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Kelvin-helmholtz Instability Theory

 

Kelvin–Helmholtz instabilities were qualitatively described by Heimholtz  and quantitatively analyzed by Kelvin . Instabilities of this kind frequently occur in nature, two such manifestations are the so-called “wind-over-water” and “clear air turbulence” instabilities. Consider two parallel streams of inviscid incompressible fluids superposed one above the other and assume that the upper and lower streams have positive and negative velocities, respectively. Since at the interface there is a discontinuity in the velocity, the vorticity is a nonzero delta-function-like distribution which can be modeled as a vortex sheet. Consider a small sinusoidal perturbation of this sheet. For the two-dimensional flow in question the vorticity is conserved under the motion of the fluid particles. Thus the vorticity has to induce a velocity in the positive (or negative) direction in parts of the sheet displaced upwards (or downwards). At the undisturbed points of the sine wave, the vorticity induces a rotational velocity which amplifies the wave and causes the instability to grow. Citations are important for a journal to get impact factor. Impact factor is a measure reflecting the average number of citations to recent articles published in the journal. The impact of the journal is influenced by impact factor, the journals with high impact factor are considered more important than those with lower ones. This information can be published in our peer reviewed journal with impact factors and are calculated using citations not only from research articles but also review articles (which tend to receive more citations), editorials, letters, meeting abstracts, short communications, and case reports. As a result, the vorticity sheet develops vortex rolls and eventually breaks in a turbulent fashion. Kelvin–Helmholtz instability is global in nature and flow-specific. Since the basic mechanism is strongly affected by specific features of the underlying flow such as its shear, as well physical forces such as gravity, viscosity, etc., it is very difficult, if not impossible, to describe Kelvin–Helmholtz instabilities of generic flows.

Last Updated on: Nov 28, 2024

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