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Three examples of Turing patterns Six stable states from Turing equations, the last one forms Turing patterns. The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state.
The Saffman–Taylor instability, also known as viscous fingering, is the formation of patterns in a morphologically unstable interface between two fluids in a porous medium or in a Hele-Shaw cell, described mathematically by Philip Saffman and G. I. Taylor in a paper of 1958.
This figure represents the evolution of the Rayleigh–Taylor instability from small wavelength perturbations at the interface (a) which grow into the ubiquitous mushroom shaped spikes (fluid structures of heavy into light fluid) and bubbles (fluid structures of light into heavy fluid) (b) and these fluid structures interact due to bubble merging and competition (c) eventually developing into ...
Hydrodynamics simulation of the Rayleigh–Taylor instability [3] Unstable flow structure generated from the collision of two impinging jets.. Fluid instabilities occur in liquids, gases and plasmas, and are often characterized by the shape that form; they are studied in fluid dynamics and magnetohydrodynamics.
The solutions of reaction–diffusion equations display a wide range of behaviours, including the formation of travelling waves and wave-like phenomena as well as other self-organized patterns like stripes, hexagons or more intricate structure like dissipative solitons. Such patterns have been dubbed "Turing patterns". [1]
Three examples of droplet detachment for different fluids: (left) water, (center) glycerol, (right) a solution of PEG in water. In fluid dynamics, the Plateau–Rayleigh instability, often just called the Rayleigh instability, explains why and how a falling stream of fluid breaks up into smaller packets with the same total volume but less surface area per droplet.
A KH instability rendered visible by clouds, known as fluctus, [2] over Mount Duval in Australia A KH instability on the planet Saturn, formed at the interaction of two bands of the planet's atmosphere Kelvin-Helmholtz billows 500m deep in the Atlantic Ocean Animation of the KH instability, using a second order 2D finite volume scheme
The waves can take the form of stripes, close-packed hexagons, or even squares or quasiperiodic patterns. Faraday waves are commonly observed as fine stripes on the surface of wine in a wine glass that is ringing like a bell. Faraday waves also explain the 'fountain' phenomenon on a singing bowl.