr;−1) distance behind the particle. Beyond this distance, the wake spreads more quickly because of a deficit of particles in the center and an excess at the periphery of the wake of a test particle. This structure is produced by lift forces, which tend to resist the advection of particles into the wake. Screening is required in order to obtain finite values of the variances of the vertical velocities of the particles and fluid. The particle diffusion is anomalous even at wavelengths larger than the screening length; the mean‐square displacements of the particles in the vertical and horizontal directions grow in proportion tot3/2andt ln2 t, respectively. The calculations are carried out for a suspension with a small degree of polydispersity.

ISSN:0899-8213    

DOI:10.1063/1.858600

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A model of selective withdrawal is considered in which a source is located above a gas–liquid interface in a gravitational field. The effects of surface tension are included, and the flow is assumed to be incompressible, inviscid, and irrotational. A perturbation solution is obtained for both the interfacial position and the velocity potential, and then improved using a Galerkin technique. The distortion of the interface by the source is found to be localized and nonmonotonic, and weakly modified by surface tension. An estimate for the stability of the interface is derived from the perturbation solution for the case of zero surface tension.

ISSN:0899-8213    

DOI:10.1063/1.858601

出版商:AIP    

年代:1993

数据来源: AIP