摘要:

The concept of eddy viscosity is generalized to include an ‘‘eddy &bgr;‐term’’ that accounts for the effect of unresolved turbulence and Rossby waves on the resolved modes in the subgrid‐scale representation of &bgr;‐plane turbulence.  

ISSN:0899-8213    

DOI:10.1063/1.858547

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

This paper considers the creeping flows generated by a disk moving edgewise parallel to a rigid wall or free surface, a disk oscillating edgewise in unbounded fluid and a hole in the rigid plane that bounds a shear flow excited by a parallel moving plane. The analyses for the three cases follow a similar pattern and several simplifying strategies are introduced to obtain significant improvements on the presentations suggested by previous work on such flows. Indeed, the resulting integral equations for the first disk problem are similar to those solved for the corresponding broadside motion. The drag force is shown to slowly approach its limit value as the disk is placed nearer to the free surface. The oscillatory hydrodynamic force is shown to have only Stokes and Basset components. The error in previously assuming the shear flow to extend to infinity is shown to be of orderH−3, whereHis the separation distance between the bounding planes.

ISSN:0899-8213    

DOI:10.1063/1.858548

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The viscometer consists of an oscillating screen immersed in a fluid and free to rotate about an axis in its plane. The viscosity can be determined from the measured ratio of the periodic driving force to the screen motion when an adequate hydrodynamical model of the immersed oscillator is available. The screen is formed by a square mesh of thin wire whose dimensions invite comparison with asymptotic results for narrow hollow bodies translating in Stokes flow. These indicate that the closed hole structure of the grid plays an important role in determining its motion. It is shown that this role diminishes as the frequency increases. The computed results, obtained from a system of linear equations, are consistent with experimental values over the appropriate range of frequency.

ISSN:0899-8213    

DOI:10.1063/1.858549

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The hydrodynamic force on a body that undergoes translational acceleration in an unbounded fluid at low Reynolds number is considered. The results extend the prior analysis of Lovalenti and Brady [to appear in J. Fluid Mech. (1993)] for rigid particles to drops and bubbles. Similar behavior is shown in that, with the inclusion of convective inertia, the long‐time temporal decay of the force (or the approach to steady state) at finite Reynolds number is faster than thet−1/2predicted by the unsteady Stokes equations.    

ISSN:0899-8213    

DOI:10.1063/1.858550

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

In their study of time‐dependent thermocapillary convection in cylindrical liquid bridges Veltenetal. [Phys. Fluids A3, 267 (1991)] determined the azimuthal flow structure by measuring the phase of the temperature oscillations at three different azimuthal angles. Their explanation of the data in terms of modes with wave numberm=0 is not always compatible with the normal‐mode decomposition of the disturbances at the threshold. A new interpretation is given that explains the peculiar phase measurements in terms of pairs ofm≠0 counterpropagating waves.

ISSN:0899-8213    

DOI:10.1063/1.858551

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

One‐dimensional models have been used extensively over the past decade to study liquid columns. While the range of validity of these models is well known in the linear limit, this is not the case when nonlinear effects are important. By comparing results of a number of one‐dimensional models with results based on a velocity‐potential model in which no approximations have been made, the present aim is to establish exactly when the one‐dimensional models are applicable. First of all it is shown how the Cosserat equations in the inviscid limit may be obtained formally from the Euler equations. Subsequently, a linearized form of the Cosserat equations is derived and results of this model are compared with results obtained by means of the well‐established inviscid‐slice model and results obtained by the velocity‐potential approach. It is found that the applicability of the inviscid‐slice model is limited by short‐wavelength effects rather than amplitude effects. The range of validity of the inviscid‐slice model can be extended by including radial momentum contributions. However, even with the inclusion of radial momentum effects the one‐dimensional models are not well suited to describe the behavior close to the bifurcation point.

ISSN:0899-8213    

DOI:10.1063/1.858552

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

In this paper, the dynamics of an interface under the influence of surface tension is studied numerically for flow in the Hele–Shaw cell, where the interface separates an expanding bubble of inviscid fluid from a displaced viscous fluid. Of special interest is the long–time behavior of the so‐calledq‐pole initial data, whose motion is explicitly known and globally smooth for the zero surface tension flow. The numerical method is spectrally accurate and based upon a boundary integral formulation of the problem, together with a special choice for the frame of motion along the interface. In 64‐bit arithmetic, a transition from the formation of side branches to tip splitting is observed as the surface tension is decreased. The tip splitting occurs on a time scale that decreases with the surface tension. This is consistent with some experimental observations. However, by increasing the arithmetic precision to 128 bits, it is found that this transition occurs at a yet smaller surface tension. The tip splitting is associated with the growth of noise in the calculation at unstable scales allowed by the surface tension, and a simple linear model of this growth seems to agree well with the observed behavior. The robustness of the various observed structures to varying amounts of noise is also investigated numerically. It is found that the appearance of side branches seems to be the intrinsic effect of surface tension, and the time scales for their appearance increases as the surface tension decreases. These results suggest, with some qualification, that surface tension acts as a regular perturbation to evolution from this initial data, even for long times.

ISSN:0899-8213    

DOI:10.1063/1.858553

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Mixing in a spatially periodic continuous mixer, the partitioned pipe mixer, is studied using bifurcation analysis with the help of geometric construction of periodic orbits and a knowledge of the symmetry of the mixing system. Mixing windows, where motion in the mixer is nearly globally chaotic, are found in the parameter space. Uniform ultimate mixtures are expected in the mixing windows as verified with the Poincare´ sections. The present analysis provides a better understanding of the existing experimental results.

ISSN:0899-8213    

DOI:10.1063/1.858554

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Solutions of the Navier–Stokes equations for flow in a curved channel have previously been computed [Bottaro, J. Fluid Mech.251, 627 (1993)] and the spatial development of the Dean flow is available at different supercritical Reynolds number. In this work the viscous instability of local longitudinal vortex structures (obtained from the nonlinear simulations) is investigated, with a focus toward the secondary instability of Dean vortices. Such a secondary instability takes the form of streamwise traveling waves. High‐frequency waves are termedtwistingwaves, low frequency are definedundulatingwaves. Instead of performing analyses in which the basic flow in the cross section is two dimensional, significant shear profiles alongyandzare considered as base flows at constantxbefore the establishment of a fully developed state. Thus one is able to discover that thetwistinstability is of shear type and is caused by inflectional spanwise profiles of the streamwise velocity component. Sinuous waves are always preferred to varicose waves, and the latter mode of instability is destabilized only at large Reynolds numbers.Undulatingwaves are related to normal profiles of the streamwise velocity; this type of secondary instability is of centrifugal origin. Results of the analyses for both types of waves are in good agreement with experiments.

ISSN:0899-8213    

DOI:10.1063/1.858555

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The effects of cross‐diffusion on the onset of convective instability in a horizontally unbounded, triply diffusive, and triply stratified fluid layer (triply cross‐diffusive fluid layer) are investigated. Analytical solutions are obtained for steady and oscillatory onset when imposed gradients of the stratifying agencies are constant and vertical. Numerical results are based on diffusivity data for the system water/potassium chloride/potassium phosphate/phosphoric acid solution. Depending on the magnitude of the stratifying agencies, linear stability analysis shows that cross‐diffusion can either stabilize or destabilize a fluid layer. The off‐diagonal elements of the diffusivity matrix, which arise naturally as a result of the coupling among the various stratifying agencies, may strongly affect boundaries of convective stability and neutral curves. Discrepancies in the linear stability criteria were observed for seemingly negligible off‐diagonal elements of the diffusivity matrix.

ISSN:0899-8213    

DOI:10.1063/1.858556

出版商:AIP    

年代:1993

数据来源: AIP