scholarly journals On the Stability of Two-Dimensional Flows Close to the Shear

2019 ◽  
Vol 12 (3) ◽  
pp. 28-41
Author(s):  
O.V. Kirichenko ◽  
◽  
S.V. Revina ◽  
Keyword(s):  
Two Dimensional ◽  
The Stability ◽  
Two Dimensional Flows

Determining the stability of steady two-dimensional flows through imperfect velocity-impulse diagrams

2012 ◽  
Vol 706 ◽  
pp. 323-350 ◽  
Author(s):  
P. Luzzatto-Fegiz ◽  
C. H. K. Williamson
Keyword(s):  
Bifurcation Diagram ◽  
Positive Energy ◽  
Steady Flows ◽  
Two Dimensional ◽  
Specific Flow ◽  
Stability Data ◽  
The Stability ◽  
Velocity Impulse ◽  
Lord Kelvin ◽  
Two Dimensional Flows

AbstractIn 1875, Lord Kelvin stated an energy-based argument for equilibrium and stability in conservative flows. The possibility of building an implementation of Kelvin’s argument, based on the construction of a simple bifurcation diagram, has been the subject of debate in the past. In this paper, we build on work from dynamical systems theory, and show that an essential requirement for constructing a meaningful bifurcation diagram is that families of solutions must be accessed through isovortical (i.e. vorticity-preserving), incompressible rearrangements. We show that, when this is the case, turning points in fluid impulse are linked to changes in the number of the positive-energy modes associated with the equilibria (and therefore in the number of modes likely to be linearly unstable). In addition, the shape of a velocity-impulse diagram, for a family of solutions, determines whether a positive-energy mode is lost or gained at the turning point. Further to this, we detect bifurcations to new solution families by calculating steady flows that have been made ‘imperfect’ through the introduction of asymmetries in the vorticity field. The resulting stability approach, which employs ‘imperfect velocity-impulse’ (IVI) diagrams, can be used to determine the number of positive-energy (likely unstable) modes for each equilibrium flow belonging to a family of steady states. As an illustration of our approach, we construct IVI diagrams for several two-dimensional flows, including elliptical vortices, opposite-signed vortex pairs (of both rotating and translating type), single and double vortex rows, as well as gravity waves. By also considering an example involving the Chaplygin–Lamb dipole, we illustrate how the stability of a specific flow may be determined, by embedding it within a properly constructed solution family. The stability data from our IVI diagrams agree precisely with results in the literature. To the best of our knowledge, for a few of the flows considered here, our work yields the first available stability boundaries. Further to this, for several of the flows that we examine, the IVI diagram methodology leads us to the discovery of new families of steady flows, which exhibit lower symmetry.

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.

scholarly journals The strain rate in evolutions of (elliptical) vortices in inviscid two-dimensional flows

2001 ◽  
Vol 13 (12) ◽  
pp. 3699-3708 ◽  
Author(s):  
P. W. C. Vosbeek ◽  
G. J. F. van Heijst ◽  
V. P. Mogendorff
Keyword(s):  
Strain Rate ◽  
Two Dimensional ◽  
Two Dimensional Flows

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.

Detonation induced two-dimensional flows

1974 ◽  
Vol 1 (3-4) ◽  
pp. 373-384 ◽  
Author(s):  
Charles L. Mader
Keyword(s):  
Two Dimensional ◽  
Two Dimensional Flows

Dynamics of Vortex Interactions in Two-Dimensional Flows

2001 ◽  
Vol T98 (1) ◽  
pp. 29 ◽  
Author(s):  
Jens Juul Rasmussen ◽  
Anders H. Nielsen ◽  
Volker Naulin
Keyword(s):  
Two Dimensional ◽  
Vortex Interactions ◽  
Two Dimensional Flows
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