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, 2004 Hydrodynamic stability is of fundamental importance in fluid mechanics and is concerned with the problem of transition from laminar to turbulent flow. Drazin and Reid emphasise throughout the ideas involved, the physical mechanisms, the methods used, and the results obtained, and, wherever possible, relate the theory to both experimental and numerical ...
P. G. Drazin, W. H. Reid
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2023
Continuation methods and turning on bifurcations with Nektar++Continuation methods are often used when tracking interesting states of a dynamical system, such as unstable saddle points that are important for the organization of system’s dynamics. In turbulent flows and turbulent transition process itself such states play an organizing role and act by ...
Stan Gepner +2 more
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Continuation methods and turning on bifurcations with Nektar++Continuation methods are often used when tracking interesting states of a dynamical system, such as unstable saddle points that are important for the organization of system’s dynamics. In turbulent flows and turbulent transition process itself such states play an organizing role and act by ...
Stan Gepner +2 more
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Journal of Applied Mechanics, 1983
Theoretical and experimental developments for the stability and transition of plane Poiseuille flow and for Couette flow between rotating concentric cylinders are reviewed. The paper concludes with brief comments on the stability of Hagen-Poiseuille flow in a pipe and brief comments on the stability of slowly varying flows.
R. C. DiPrima, J. T. Stuart
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Theoretical and experimental developments for the stability and transition of plane Poiseuille flow and for Couette flow between rotating concentric cylinders are reviewed. The paper concludes with brief comments on the stability of Hagen-Poiseuille flow in a pipe and brief comments on the stability of slowly varying flows.
R. C. DiPrima, J. T. Stuart
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Hydrodynamic Stability Without Eigenvalues
Science, 1993Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem, but the results of such investigations agree poorly in many cases with experiments ...
L N, Trefethen +3 more
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Stability of a hydrodynamic discontinuity
Physica Scripta, 2014While looking from a far field at a discontinuous front separating incompressible ideal fluids of different densities, we identify two qualitatively different behaviors of the front—unstable and stable—depending upon whether the energy flux produced by the perturbed front is large or small compared to the flux of kinetic energy across the planar front.
Snezhana I Abarzhi +2 more
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Generalised entropy production and hydrodynamic stability [PDF]
Physics Letters, 1963 A generalized from of an evolution criterion for macroscopic systems with time-independent boundary conditions is given. It includes mechanical processes, such as convection, as well as the components of the entropy production. The variational method is tested in the stability of a horizontal layer of fluid at rest and heated from below.
Glansdorff, Paul, Prigogine, Ilya
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Bifurcation in Nonlinear Hydrodynamic Stability
SIAM Review, 1975The appearance of secondary motions in a viscous fluid field can be understood to some extent as a bifurcation phenomenon with exchange of stability between the basic and the secondary flow. This article summarizes the main mathematical results of bifurcation and stability in hydrodynamic stability theory so far obtained.
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Concept of hydrodynamic stability
2012In the beginning of this chapter, based on elementary physical example, a general idea of stability of motion with respect to disturbances is introduced. Then it is conceptualized for fluid dynamic applications. Stability of fluid flows is categorized in regards of the behavior of kinetic energy of a disturbance in time and space.
Andrey V. Boiko +3 more
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An Introduction to Hydrodynamic Stability
2010In this chapter, our objective is twofold: (1) to describe common physical mechanisms which cause flows to become unstable, and (2) to introduce recent viewpoints on the subject. In the former, we present some well-known instabilities, and also discuss how surface tension and viscosity can act as both stabilisers and destabilisers.
Anubhab Roy, Rama Govindarajan
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