scholarly journals Effect of shear flow on the stability of domains in two-dimensional phase-separating binary fluids

1997 ◽  
Vol 56 (6) ◽  
pp. 6970-6980 ◽  
Author(s):  
Amalie Frischknecht
Keyword(s):  
Shear Flow ◽  
Two Dimensional ◽  
Binary Fluids ◽  
The Stability

The stability of filamentary vorticity in two-dimensional geophysical vortex-dynamics models

1991 ◽  
Vol 231 ◽  
pp. 575-598 ◽  
Author(s):  
D. W. Waugh ◽  
D. G. Dritschel
Keyword(s):  
Green Function ◽  
Shear Flow ◽  
Stream Function ◽  
Potential Vorticity ◽  
Two Dimensional ◽  
Interaction Range ◽  
Inversion Operator ◽  
The Green Function ◽  
The Stability ◽  
Background Shear

The linear stability of filaments or strips of ‘potential’ vorticity in a background shear flow is investigated for a class of two-dimensional, inviscid, non-divergent models having a linear inversion relation between stream function and potential vorticity. In general, the potential vorticity is not simply the Laplacian of the stream function – the case which has received the greatest attention historically. More general inversion relationships between stream function and potential vorticity are geophysically motivated and give an impression of how certain classic results, such as the stability of strips of vorticity, hold under more general circumstances.In all models, a strip of potential vorticity is unstable in the absence of a background shear flow. Imposing a shear flow that reverses the total shear across the strip, however, brings about stability, independent of the Green-function inversion operator that links the stream function to the potential vorticity. But, if the Green-function inversion operator has a sufficiently short interaction range, the strip can also be stabilized by shear having the same sense as the shear of the strip. Such stabilization by ‘co-operative’ shear does not occur when the inversion operator is the inverse Laplacian. Nonlinear calculations presented show that there is only slight disruption to the strip for substantially less adverse shear than necessary for linear stability, while for co-operative shear, there is major disruption to the strip. It is significant that the potential vorticity of the imposed flow necessary to create shear of a given value increases dramatically as the interaction range of the inversion operator decreases, making shear stabilization increasingly less likely. This implies an increased propensity for filaments to ‘roll-up’ into small vortices as the interaction range decreases, a finding consistent with many numerical calculations performed using the quasi-geostrophic model.

An advanced experimental investigation of quasi-two-dimensional shear flow

1992 ◽  
Vol 241 ◽  
pp. 705-722 ◽  
Author(s):  
F. V. Dolzhanskii ◽  
V. A. Krymov ◽  
D. Yu. Manin
Keyword(s):  
Experimental Investigation ◽  
Shear Flow ◽  
Viscous Fluid ◽  
Thin Layer ◽  
Driving Force ◽  
Flow Characteristics ◽  
Vortical Flow ◽  
Two Dimensional ◽  
Dimensional Approximation ◽  
The Stability

Forced shear flows in a thin layer of an incompressible viscous fluid are studied experimentally. Streak photographs are used to obtain the stream function of vortical flow patterns arising after the primary shear flow loses stability. Various flow characteristics are determined and results are compared to the stability theory of quasi-two-dimensional flows. The applicability of the quasi-two-dimensional approximation is directly verified and the possibility of reconstruction of the driving force from the secondary flow pattern is demonstrated.

Non-parallel flow corrections for the stability of shear flows

1973 ◽  
Vol 59 (3) ◽  
pp. 571-591 ◽  
Author(s):  
Chi-Hai Ling ◽  
W. C. Reynolds
Keyword(s):  
Boundary Layer ◽  
Shear Flow ◽  
Parallel Flow ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Blasius Boundary Layer ◽  
Stability Of Shear Flows ◽  
Parallel Shear Flow ◽  
The Stability ◽  
Small Disturbances

The proper corrections for non-parallel flow to the eigenvalues for small disturbances on a nearly parallel shear flow have been determined through a perturbation about the parallel flow solutions. The resulting shifts in the neutral stability curves have been calculated for the Blasius boundary layer, for the two-dimensional jet, and for the two-dimensional flat-plate wake.

scholarly journals The two-dimensional hydrodynamical theory of moving aerofoils. IV

1947 ◽  
Vol 188 (1015) ◽  
pp. 439-463
Keyword(s):  
Stability Problem ◽  
Two Dimensional ◽  
Centre Of Gravity ◽  
First Approximation ◽  
Von Karman ◽  
Moving Cylinder ◽  
Period Equation ◽  
The Stability ◽  
Von Kármán ◽  
Hydrodynamical Theory

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

Distributed learning and mutual adaptation

2006 ◽  
Vol 14 (2) ◽  
pp. 313-332 ◽  
Author(s):  
Daniel L. Schwartz ◽  
Taylor Martin
Keyword(s):  
Distributed Cognition ◽  
Dimensional Space ◽  
Distributed Learning ◽  
Early Learning ◽  
Learning Technologies ◽  
Two Dimensional ◽  
Present Evidence ◽  
Mutual Adaptation ◽  
Initial Learning ◽  
The Stability

If distributed cognition is to become a general analytic frame, it needs to handle more aspects of cognition than just highly efficient problem solving. It should also handle learning. We identify four classes of distributed learning: induction, repurposing, symbiotic tuning, and mutual adaptation. The four classes of distributed learning fit into a two-dimensional space defined by the stability and adaptability of individuals and their environments. In all four classes of learning, people and their environments are highly interdependent during initial learning. At the same time, we present evidence indicating that certain types of interdependence in early learning, most notably mutual adaptation, can help prepare people to be less dependent on their immediate environment and more adaptive when they confront new environments. We also describe and test examples of learning technologies that implement mutual adaptation.

Interactions between steady and oscillatory convection in mushy layers

2010 ◽  
Vol 645 ◽  
pp. 411-434 ◽  
Author(s):  
PETER GUBA ◽  
M. GRAE WORSTER
Keyword(s):  
Standing Waves ◽  
Mushy Layer ◽  
Two Dimensional ◽  
Oscillatory Convection ◽  
Mushy Layers ◽  
Theoretical Predictions ◽  
Convection Patterns ◽  
The Stability ◽  
Nonlinear Solutions ◽  
Steady Convection

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.

Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number

2009 ◽  
Vol 626 ◽  
pp. 367-393 ◽  
Author(s):  
STEFAN MÄHLMANN ◽  
DEMETRIOS T. PAPAGEORGIOU
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Electric Field ◽  
Electric Fields ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Liquid Drops

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

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