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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, 1975
The 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

2012
In 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, Alexander V. Dovgal, Genrih R. Grek, Victor V. Kozlov   +3 more
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An Introduction to Hydrodynamic Stability

2010
In 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, 1969
Questions 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

1985
Let 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, 1936
AbstractThe 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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Stability of hydrodynamic model for semiconductor.

2005
Summary: We study the stability of transonic strong shock solutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construction of a pseudo-local symmetrizer and on the paradifferential calculus with parameters, which combines the work of Bony-Meyer and the ...
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Introduction to Hydrodynamic Stability

2002
Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course,
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Single phase nanofluids in fluid mechanics and their hydrodynamic linear stability analysis

Computer Methods and Programs in Biomedicine, 2020
Mustafa Turkyilmazoglu
exaly