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hydrodynamic stability
In fluid dynamics, hydrodynamic stability is the field which analyses the stability and the onset of instability of fluid flows. The study of hydrodynamic stability aims to find out if a given flow is stable or unstable, and if so, how these instabilities will cause the development of turbulence.〔See Drazin (2002), ''Introduction to hydrodynamic stability''〕 The foundations of hydrodynamic stability, both theoretical and experimental, were laid most notably by Helmholtz, Kelvin, Rayleigh and Reynolds during the nineteenth century.〔 These foundations have given many useful tools to study hydrodynamic stability. These include Reynolds number, the Euler equations, and the Navier–Stokes equations. When studying flow stability it is useful to understand more simplistic systems, e.g. incompressible and inviscid fluids which can then be developed further onto more complex flows.〔 Since the 1980s, more computational methods are being used to model and analyse the more complex flows.
==Stable and unstable flows==
To distinguish between the different states of fluid flow one must consider how the fluid reacts to a disturbance in the initial state.〔See Chandrasekhar (1961) "Hydrodynamic and Hydromagnetic stability"〕 These disturbances will relate to the initial properties of the system, such as velocity, pressure, and density. James Clerk Maxwell expressed the qualitative concept of stable and unstable flow nicely when he said:〔 "when an infinitely small variation of the present state will alter only by an infinitely small quantity the state at some future time, the condition of the system, whether at rest or in motion, is said to be stable but when an infinitely small variation in the present state may bring about a finite difference in the state of the system in a finite time, the system is said to be unstable."
That means that for a stable flow, any infinitely small variation, which is considered a disturbance, will not have any noticeable affect on the initial state of the system and will eventually die down in time.〔 For a fluid flow to be considered stable it must be stable with respect to every possible disturbance. This implies that there exists no mode of disturbance for which it is unstable.〔
On the other hand, for an unstable flow, any variations will have some noticeable affect on the state of the system which would then cause the disturbance to grow in amplitude in such a way that the system progressively departs from the initial state and never returns to it.〔 This means that there is at least one mode of disturbance with respect to which the flow is unstable, and the disturbance will therefore distort the existing force equilibrium.〔See V.Shankar – Department of Chemical Engineering IIT Kanpur (2014), "Introduction to hydrodynamic stability"〕
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