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Kelvin–Helmholtz instability

Kelvin–Helmholtz instability

The Kelvin–Helmholtz instability (after Lord Kelvin and Hermann von Helmholtz) can occur when there is velocity shear in a single continuous fluid, or where there is a velocity difference across the interface between two fluids. An example is wind blowing over water: The instability manifests in waves on the water surface. More generally, clouds, the ocean, Saturn's bands, Jupiter's Red Spot, and the sun's corona show this instability.[1]

Overview

The theory predicts the onset of instability and transition to turbulent flow in fluids of different densities moving at various speeds.[3] Helmholtz studied the dynamics of two fluids of different densities when a small disturbance, such as a wave, was introduced at the boundary connecting the fluids.

For some short enough wavelengths, if surface tension is ignored, two fluids in parallel motion with different velocities and densities yield an interface that is unstable for all speeds. Surface tension stabilises the short wavelength instability however, and theory predicts stability until a velocity threshold is reached. The theory, with surface tension included, broadly predicts the onset of wave formation in the important case of wind over water.

It was recently discovered that the fluid equations governing the linear dynamics of the system admit a parity-time symmetry, and the Kelvin-Helmholtz instability occurs when and only when the parity-time symmetry breaks spontaneously.[4]

For a continuously varying distribution of density and velocity (with the lighter layers uppermost, so that the fluid isRT-stable), the dynamics of the KH instability is described by theTaylor–Goldstein equationand its onset is given by theRichardson number. Typically the layer is unstable for. These effects are common in cloud layers. The study of this instability is applicable in plasma physics, for example ininertial confinement fusionand theplasmaberylliuminterface.

Numerically, the KH instability is simulated in a temporal or a spatial approach. In the temporal approach, experimenters consider the flow in a periodic (cyclic) box "moving" at mean speed (absolute instability). In the spatial approach, experimenters simulate a lab experiment with natural inlet and outlet conditions (convective instability).

See also

  • Rayleigh–Taylor instability

  • Richtmyer–Meshkov instability

  • Mushroom cloud

  • Plateau–Rayleigh instability

  • Kármán vortex street

  • Taylor–Couette flow

  • Fluid mechanics

  • Fluid dynamics

References

[1]
Citation Linkwww.nasa.govFox, Karen C. "NASA's Solar Dynamics Observatory Catches "Surfer" Waves on the Sun". NASA-The Sun-Earth Connection: Heliophysics. NASA.
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[2]
Citation Linkwww.theweathernetwork.comSutherland, Scott (March 23, 2017). "Cloud Atlas leaps into 21st century with 12 new cloud types". The Weather Network. Pelmorex Media. Retrieved 24 March 2017.
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[3]
Citation Link//doi.org/10.1016%2FB978-0-12-382225-3.00190-0Drazin, P. G. (2003). Encyclopedia of Atmospheric Sciences. Elsevier Ltd. p. 1068–1072. doi:10.1016/B978-0-12-382225-3.00190-0.
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[4]
Citation Link//doi.org/10.1063%2F1.5088498Qin, H.; et al. (2019). "Kelvin-Helmholtz instability is the result of parity-time symmetry breaking". Physics of Plasmas. 26 (3): 032102. arXiv:1810.11460. Bibcode:2019PhPl...26c2102Q. doi:10.1063/1.5088498.}
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[5]
Citation Linkwww.nytimes.com"In Deep Sea, Waves With a Familiar Curl"
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Citation Link//doi.org/10.1029%2F2011JA01725610.1029/2011JA017256
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[8]
Citation Linknews.yahoo.comGiant Tsunami-Shaped Clouds Roll Across Alabama Sky
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[9]
Citation Linkuk.news.yahoo.comTsunami Cloud Hits Florida Coastline
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Citation Linkwww.youtube.comVortex formation in free jet
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[11]
Citation Linkyeahnahproductions.co.nzWave clouds over Christchurch City
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[12]
Citation Linkichef.bbci.co.ukKelvin-Helmholtz clouds, in Barmouth, Gwynedd, on 18 February 2017
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[13]
Citation Linkwww.nasa.gov"NASA's Solar Dynamics Observatory Catches "Surfer" Waves on the Sun"
Sep 30, 2019, 9:36 AM
[14]
Citation Linkwww.theweathernetwork.com"Cloud Atlas leaps into 21st century with 12 new cloud types"
Sep 30, 2019, 9:36 AM
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Citation Linkdoi.org10.1016/B978-0-12-382225-3.00190-0
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Citation Linkarxiv.org1810.11460
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Citation Linkui.adsabs.harvard.edu2019PhPl...26c2102Q
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[18]
Citation Linkdoi.org10.1063/1.5088498
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[19]
Citation Linkwww.nytimes.com"In Deep Sea, Waves With a Familiar Curl"
Sep 30, 2019, 9:36 AM
[20]
Citation Linkui.adsabs.harvard.edu2012JGRA..117.8233H
Sep 30, 2019, 9:36 AM