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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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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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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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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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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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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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Computing Problems in Nonlinear Hydrodynamic Stability
The Physics of Fluids, 1969Questions arising in nonlinear hydrodynamic stability such as the calculation of an equilibrium flow field when the basic flow is unstable, wavenumber selection, and successive instabilities are considered for the classical problem of flow between concentric rotating cylinders. Recent numerical and analytical work dealing with calculation of the Taylor
DiPrima, R. C., Rogers, E. H.
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Classical Hydrodynamic Stability
1985Let Ω ⊂ R 3 be a domain (i.e. an open connected set) in which the flow of an incompressible viscous Newtonian fluid, acted upon by the body force f(x, t) takes place.
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On the Stability Problem in Hydrodynamics
Mathematical Proceedings of the Cambridge Philosophical Society, 1936AbstractThe paper deals with the problem of the effect of two-dimensional first order disturbances on the linear and parabolic flows of a viscous fluid. If the laminar flow is in the direction x and is bounded by the planes y = ±h, and if the stream function of the disturbance is assumed to be of the form , it is found that, for small Reynolds numbers ...
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