User:Sara J Mahmoud/sandbox

Goal: The Kelvin-Helmholtz instability article provides relevant information in a clear and concise way. However, I believe the article would benefit by some provided examples or real world applications. The article is general could also be enchanted through further explanation of the Kelvin-Helmholtz instability constant. I also hope to organize the article and its headings with appropriate titles.

Theory Overview
Added: Kelvin-Helmholtz instability can thus be characterized as unstable small scale motions occurring vertically and laterally. It should be noted that at times, the small scale instabilities can be limited through the prescience of a boundary. The boundaries are evident in the vertical direction, through an upper and lower boundary. The upper boundary can be seen as through examples as the free surface of an ocean and lower boundary as a wave breaking on a coast The linear stability theory, with surface tension included, broadly predicts the onset of wave formation as well as the transition to turbulence in the important case of wind over water.

For a continuously varying distribution of density and velocity (with the lighter layers uppermost, so that the fluid is RT-stable), the dynamics of the Kelvin-Helmholtz instability is described by the Taylor–Goldstein equation$$(U-c)[\psi-k^2\psi]+[\frac{N^2}{U-c}-U]\psi=0$$and its onset is given by the Richardson number$$Ri$$ It should be noted that at times a situation in which there in a state of static stability, evident by heavier fluids found below than the lower fluid, the Rayleigh-Taylor instability can be ignored as the Kelvin-Helmholtz instability is sufficient given the conditions.

It is understood that in the case of small-scale turbulence, an increase of the Reynolds number, $${\displaystyle \mathrm {Re} ={\frac {\rho uD}{\mu }}={\frac {uD}{\nu }}}$$, corresponds with an increase of small scale motions. Introducing the Reynolds number is comparable to introducing a measure of viscosity to a relationship that was previously defined as velocity shear and instability. In terms of viscosity, a high Reynolds number is denoted by low viscosity.Essentially, high Reynolds number results in the increase of small scale motion. This sentiment is considered to be in line with the nature of the Kelvin-Helmholtz instability. When increasing the Reynolds number within a case of the Kelvin-Helmholtz instability, the initial large-scale structures of the instability are shown to still persist in the form of supersonic forms.

Importance and Additional Real Life Applications
Created new heading and content: The Kelvin-Helmholtz instability phenomena is an all encompassing occurrence of fluid flow seen time and time again in nature. From the waves of the ocean to the clouds above in the sky, the Kelvin-Helmholtz instability is responsible for some of nature's most basic structures. Further analysis and modeling of the Kelvin-Helmholtz instability can result in an understanding of the worlds natural phenomena and more.